Biography.

Childhood to war years (1910–45).

Childhood and youth (1910–35).

Kurosawa was born on March 23, 1910, in Ōimachi in the Ōmori district of Tokyo. His father Isamu (1864–1948), a member of a samurai family from Akita Prefecture, worked as the director of the Army's Physical Education Institute's lower secondary school, while his mother Shima (1870–1952) came from a merchant's family living in Osaka. Akira was the eighth and youngest child of the moderately wealthy family, with two of his siblings already grown up at the time of his birth and one deceased, leaving

Director in training (1935–41).

In 1935, the new film studio Photo Chemical Laboratories, known as P.C.L. (which later became the major studio Toho), advertised for assistant directors. Although he had demonstrated no previous interest in film as a profession, Kurosawa submitted the required essay, which asked applicants to discuss the fundamental deficiencies of Japanese films and find ways to overcome them. His half-mocking view was that if the deficiencies were fundamental, there was no way to correct them. Kurosawa's essay earned him a call to take the follow-up exams, and director Kajirō Yamamoto, who was among the examiners, took a liking to Kurosawa and insisted that the studio hire him. The 25-year-old Kurosawa joined P.C.L. in February 1936.  During his five years as an assistant director, Kurosawa worked under numerous directors, but by

Wartime films and marriage (1942–45).

In the two years following the release of "Horse" in 1941, Kurosawa searched for a story he could use to launch his directing career. Towards the end of 1942, about a year after the Japanese attack on Pearl Harbor, novelist Tsuneo Tomita published his Musashi Miyamoto-inspired judo novel, "Sanshiro Sugata", the advertisements for which intrigued Kurosawa. He bought the book on its publication day, devoured it in one sitting, and immediately asked Toho to secure the film rights. Kurosawa's initial instinct proved correct as, within a few days, three other major Japanese studios also offered to buy the rights. Toho prevailed, and Kurosawa began pre-production on his debut work as director. Shooting of "Sanshiro Sugata" began on location in Yokohama in December 1942. Production proceeded smoothly, but getting the completed film past the censors was an entirely different matter. The censorship office considered the work to be objectionably "British-American" by the standards of wartime Japan, and it was only through the intervention of director Yasujirō Ozu, who championed the film, that "Sanshiro Sugata" was finally accepted for release on March 25, 1943. (Kurosawa had just turned 33.) The movie became both a critical and commercial success. Nevertheless, the censorship office would later decide to cut out some 18 minutes of footage, much of which is now considered lost.  He next turned to the subject of wartime female factory workers in "The Most Beautiful", a propaganda film which

Early postwar years to "Red Beard" (1946–65).

First postwar works (1946–50).

After the war, Kurosawa, influenced by the democratic ideals of the Occupation, sought to make films that would establish a new respect towards the individual and the self. The first such film, "No Regrets for Our Youth" (1946), inspired by both the 1933 Takigawa incident and the Hotsumi Ozaki wartime spy case, criticized Japan's prewar regime for its political oppression. Atypically for the director, the heroic central character is a woman, Yukie (Setsuko Hara), who, born into upper-middle-class privilege, comes to question her values in a time of political crisis. The original script had to be extensively rewritten and, because of its controversial theme and gender of its protagonist, the completed work divided critics. Nevertheless, it managed to win the approval of audiences, who turned variations on the film's title into a postwar catchphrase.

International recognition (1950–58).

After finishing "Scandal", Kurosawa was approached by Daiei studios to make another film for them. Kurosawa picked a script by an aspiring young screenwriter, Shinobu Hashimoto, who would eventually work on nine of his films. Their first joint effort was based on Ryūnosuke Akutagawa's experimental short story "In a Grove", which recounts the murder of a samurai and the rape of his wife from various different and conflicting points-of-view. Kurosawa saw potential in the script, and with Hashimoto's help, polished and expanded it and then pitched it to Daiei, who were happy to accept the project due to its low budget.  The shooting of "Rashomon" began on July 7, 1950, and, after extensive location work in the primeval forest of Nara, wrapped on August 17. Just one week was spent in hurried post-production, hampered by a studio fire, and the finished film premiered at Tokyo's Imperial Theatre on August 25, expanding nationwide the following day. The movie was met by lukewarm reviews, with many critics puzzled by its unique theme and treatment, but it was nevertheless a moderate financial success for Daiei. Kurosawa's next film, for Shochiku, was "The Idiot", an adaptation of the novel by the director's favorite writer, Fyodor Dostoyevsky. The story is relacated from Russia to Hokkaido, but otherwise adheres closely to the original, a fact seen by many critics as detrimental to the work. A studio-mandated edit shortened it from Kurosawa's original cut of 265 minutes to just 166 minutes, making the resulting narrative exceedingly difficult to follow. The severely edited film version is widely considered to be one of the director's least successful works and the original full length version no longer exists. Contemporary reviews of the much shortened edited

Birth of a company and "Red Beard" (1959–65).

Starting with "Rashomon", Kurosawa's productions had become increasingly large in scope and so had the director's budgets. Toho, concerned about this development, suggested that he might help finance his own works, therefore making the studio's potential losses smaller, while in turn allowing himself more artistic freedom as co-producer. Kurosawa agreed, and the Kurosawa Production Company was established in April 1959, with Toho as the majority shareholder.  Despite risking his own money, Kurosawa chose a story that was more directly critical of the Japanese business and political elites than any previous work. "The Bad Sleep Well", based on a script by Kurosawa's nephew Mike Inoue, is a revenge drama about a young man who is able to infiltrate the hierarchy of a corrupt Japanese company with the intention of exposing the men responsible for his father's death. Its theme proved topical: while the film was in production, mass demonstrations were held against the new U.S.–Japan Security treaty, which was seen by many Japanese, particularly the young, as threatening the country's democracy by giving too much power to corporations and politicians. The film opened in September 1960 to positive critical reaction and modest box office success. The 25-minute opening sequence depicting a corporate wedding reception is widely regarded as one of Kurosawa's most skillfully executed set pieces, but the remainder of the film is often perceived as disappointing by comparison. The movie has also been criticized for employing the conventional Kurosawan hero to combat a social evil that cannot be resolved through the actions of individuals, however courageous or cunning.  "Yojimbo" ("The Bodyguard"), Kurosawa Production's second film, centers on a masterless samurai, Sanjuro, who strolls into a 19th-century town ruled by two opposing violent factions and provokes them into destroying each other. The director used this work to play with many genre conventions, particularly the Western, while at the same time offering an unprecedentedly (for the Japanese screen) graphic portrayal of violence. Some commentators have seen the Sanjuro character in this film as a fantasy figure who magically reverses the historical triumph of the corrupt merchant class over the samurai class. Featuring Tatsuya Nakadai in his first major role in a Kurosawa movie, and with innovative photography by Kazuo Miyagawa (who shot "Rashomon") and Takao Saito, the film premiered in April 1961 and was a critically and commercially successful venture, earning more than any previous Kurosawa film. The movie and its blackly comic tone were also widely imitated abroad. Sergio Leone's "A Fistful of Dollars" was a virtual (unauthorized) scene-by-scene remake with Toho filing a lawsuit on Kurosawa's behalf and prevailing. Following the success of "Yojimbo", Kurosawa found himself under pressure from Toho to create a sequel. Kurosawa turned to a script he had written before "Yojimbo", reworking it to include the hero of his previous film. "Sanjuro" was the first of three Kurosawa films to

Hollywood ambitions to last films (1966–98).

Hollywood detour (1966–68).

When Kurosawa's exclusive contract with Toho came to an end in 1966, the 56-year-old director was seriously contemplating change. Observing the troubled state of the domestic film industry, and having already received dozens of offers from abroad, the idea of working outside Japan appealed to him as never before.  For his first foreign project, Kurosawa chose a story based on a "Life" magazine article. The Embassy Pictures action thriller, to be filmed in English and called simply "Runaway Train", would have been his first in color. But the language barrier proved a major problem, and the

A difficult decade (1969–77).

Knowing that his reputation was at stake following the much publicised "Tora! Tora! Tora!" debacle, Kurosawa moved quickly to a new project to prove he was still viable. To his aid came friends and famed directors Keisuke Kinoshita, Masaki Kobayashi and Kon Ichikawa, who together with Kurosawa established in July 1969 a production company called the Club of the Four Knights (Yonki no kai). Although the plan was for the four directors to create a film each, it has been suggested that the real motivation for the other three directors was to make it easier for Kurosawa to successfully complete a film,

Two epics (1978–86).

In 1977, American director George Lucas released "Star Wars", a wildly successful science fiction film influenced by Kurosawa's "The Hidden Fortress", among other works. Lucas, like many other New Hollywood directors, revered Kurosawa and considered him a role model, and was shocked to discover that the Japanese filmmaker was unable to secure financing for any new work. The two met in San Francisco in July 1978 to discuss the project Kurosawa considered most financially viable: "Kagemusha", the epic story of a thief hired as the double of a medieval Japanese lord of a great clan. Lucas, enthralled by the screenplay and Kurosawa's illustrations, leveraged his influence over 20th Century Fox to coerce the studio that had fired Kurosawa just ten

Final works and last years (1987–98).

For his next movie, Kurosawa chose a subject very different from any that he had ever filmed before. While some of his previous pictures (for example, "Drunken Angel" and "Kagemusha") had included brief dream sequences, "Dreams" was to be entirely based upon the director's own dreams. Significantly, for the first time in over forty years, Kurosawa, for this deeply personal project, wrote the screenplay alone. Although its estimated budget was lower than the films immediately preceding it, Japanese studios were still unwilling to back one of his productions, so Kurosawa turned to another famous American fan, Steven Spielberg, who convinced Warner Bros. to buy the international rights to the completed film. This made it easier for Kurosawa's son, Hisao, as co-producer and soon-to-be head of Kurosawa Production, to negotiate a loan in Japan that would cover the film's production costs. Shooting took more than eight months to complete, and "Dreams" premiered at Cannes in May 1990 to a polite but muted reception, similar to the reaction the picture would generate elsewhere in the world. In 1990, he accepted the Academy Award for Lifetime Achievement. Kurosawa now turned to a more conventional story with "Rhapsody in August"—the director's first film fully produced in Japan since "Dodeskaden" over twenty years before—which explored the scars of the nuclear bombing which destroyed Nagasaki at the very end of World War II. It was adapted from a Kiyoko Murata novel, but the film's references to the Nagasaki bombing came from the director rather than from the book. This was his only movie to include

Creative works/filmography.

Although Kurosawa is primarily known as a filmmaker, he also worked in theater, television

Style and main themes.

Kurosawa displayed a bold, dynamic style, strongly influenced by Western cinema yet distinct from it; he was involved with all aspects of film production. He was a gifted screenwriter and worked closely with his co-writers from the film's development onward to ensure a high-quality script, which he considered the firm foundation of a good film. He frequently served as editor of his own films. His team, known as the "Kurosawa-gumi" (Kurosawa group), which included the cinematographer Asakazu Nakai, the production assistant Teruyo Nogami and the actor Takashi Shimura, was notable for its loyalty and dependability.  Kurosawa's style is marked by a number of devices and techniques. In his films of the 1940s and 1950s, he frequently employs the "axial cut", in which the camera moves toward or away from the subject through a series of matched jump cuts rather than tracking shots or dissolves. Another stylistic trait is "cut on motion," which displays the motion on the screen in two or more shots

Legacy.

Legacy of general criticism.

Kenji Mizoguchi, the acclaimed director of "Ugetsu" (1953) and "Sansho the Bailiff" (1954) was 14 years Kurosawa's senior. After the mid-1950s, some critics of the French New Wave began to favor Mizoguchi to Kurosawa. New Wave critic-filmmaker Jacques Rivette, in particular, thought Mizoguchi to be the only Japanese director whose work was at once entirely Japanese and truly universal; Kurosawa, by contrast was thought to be more influenced by Western cinema and culture, a view that has been disputed.  In Japan, some critics and filmmakers considered Kurosawa to be elitist. They viewed him to center his effort and attention on exceptional or heroic characters. In her DVD commentary on "Seven Samurai", Joan

Reputation among filmmakers.

Many filmmakers have been influenced by Kurosawa's work. Ingmar Bergman called his film "The Virgin Spring" a "touristic, a lousy imitation of Kurosawa", and added, "At that time my admiration for the Japanese cinema was at its height. I was almost a samurai myself!" Federico Fellini considered Kurosawa to be "the greatest living example of all that an author of the cinema should be". Satyajit Ray, who was posthumously awarded the "Akira Kurosawa Award for Lifetime Achievement in Directing" at the San Francisco International Film Festival in 1992, had said earlier of "Roshomon": "The effect of the film on me [upon first seeing it in Calcutta in 1952] was electric. I saw it three times on consecutive days, and wondered each time if there was another film anywhere which gave such sustained and dazzling proof of a director's command over every aspect of film making."  Roman Polanski considered Kurosawa to be among the three filmmakers he favored most, along with

Posthumous screenplays.

Following Kurosawa's death, several posthumous works based on his unfilmed screenplays have been produced. "After the Rain", directed by Takashi Koizumi, was released in 1999, and "The Sea Is Watching", directed by Kei Kumai, premiered in 2002. A script created by the Yonki no Kai ("Club of the Four Knights") (Kurosawa, Keisuke Kinoshita, Masaki Kobayashi, and Kon Ichikawa), around the time that

Kurosawa Production Company.

In September 2011, it was reported that remake rights to most of Kurosawa's movies and unproduced screenplays were assigned by the Akira Kurosawa 100 Project to the L.A.-based company Splendent. Splendent's chief Sakiko Yamada, stated that he aimed to "help contemporary film-makers introduce a new generation of moviegoers to these unforgettable stories".  Kurosawa Production Co., established in 1959, continues to oversee many of the aspects of Kurosawa's legacy. The director's

Film studios and awards.

In 1981, the Kurosawa Film Studio was opened in Yokohama; two additional locations have since been launched in Japan. A large collection of archive material, including scanned screenplays, photos and news articles, has been made available through the Akira Kurosawa Digital Archive, a Japanese proprietary website maintained by Ryukoku University Digital Archives Research Center in collaboration with Kurosawa Production. Anaheim University's Akira Kurosawa School of Film was launched in spring 2009 with the backing of Kurosawa Production. It offers online programs in digital film making, with headquarters in Anaheim and a learning center in Tokyo.  Two film awards have also been named in Kurosawa's honor. The Akira Kurosawa Award for Lifetime Achievement in Film Directing is awarded during the San Francisco International

Documentaries.

A significant number of full-length and short documentaries concerning the life and films of Kurosawa were made during his lifetime and after his death. "AK" was filmed in 1985 and is a French documentary film directed by Chris Marker. Though it was filmed while Kurosawa was working on "Ran", the film focuses more on Kurosawa's remote but polite personality than on the making of the film. The documentary is sometimes seen as being reflective of Marker's fascination with Japanese culture, which he also drew on for one of his best-known films, "Sans Soleil". The film was screened in the Un Certain Regard section at the 1985 Cannes Film Festival. Other documentaries concerning Kurosawa's life and works produced posthumously include:

Akira Kurosawa ( "Kurosawa Akira"; March 23, 1910 – September 6, 1998) was a Japanese film director and screenwriter, who directed 30 films in a career spanning 57 years. He is regarded as one of the most important and influential filmmakers in the history of cinema.

黑泽明(,1910年-3月23日-1998年-9月6日),日本著名导演。一生共执导了三十部电影,其中许多具有世界知名与影响力,如《罗生门》、《七武士》、《大镖客》、《天国与地狱》、《德苏乌扎拉》、《影武者》、《乱》等代表作。是使日本电影走向国际化的重要导演,也是日本近代电影史的重要人物,被誉为「电影界的莎士比亚」。法号为「映明院殿纮国慈爱大居士」。


Overview.

With the London Protocol of 1944 signed on September 12, 1944, the United States, the United Kingdom and the Soviet Union decided to divide Germany into three occupation zones and to establish a special area of Berlin, which was occupied by the three Allied Forces together. In May 1945, the Soviet Union installed a city government for the whole city that was called "Magistrate of Greater Berlin", which existed until 1947. After the war, the Allied Forces initially administered the city together within the Allied Kommandatura, which served as the governing body of the city. However, in 1948 the Soviet representative left the Kommandatura and the common administration broke apart during the following months. In the Soviet sector, a separate city government was established, which continued to call itself "Magistrate of Greater Berlin".  When the German Democratic Republic was established in 1949, it immediately claimed East Berlin as its capital—a claim that was recognised by all communist countries. Nevertheless, its representatives to the People's Chamber were not directly elected and did not have full voting rights until 1981.  In June 1948, all railways and roads leading to West Berlin were blocked, and East Berliners were not allowed to emigrate. Nevertheless, more than 1,000 East Germans were escaping to West Berlin each day by 1960, caused by the strains on the East German economy from war reparations owed to the Soviet Union, massive destruction of industry, and lack of assistance from the Marshall Plan. In August 1961, the East German Government tried to stop the population exodus by enclosing West Berlin within the Berlin Wall. It was very dangerous for fleeing residents to cross because armed soldiers were trained to shoot illegal migrants.  East Germany was a socialist republic, but there was not complete economic equality. Privileges such as prestigious apartments and good schooling were given to members of the ruling party and their family. Eventually, Christian churches were allowed to operate without restraint after years of harassment by authorities. In the 1970s, wages of East Berliners rose and working hours fell.  The Western Allies (the US, UK, and France) never formally acknowledged the authority of the East German government to govern East Berlin; the official Allied protocol recognised only the authority of the Soviet Union in East Berlin in accordance with the occupation status of Berlin as a whole. The United States Command Berlin, for example, published detailed instructions for U.S. military and civilian personnel wishing to visit East Berlin. In fact, the three Western commandants regularly protested against the presence of the East German National People's Army (NVA) in East Berlin, particularly on the occasion of military parades. Nevertheless, the three Western Allies eventually established embassies in East Berlin in the 1970s, although they never recognised it as the capital of East Germany. Treaties instead used terms such as "seat of government."  On 3 October 1990, East and West Germany and East and West Berlin were reunited, thus formally ending the existence of East Berlin. City-wide elections in December 1990 resulted in the first “all Berlin” mayor being elected to take office in January 1991, with the separate offices of mayors in East and West Berlin expiring at the time, and Eberhard Diepgen (a former mayor of West Berlin) became the first elected mayor of a reunited Berlin.

East Berlin today.

Since reunification, the German government has spent vast amounts of money on reintegrating the two halves of the city and bringing services and infrastructure in the former East Berlin up to the standard established in West Berlin.  After reunification, the East German economy suffered significantly. Under the adopted policy of privatisation of state-owned firms under the auspices of the Treuhandanstalt, many East German factories were shut down—which also led to mass unemployment—due to gaps in productivity with and investment compared to West German companies, as well as an inability to comply with West German pollution and safety standards in a way that was deemed cost effective. Because of this, a massive amount of West German economic aid was poured into East Germany to revitalize it. This stimulus was part-funded through a 7.5% tax on income for individuals and companies (in addition to normal income tax or company tax) known as the "Solidaritätszuschlaggesetz" (SolZG) or "solidarity surcharge", which though only in effect for 1991-1992 (later reintroduced in 1995 at 7.5 and then dropped down to 5.5% in 1998 and continues to be levied to this day) led to a great deal of resentment toward the East Germans.  Despite the large sums of economic aid poured into East Berlin, there still remain obvious differences between the former East and West Berlins. East Berlin has a distinct visual style; this is partly due to the greater survival of prewar façades and streetscapes, with some even still showing signs of wartime damage. The unique look of Stalinist architecture that was used in East Berlin (along with the rest of the former GDR) also contrasts markedly with the urban development styles employed in the former West Berlin. Additionally, the former East Berlin (along with the rest of the former GDR) retains a small number of its GDR-era street and place names commemorating German socialist heroes, such as Karl-Marx-Allee, Rosa-Luxemburg-Platz, and Karl-Liebknecht-Straße. Many such names, however, were deemed inappropriate (for various reasons) and, through decommunization, changed after a long process of review (so, for instance, Leninallee reverted to Landsberger Allee in 1991, and Dimitroffstraße reverted to Danziger Straße in 1995).  Another symbolic icon of the former East Berlin (and of East Germany as a whole) is the "Ampelmännchen" (tr. "little traffic light men"), a stylized version of a fedora-wearing man crossing the street, which is found on traffic lights at many pedestrian crosswalks throughout the former East. Following a civic debate about whether the Ampelmännchen should be abolished or disseminated more widely (due to concerns of consistency), several crosswalks in some parts of the former West Berlin also employ the Ampelmännchen.  Twenty-five years after the two cities were reunified, the people of East and West Berlin still had noticeable differences between them, which became more apparent among the older generations. The two groups also had sometimes-derogatory slang terms to refer to each other. A former East Berliner (or East German) was known as an ""Ossi"" (from the German word for east, "Ost"), and a former West Berliner (or West German) was known as a ""Wessi"" (from the German word for west, "West"). Both sides also engaged in stereotyping the other. A stereotypical "Ossi" had little ambition or poor work ethic and was chronically bitter, while a stereotypical "Wessi" was arrogant, selfish, impatient and pushy.

Boroughs of East Berlin.

At the time of German reunification, East Berlin comprised the boroughs of

East Berlin was the capital city of the German Democratic Republic from 1949 to 1990. Formally, it was the Soviet sector of Berlin, established in 1945. The American, British, and French sectors were known as West Berlin. From 13 August 1961 until 9 November 1989, East Berlin was separated from West Berlin by the Berlin Wall. The Western Allied powers did not recognise East Berlin as the GDR's capital, nor the GDR's authority to govern East Berlin. On 3 October 1990, the day Germany was officially reunified, East and West Berlin formally reunited as the city of Berlin.

东柏林()是对1949-1990年间柏林东部地区的称呼,亦为德意志民主共和国(东德)首都,源于1945年苏联武装力量设立的苏联占领区。美国,英国和法国管制区被称为西柏林。1961年8月13日至1989年11月9日,西柏林与东柏林被柏林墙隔开。西方盟国没有承认东柏林是东德的首都,也没有承认东德管理东柏林的权力。


Etymology.

The origin of "kapo" is unclear. According to the Jewish Virtual Library it is an abbreviated form of the word "Kameradschaftpolizei" (roughly, "comrade police force") or perhaps "Kameradschafts-Polizei". It could have also come from the Italian word for "head" and "boss", "capo". According to the Duden, it is derived from the French word for "Corporal" (""). Pulitzer Prize-winning journalist Robert D. McFadden believes that the word "kapo" is derived from the German word "Lagercapo" meaning camp captain.

System of thrift and manipulation.

Concentration camps were controlled by the SS, but day-to-day organization was supplemented by the system of functionary prisoners, a second hierarchy that made it easier for the Nazis to control the camps. These prisoners made it possible for the camps to function with fewer SS personnel. The prisoner functionaries sometimes numbered as high as 10% of the inmates. The Nazis were able to keep the number of paid staff who had direct contact with the prisoners very low in comparison to normal prisons today. Without the functionary prisoners, the SS camp administrations would not have been able to keep the day-to-day operations of the camps running smoothly. The kapos often did this work for extra food, cigarettes, alcohol or other privileges.  At Buchenwald, these tasks were originally assigned to criminal prisoners, but after 1939, political prisoners began to displace the criminal prisoners, though criminals were preferred by the SS. At Mauthausen, on the other hand, functionary positions remained dominated by criminal prisoners until just before liberation. The system and hierarchy also inhibited solidarity among the prisoners. There were tensions between the various nationalities as well as between the various prisoner groups, who were distinguished by different Nazi concentration camp badges. Jews wore yellow stars, other prisoners wore colored triangles pointed downward.  Prisoner functionaries were often hated by other prisoners as Nazi henchmen and were spat upon. While some barrack leaders ("Blockälteste") tried to assist the prisoners under their command by secretly helping them get extra food or easier jobs, others were more concerned with their own survival and, to that end, did more to assist the SS.  Identified by green triangles, the "Berufsverbrecher" or "BV" ("career criminals") kapos, were called "professional criminals" by other prisoners and were known for their brutality and lack of scruples. Indeed, they were selected by the SS because of those qualities. According to former prisoners, the criminal functionaries were more apt to be helpful to the SS than political functionaries, who were more apt to be helpful to other prisoners.  From Oliver Lustig's "Dictionary of the Camp":

Domination and terror.

The SS used domination and terror to control the camps' large populations with just a few SS functionaries. The system of prisoner guards was a "key instrument of domination", and was commonly called "prisoner self-government" ("Häftlings-Selbstverwaltung") in SS parlance.  The camp draconian rules, constant threat of beatings, humiliation, punishment, and the practice of punishing whole groups for the actions of one prisoner were psychological and physical torments on top of the starvation, and physical exhaustion from back-breaking labor. Prisoner guards were used to push other inmates to work harder, saving the need for paid SS supervision. Many "kapos" felt caught in the middle, being both victims and perpetrators. Though "kapos" generally had a bad reputation, many suffered guilt about their actions, both at the time and after the war, as revealed in a book about Jewish kapos.  Many prisoner functionaries, primarily from the ranks of the "greens" or criminal prisoners, could be quite ruthless in order to justify their privileges, especially when an SS man was around. They also played an active role in the beatings, even killing fellow prisoners. One non-criminal functionary was, a notorious Austrian political prisoner. Feared and hated, he was known as a sadist and was responsible for several deaths. He was released from Dachau in 1942 and became a member of the Waffen SS. Some guards were personally involved in the mass murder of other prisoners. Beginning in October 1944, criminal functionaries from among the German "Reichsdeutsche" were sought out for transfer to the Dirlewanger Brigade.

Ranks of functionary.

The important functionary positions inside the camp were "Lagerältester" (camp leader or camp senior), "Blockältester" (block or barracks leader or senior) and "Stubenältester" (room leader). The highest position that a prisoner could reach was "Lagerältester". He was placed directly under the camp commandant, had to implement his orders, ensure that the camp's normal daily routines ran smoothly and satisfy the superior regulations. The "Lagerälteste" had a key role in the selection of other prisoners as functionaries, making recommendations to the SS. Though dependent on the goodwill of the SS, through them, he had access to special privileges, such as access to civilian clothes or a private room.  The "Blockältester" (block or barracks leader) had to ensure that rules were followed in the individual barracks. He or she was also responsible for the prisoners in the barracks. The "Stubenälteste" (room leader) was responsible for the hygiene, such as delousing, and order of each room in a barracks. The "Blockschreiber" (registrar or barrack clerk) was a record-keeping job, such as keeping track at roll calls.  Work crews outside the camp were supervised by a "Vorarbeiter" (foreman), a Kapo, or "Oberkapo" (chief kapo). These functionaries pushed their fellow prisoners, hitting and beating them, even killing them.  Prisoner functionaries could often help other prisoners by getting them into better barracks or getting them assigned to lighter work. On occasion, the functionaries could effect other prisoners' removal from transport lists or even secure new identities in order to protect them from persecution. This assistance was generally limited to the prisoners in the functionary's own group (fellow citizens or political comrades). The prisoner functionaries were in a precarious hierarchy between their fellow inmates and the SS. This situation was intentionally created, as revealed in a speech by Heinrich Himmler.  In National Socialism's racial ideology, some races were "superior" and others "inferior". Similarly, the SS sometimes had racial criteria for the prisoner functionaries, sometimes one had to be racially "superior" to be a functionary. The group category was also sometimes a factor. A knowledge of foreign languages was also advantageous, particularly as the international population of the camps increased and they preferred a certain level of education.  An eager prisoner functionary could have a camp "career" as an SS favorite and be promoted from "Kapo" to "Oberkapo" and eventually to "Lagerältester", but he could also just as easily run foul of the SS and be sent to the gas chambers.

Prosecution of kapos.

During the Stutthof trials in Gdańsk, Poland, which took place in 1946 and 1947 for the prosecution of the Stutthof concentration camp personnel, five kapos were sentenced to death, with extreme brutality cited. Four of them were executed on 4 July 1946, and one on 10 October 1947. Another kapo was sentenced to three years' imprisonment and one acquitted and released on 29 November 1947.  The Israeli Nazi and Nazi Collaborators (Punishment) Law of 1950, most famously used to prosecute Adolf Eichmann in 1961 and Ivan Demjanjuk in 1986, was originally introduced with the principal purpose of prosecuting Jewish collaborators with the Nazis. Between 1951 and 1964, approximately 40 trials were held, mostly of people alleged to have been kapos. Fifteen are known to have resulted in convictions, but only rough details are available since the records were sealed in 1995 for a period of 70 years from the trial date. One person - Yehezkel Jungster - was convicted of crimes against humanity, which carried a mandatory death penalty, but the sentence was commuted for two years in prison. Jungster died in jail in July 1952, from natural causes.  According to teacher and researcher Dan Porat, the way in which former kapos were officially viewed – and tried – by the state of Israel went through four distinct phases. Initially viewed as co-perpetrators of the Nazi atrocities, they eventually came to be perceived as victims themselves. During Porat’s first stage (August 1950 –January 1952), those alleged of having served or collaborated with the Nazis were placed on an equal footing with their captors, with some measure of leniency appearing only in the sentencing phase for some cases. It was during this phase that Jungster was sentenced to death; six other former kapos were each sentenced to an average of almost five years in prison. Jungster’s death sentence had been anticipated by neither the legislators nor the prosecutors, according to Porat, and triggered a number of amendments to pre-trial charges in order to remove any indictment that would potentially carry a death penalty. During this second phase (February 1952 – 1957), the Supreme Court overturned Jungster’s sentence and essentially ruled that while Nazis could be charged with crimes against humanity and war crimes, their former collaborators could not. While prosecutions of the kapos continued, doubts emerged amongst some of those in the public sphere as to whether the trials should continue at all. The official view remained that kapos had been Jewish collaborators, although not Nazis themselves. By 1958, when the third phase commenced (lasting until 1962), the legal system had begun to view kapos as having committed wrongs but with good intentions. Thus only those who prosecutors believed had aligned themselves with the Nazi’s aims were brought to trial. There were also calls from some survivors that the trials should end, although other survivors still demanded that justice be served. The fourth phase (1963-1972) was marked by the trial of Adolf Eichmann, one of the principal architects of the Final Solution, and that of Hirsch Barenblat two years later. Kapos and collaborators were now seen by the courts as ordinary victims, a complete reversal from the initial official perspective. Eichmann’s prosecutor was very clear in drawing a line between the Jewish collaborators and camp functionaries, and the evil Nazis. Barenblat’s trial in 1963 drove this point home. Barenblat, the conductor of the Israel National Opera, was tried for having turned Jews over to the Nazis as head of the Jewish police in the Bendzin ghetto, Poland. Having arrived in Israel in 1958-9, Barenblat was arrested after a ghetto survivor recognised him while he was conducting an opera. Found guilty of helping the Nazis by ensuring that Jews selected for the death camps did not escape, Barenblat was sentenced to five years in prison. On May 1, 1964, having served three months of the sentence, Barenblat was freed and Israel’s Supreme Court quashed his conviction. The acquittal may have been due to the Court’s aim of putting an end to the trials against kapos and other alleged Nazi collaborators.  A small number of kapos were prosecuted in East and West Germany. In a well-publicised 1968 case, two Auschwitz kapos were put on trial in Frankfurt. They were indicted for 189 murders and multiple assaults, found guilty of several murders, and sentenced to life imprisonment.

Significance.

German historian wrote that there was hardly a measure so perfidious as the SS attempt to delegate the implementation of terror and violence to the victims themselves. Eugen Kogon, an avowed opponent of Nazism from prewar Germany and Buchenwald concentration camp survivor, wrote after the war ended that the concentration camp system owed its stability in no small way to a cadre of "kapos", who took over the daily operations of the camp, thus relieving the SS personnel. The absolute power was ubiquitous. The system of discipline and supervision would have promptly disintegrated, according to Kogon, without the delegation of power downwards. The rivalry over supervisory and warehouse functionary jobs was, for the SS, an opportunity to pit prisoners against each other. Thus, the regular prisoner was at the mercy of a dual authority, the SS, who often hardly seemed to be at the camp, and the prisoner "kapos", who were always there.  The term "kapo" is used as a slur in the twenty-first century.

A kapo or prisoner functionary (, see ) was a prisoner in a Nazi concentration camp who was assigned by the SS guards to supervise forced labor or carry out administrative tasks.

囚监(英文:Kapo,德文:Funktionshäftling),又称为功能性犯人,指的是被纳粹党卫军委任监督集中营中的劳工工作、承担管理任务的犯人。犯人的自我管理制度使得集中营对纳粹党卫军监工的需求下降,从而节省了人力资源。在这种发动受害者相互对抗的自我管理制度之下,集中营守卫通过压迫普通的劳工来讨他们的党卫军上司欢心。


Dietary law.

The 6th-century recension of "Liber Pontificalis" ('Book of the Popes') known as the "Felician Catalog" includes additional commentary to the work's earlier entry on Eleutherius. One addition ascribes to Eleutherius the reissuance of a decree: "And he again affirmed that no food should be repudiated by Christians strong in their faith, as God created it, [provided] however that it is sensible and edible." Such a decree might have been issued against early continuations of Jewish dietary law and against similar laws practiced by the Gnostics and Montanists. It is also possible, however, that the editor of the passage attributed to Eleutherius a decree similar to another issued around the year 500 in order to give it greater authority.

British mission.

Another addition credited Eleutherius with receiving a letter from "Lucius, King of Britain" or "King of the Britons", declaring an intention to convert to Christianity. No earlier accounts of this mission have been found. It is now generally considered to be a pious forgery, although there remains disagreement over its original purpose. Haddan, Stubbs, and Wilkins considered the passage "manifestly written in the time and tone" of Prosper of Aquitaine, secretary to Pope Leo the Great in the mid-5th century, and supportive of the missions of Germanus of Auxerre and Palladius of Galatia. Duchesne dated the entry a little later to the pontificate of Boniface II around 530, and Mommsen to the early 7th century. Only the last would support the conjecture that it aimed to support the Gregorian mission to the Anglo-Saxons led by Augustine of Canterbury, who encountered great difficulty with the native British Christians, as at the Synod of Chester. Indeed, the Celtic Christians invoked the antiquity of their church to generally submission to Canterbury until the Norman conquest, but no arguments invoking the mission to Lucius appear to have been made by either side during the synods among the Welsh and Saxon bishops.  The first Englishman to mention the story was Bede and he seems to have taken it, not from native texts or traditions, but from "The Book of the Popes". Subsequently, it appeared in the 9th-century "History of the Britons" traditionally credited to Nennius: The account relates that a mission from the pope baptised "Lucius, the Britannic king, with all the petty kings of the whole Britannic people". The account, however, dates this baptism to AD 167 (a little before Eleutherius's pontificate) and credits it to Evaristus (reigned ). In the 12th century, more details began to be added to the story. Geoffrey of Monmouth's pseudohistorical "History of the Kings of Britain" goes into great detail concerning Lucius and names the pope's envoys to him as Fagan and Duvian.  An echo of this legend penetrated even to Switzerland. In a homily preached at Chur and preserved in an 8th- or 9th-century manuscript, Timothy is represented as an apostle to Gaul, whence he went into Roman Britain and baptised a king named Lucius, who himself became a missionary to Gaul and finally settled at Chur, where he preached the gospel with great success. In this way Lucius, the early missionary of the Swiss district of Chur, became identified with the alleged British king of the "Liber Pontificalis".  Harnack suggests that in the document which the compiler of the "Liber Pontificalis" drew his information, the name found was not ', but '. Now this is the name (', ') of the fortress of Edessa. The king in question is, therefore, Lucius Ælius Septimus Megas Abgar IX, of Edessa, a Christian king as is well known. The original statement of the "Liber Pontificalis", in this hypothesis, had nothing to do with Britain; the compiler of the "Liber Pontificalis" changed'to ', and in this way made a British king of the Syrian Lucius.

Death.

According to the "Liber Pontificalis", Pope Eleutherius died on 24 May and was buried on the Vatican Hill ("") near the body of Peter the Apostle. Later tradition has his body moved to the church of San Giovanni della Pigna, near the pantheon. In 1591, his remains were again moved to the church of Santa Susanna at the request of Camilla Peretti, the sister of Pope Sixtus V. His feast is celebrated on 26 May.

Pope Eleutherius (died 24 May 189), also known as Eleutherus, was the Bishop of Rome of the Catholic Church from c. 174 to his death. (The Vatican cites 171 or 177 to 185 or 193.) According to the "Liber Pontificalis", he was a Greek born in Nicopolis in Epirus, Greece. His contemporary Hegesippus wrote that he was a deacon of the Roman Church under Pope Anicetus (c. 154–164), and remained so under Pope Soter, whom he succeeded around 174.

教宗圣义禄(;?-189年,原名不详,于171年或177年-185年或193年出任教宗),出生于希腊北部伊庇鲁斯地区的尼哥波立。


Etymology.

The city takes its name from George Vancouver, who explored the inner harbour of Burrard Inlet in 1792 and gave various places British names. The

History.

Before 1850.

Archaeological records indicate that Aboriginal people were already living in the "Vancouver" area from 8,000 to 10,000 years ago. The city is located in the traditional and presently unceded territories of the Squamish, Musqueam, and Tsleil-Waututh (Burrard) peoples of the Coast Salish group. They had villages in various parts of present-day Vancouver, such as Stanley Park, False Creek, Kitsilano, Point Grey and near

Early growth.

The Fraser Gold Rush of 1858 brought over 25,000 men, mainly from California, to nearby New Westminster (founded February 14, 1859) on the Fraser River, on their way to the Fraser Canyon, bypassing what would become Vancouver. Vancouver is among British Columbia's youngest cities; the first European settlement in what is now Vancouver was not until 1862 at McCleery's Farm on the Fraser River, just east of the ancient village of Musqueam in what is now Marpole. A sawmill established at Moodyville (now the City of North Vancouver) in 1863, began the city's long relationship with logging. It was quickly followed by mills owned by Captain Edward Stamp on the south shore of the inlet. Stamp, who had begun logging in the Port Alberni area, first attempted to run a mill at Brockton

Incorporation.

The City of Vancouver was incorporated on April 6, 1886, the same year that the first transcontinental train arrived. CPR president William Van Horne arrived in Port Moody to establish the CPR terminus recommended by Henry John Cambie, and gave the city its name in honour of George Vancouver. The Great Vancouver Fire on June 13, 1886, razed the entire city. The Vancouver Fire Department was established that year and the city quickly rebuilt. Vancouver's population grew from a settlement of 1,000 people in 1881 to over 20,000 by the turn of the century and 100,000 by 1911.  Vancouver merchants

Twentieth century.

The dominance of the economy by big business was accompanied by an often militant labour movement. The first major sympathy strike was in 1903 when railway employees struck against the CPR for union recognition. Labour leader Frank Rogers was killed by CPR police while picketing at the docks, becoming the movement's first martyr in British Columbia. The rise of industrial tensions throughout the province led to Canada's first general strike in 1918, at the Cumberland coal mines on Vancouver Island. Following a lull in the 1920s, the strike wave peaked in 1935 when unemployed men flooded the city to protest conditions in the relief camps run by the military in remote areas throughout the province. After two tense months of daily and disruptive protesting, the relief camp strikers decided to take their grievances to the federal government and embarked on the On-to-Ottawa Trek, but their protest was put down by force. The workers were arrested near Mission and interned in work camps for the duration of the Depression.  Other social movements, such as the first-wave feminist, moral reform, and temperance movements were also

Geography.

Located on the Burrard Peninsula, Vancouver lies between Burrard Inlet to the north and the Fraser River to the south. The Strait of Georgia, to the west, is shielded from the Pacific Ocean by Vancouver Island. The city has an area of, including both flat and hilly ground and is in the Pacific Time Zone (UTC−8) and the Pacific Maritime Ecozone.  Until the city's naming in 1885, "Vancouver" referred to Vancouver Island and it remains a common misconception that the city is located on the island. The island and the city are both named after Royal Navy Captain George Vancouver (as is the city of Vancouver, Washington, in the United States).  Vancouver has one of the largest urban parks in North America, Stanley Park, which covers. The North Shore Mountains dominate the cityscape, and on a clear day, scenic vistas include the snow-capped volcano Mount Baker in the state of Washington to the southeast, Vancouver Island across the Strait of Georgia to the west and southwest, and Bowen Island to the northwest.

Ecology.

The vegetation in the Vancouver area was originally temperate rain forest, consisting of conifers with scattered pockets of maple and alder and large areas of swampland (even in upland areas, due to poor drainage). The conifers were a typical coastal British Columbia mix of Douglas fir, western red cedar and western hemlock. The area is thought to have had the largest trees of these species on the British Columbia Coast. Only in Elliott Bay, Seattle, did the size of trees rival those of Burrard Inlet and English Bay. The largest trees in Vancouver's old-growth forest were in the Gastown area, where the first logging occurred and on the southern slopes

Climate.

Vancouver is one of Canada's warmest cities in the winter. Vancouver's climate is temperate by Canadian standards and is classified as oceanic or marine west coast, (Köppen climate classification "Cfb") that borders on a warm-summer Mediterranean climate ("Csb"). While during summer months the inland temperatures are significantly higher, Vancouver has the coolest summer average high of all major Canadian metropolitan areas. The summer months are typically dry, with an average of only one in five days during July and August receiving precipitation. In contrast, there is some precipitation during nearly half the days from November through March.  Vancouver is also one of the wettest Canadian cities. However, precipitation varies throughout the metropolitan area. Annual precipitation as

Cityscape.

Urban planning.

, Vancouver is the most densely populated city in Canada. Urban planning in Vancouver is characterized by high-rise residential and mixed-use development in urban centres, as an alternative to sprawl. As part of the larger Metro Vancouver region, it is influenced by the policy direction of livability as illustrated in Metro Vancouver's Regional Growth Strategy.  Vancouver has been ranked one of the most livable cities in the world for more than a decade., Vancouver has been ranked as having the third-highest quality of living of any city on Earth. In contrast, according to "Forbes", Vancouver had the fourth-most expensive real estate market in the world in 2019. Vancouver

Architecture.

The Vancouver Art Gallery is housed downtown in the neoclassical former courthouse built in 1906. The courthouse building was designed by Francis Rattenbury, who also designed the British Columbia Parliament Buildings and the Empress Hotel in Victoria, and the lavishly decorated second Hotel Vancouver. The 556-room Hotel Vancouver, opened in 1939 and the third by that name, is across the street with its copper roof. The Gothic-style Christ Church Cathedral, across from the hotel, opened in 1894 and was declared a heritage building in 1976.  There are several modern buildings in the downtown area, including the Harbour Centre, the Vancouver Law Courts and surrounding plaza known as Robson Square (designed by Arthur Erickson) and the Vancouver Library Square (designed by Moshe Safdie and DA Architects), reminiscent of the Colosseum in Rome, and the recently completed Woodward's building Redevelopment (designed by Henriquez Partners Architects).  The original BC Hydro headquarters building (designed by Ron Thom and Ned Pratt) at Nelson and Burrard Streets is a modernist high-rise, now converted into the Electra condominia. Also notable is the "concrete

Demographics.

The 2016 census recorded more than 631,000 people in the city, making it the eighth-largest among Canadian cities. More specifically, Vancouver is the fourth-largest in Western Canada after Calgary, Edmonton and Winnipeg. The metropolitan area referred to as Greater Vancouver, with more than 2.4million residents, is the third-most populous metropolitan area in the country and the most populous in Western Canada. The larger Lower Mainland-Southwest economic region (which includes also the Squamish-Lillooet, Fraser Valley, and Sunshine Coast Regional District) has a population of over 2.93million. With 5,249 people per square km (13,590 per sq mi), the City of Vancouver is the most densely populated of Canadian municipalities having more than 5,000 residents. Approximately 74 percent of the people living in Metro Vancouver live outside the city.  Vancouver has been called a "city of neighbourhoods". Each neighbourhood in Vancouver has a distinct character and ethnic mix. People of English, Scottish, and Irish origins were historically the largest ethnic groups in the city, and elements of British society and culture are still visible in some areas, particularly South Granville and Kerrisdale. Germans are the next-largest European ethnic group in Vancouver and were a leading force in the city's society and economy until the rise of anti-German sentiment with the outbreak of World War I in 1914. Today the Chinese are the largest visible ethnic group in the city, with a diverse Chinese-speaking community, and several dialects, including Cantonese and Mandarin. Neighbourhoods with distinct ethnic commercial areas include Chinatown, Punjabi Market, Little Italy, Greektown, and (formerly) Japantown.  Since the 1980s, immigration increased substantially, making the city more ethnically and linguistically

Economy.

With its location on the Pacific Rim and at the western terminus of Canada's transcontinental highway and rail routes, Vancouver is one of the nation's largest industrial centres. Port Metro Vancouver, Canada's largest and most diversified port, does more than C$172billion in trade with over 160 different trading economies annually. Port activities generate $9.7billion in gross domestic product and $20.3billion in economic output. Vancouver is also the headquarters of forest product and mining companies. In recent years, Vancouver has become a centre for software development, biotechnology, aerospace, video game development, animation studios and television production and film industry. Vancouver hosts approximately 65 movies and 55 TV series annually and is the 3rd largest film & TV production centre in North America, supporting 20,000 jobs. The city's strong focus on lifestyle and health culture also makes it a hub for many lifestyle brands with Lululemon, Arc'teryx, Kit and Ace, Mountain Equipment Co-op, Herschel Supply Co., Aritzia, Reigning Champ, and Nature's Path Foods all founded and headquartered in Vancouver. Vancouver was also the birthplace of 1-800-GOT-JUNK? and Western Canada's largest online-only publication, "Daily Hive".  Vancouver's scenic location makes it a major tourist destination. Over 10.3million people visited Vancouver in 2017. Annually, tourism contributes approximately $4.8billion to the Metro Vancouver economy and supports over 70,000 jobs. Many visit to see

Government.

Vancouver, unlike other British Columbia municipalities, is incorporated under the "Vancouver Charter". The legislation, passed in 1953, supersedes the "Vancouver Incorporation Act, 1921" and grants the city more and different powers than other communities possess under BC's "Municipalities Act".  The civic government was dominated by the centre-right Non-Partisan Association (NPA) since World War II, albeit with some significant centre-left interludes until 2008. The NPA fractured over the issue of drug policy in 2002, facilitating a landslide victory for the Coalition of Progressive Electors (COPE) on a harm reduction platform. Subsequently, North America's only legal safe injection site was opened for the significant number of intravenous heroin users in the city.  Vancouver is governed by the eleven-member Vancouver City Council, a nine-member School Board, and a seven-member Park Board, all of whom serve four-year terms. Unusually for a city of Vancouver's size, all municipal elections are on an at-large basis. Historically, in all levels of government, the more affluent west side of Vancouver has voted along conservative or liberal lines while the eastern side of the city has voted along left-wing lines. This was reaffirmed with the results of the 2005 provincial election and the 2006 federal election.  Though polarized, a political consensus has emerged in Vancouver around a number of issues. Protection of urban parks, a focus on the development of rapid transit as opposed to a freeway system, a harm-reduction approach to illegal drug use, and a general concern about community-based development are examples of policies that have come to have broad support across the political spectrum in Vancouver.  In the 2008 Municipal Election campaign, NPA incumbent mayor Sam Sullivan was ousted as mayoral candidate by the party in a close vote, which instated Peter Ladner as the new mayoral candidate for the NPA. Gregor Robertson, a former MLA for Vancouver-Fairview and head of Happy Planet, was the mayoral candidate for Vision Vancouver, the other main contender. Vision Vancouver candidate Gregor Robertson defeated Ladner by a considerable margin, nearing 20,000 votes. The balance of power was significantly shifted to Vision Vancouver, which held seven of the 10 spots for councillor. Of the remaining three, COPE received two and the NPA one. For park commissioner, four spots went to Vision Vancouver, one to the Green Party, one to COPE, and one to NPA. For school trustee, there were four Vision Vancouver seats, three COPE seats, and two NPA seats. In the 2018 Vancouver municipal election, independent Kennedy Stewart was elected mayor of Vancouver.  Vancouver's budget consists of a capital and an operating component. The 2017 operating budget was $1.323billion, while the 2018 operating budget is $1.407billion (a year over year increase of 6.4%). The capital budget for 2018 is unchanged from 2017 and stands at $426.4million. Budget increases are largely funded through increases in property taxes and community amenity contributions imposed in exchange for increases in allowable density as part of the construction permitting process. Utility fees and other user fees have also been increased, but represent a comparatively small portion of Vancouver's overall budget.

Education.

The Vancouver School Board enrolls more than 110,000 students in its elementary, secondary, and post-secondary institutions, making it the second-largest school district in the province. The district administers about 76 elementary schools, 17 elementary annexes, 18 secondary schools, 7 adult education centres, 2 Vancouver Learning Network schools, which include 18 French immersion, a Mandarin bilingual, a fine arts, gifted, and Montessori schools. The "Conseil scolaire francophone de la Colombie-Britannique" operates three Francophone schools in that city: the primary schools "école Rose-des-vents" and "école Anne-Hébert" as well as the "école secondaire Jules-Verne". More than 46 independent schools of a wide variety are also eligible for partial provincial funding and educate approximately 10% of pupils in the city.  There are five public universities in the Greater Vancouver area, the largest being the University of British Columbia (UBC) and Simon Fraser University (SFU), with a combined enrolment of more than 90,000 undergraduates, graduates, and professional students in 2008. UBC often ranks among the 40 best universities in the world and is among

Arts and culture.

Theatre, dance, film and television.

Theatre.

Prominent theatre companies in Vancouver include the Arts Club Theatre Company on Granville Island, and Bard on the Beach. Smaller companies include Touchstone Theatre, and Studio 58. The Cultch, The Firehall Arts Centre, United Players, Pacific and Metro

Dance.

The Scotiabank Dance Centre, a converted bank building on the corner of Davie and Granville,

Film.

The Vancouver International Film Festival, which runs for two weeks each September, shows over 350 films and is one of the larger film festivals in North America. The Vancouver International Film Centre venue, the Vancity Theatre, runs independent non-commercial films throughout the rest of the year, as do the Pacific Cinémathèque, and the Rio theatres.

Television shows produced in Vancouver.

Many past and current TV shows have been filmed and in Vancouver. The first Canadian prime time national series to be produced out of Vancouver was "Cold Squad" and its storyline was also physically set in the city. Other series set in or around the city of Vancouver include "Continuum", "Da Vinci's Inquest", "Danger Bay", "Edgemont", "Godiva's", "Intelligence", "Motive", "Northwood", "", "Robson Arms", "The Romeo Section", "Shattered", "The Switch", and "These Arms of Mine".  Television shows (but not set) in Vancouver (that have been produced by American and Canadian studios alike) include "21 Jump Street", "The 100", "The 4400", "Airwolf", "Almost Human", "Arrow", "Backstrom", "Caprica", "Cedar Cove", "Chesapeake Shores", "The Commish", "Dark Angel", "Dirk Gently's Holistic Detective Agency", "The Flash", "The Good Doctor", "Haters Back Off", "Hellcats", "Intelligence", "iZombie", "The Killing", "The L Word", "Life Unexpected", "The Man in the High Castle", "Once Upon a Time", "Psych", "Reaper", "Riverdale", "Rogue", "Smallville", "Stargate SG-1", "Supergirl", "Supernatural", "The Tomorrow People", "The Magicians", "Tru Calling", "Van Helsing", "Witches of East End", and "The X-Files".

Libraries and museums.

Libraries in Vancouver include the Vancouver Public Library with its main branch at Library Square, designed by Moshe Safdie. The central branch contains 1.5million volumes. Altogether there are twenty-two branches containing 2.25million volumes. The Vancouver Tool Library is Canada's original tool lending library.  The Vancouver Art Gallery has a permanent collection of nearly 10,000 items and is the home of a significant number of works by Emily Carr. However, little or none of the

Visual art.

The Vancouver School of conceptual photography (often referred to as photoconceptualism) is a term applied to a grouping of artists from Vancouver who achieved international recognition starting in the 1980s. No formal "school" exists and the

Music and nightlife.

Musical contributions from Vancouver include performers of classical, folk and popular music. The Vancouver Symphony Orchestra is the professional orchestra based in the city. The Vancouver Opera is a major opera company in the city, and City Opera of Vancouver is the city's professional chamber opera company. The city is home to a number of Canadian composers including Rodney Sharman, Jeffrey Ryan, and Jocelyn Morlock.  The city produced a number of notable punk rock bands, including D.O.A. Other early Vancouver punk bands included the Subhumans, the Young Canadians, the Pointed Sticks, and U-J3RK5. When alternative rock became popular in the 1990s, several Vancouver groups rose to prominence, including 54-40, Odds, Moist, the Matthew Good Band, Sons of Freedom and Econoline Crush. Recent successful Vancouver bands include Gob, Marianas Trench, Theory of a Deadman and Stabilo. Today, Vancouver is home to a number of popular independent bands such as The New Pornographers, Japandroids, Destroyer, In Medias Res, Tegan and Sara, and independent labels including Nettwerk and Mint. Vancouver also produced

Media.

Vancouver is a centre for film and television production. Nicknamed Hollywood North, a distinction it shares with Toronto, the city has been used as a film making location for nearly a century, beginning with the Edison Manufacturing Company. In 2008 more than 260 productions were filmed in Vancouver. In 2011 Vancouver slipped to fourth place overall at 1.19billion, although the region still leads Canada in foreign production.  A wide mix of local, national, and international newspapers are distributed in the city. The two major English-language daily newspapers are "The Vancouver Sun" and "The Province". Also, there are two national newspapers distributed in the city, including "The Globe and Mail", which began publication of a "national edition" in BC in 1983 and recently expanded to include a three-page BC news section, and the "National Post" which centres on national news. Other local newspapers include "24H" (a local free daily), the Vancouver franchise of the national free daily "Metro", the twice-a-week "Vancouver Courier",

Transportation.

Vancouver's streetcar system began on June 28, 1890, and ran from the (first) Granville Street Bridge to Westminster Avenue (now Main Street and Kingsway). Less than a year later, the Westminster and Vancouver Tramway Company began operating Canada's first interurban line between the two cities (extended to Chilliwack in 1910). Another line (1902), the Vancouver and Lulu Island Railway, was leased by the Canadian Pacific Railway to the British Columbia Electric Railway in 1905 and ran from the Granville Street Bridge to Steveston via Kerrisdale, which encouraged residential neighbourhoods outside the central core to develop. From 1897 the British Columbia Electric Railway (BCER) became the company that operated the urban and interurban rail system, until 1958, when its last vestiges were dismantled in favour of "trackless" trolley and gasoline/diesel buses; in that same year the BCER became the core of the newly created, publicly owned BC Hydro. Vancouver currently has the second-largest trolleybus fleet in North America, after San Francisco.  Successive city councils in the 1970s and 1980s prohibited the construction of freeways as part of a long-term plan. As a result, the only major freeway within city limits is Highway 1, which passes through the north-eastern corner of the city. While the number of cars in Vancouver proper has been steadily rising with population growth, the rate of car ownership and the average distance driven by daily commuters have fallen since the early 1990s. Vancouver is the only major Canadian city with these trends. Despite the fact that the journey time per vehicle has increased by one-third and growing traffic mass, there are 7% fewer cars making trips into the downtown core. In 2012, Vancouver had the worst traffic congestion in Canada and the second-highest in North America, behind Los Angeles., Vancouver now has the worst traffic congestion in North America. Residents have been more inclined to live in areas closer to their interests, or use more energy-efficient means of travel, such as mass

Sports and recreation.

The mild climate of the city and proximity to ocean, mountains, rivers and lakes make the area a popular destination for outdoor recreation. Vancouver has over of parks, of which Stanley Park, at, is the largest. The city has several large beaches, many adjacent to one another, extending from the shoreline of Stanley Park around False Creek to the south side of English Bay, from Kitsilano to the University Endowment Lands, (which also has beaches that are not part of the city proper). The of beaches include Second and Third Beaches in Stanley Park, English Bay (First Beach), Sunset, Kitsilano Beach, Jericho, Locarno, Spanish Banks, Spanish Banks Extension, Spanish Banks West, and Wreck Beach. There is also a freshwater beach at Trout Lake in John Hendry Park. The coastline provides for many types of water sport, and the city is a popular destination for boating enthusiasts.  Within a 20- to 30-minute drive from downtown Vancouver are the North Shore Mountains, with three ski areas: Cypress Mountain, Grouse Mountain, and Mount Seymour. Mountain bikers have created world-renowned trails across the North Shore. The Capilano River, Lynn Creek and Seymour River, also on the North Shore, provide opportunities to whitewater enthusiasts during periods of rain and spring melt, though the canyons of those rivers are more utilized for hiking and swimming than whitewater.  Running races include the Vancouver Sun Run (a race) every April; the Vancouver Marathon, held every May; and the Scotiabank Vancouver Half-Marathon held

Sustainability.

The City of Vancouver has taken a number of steps to become a sustainable city. Electricity used in Vancouver is generated using sustainable resources such as hydroelectric power. The city benefits from being located close to the mountains as hydroelectric generating stations provide 93 percent of the electricity by using falling water without emitting any greenhouse gases or polluting the air. The city is also actively working towards becoming a greener city. The City of Vancouver has crafted an action plan of goals it has set to meet by 2020, including reducing greenhouse gas emissions, encouraging the growth of

Twin towns – sister cities.

The City of Vancouver was one of the first cities in Canada to enter into an international sister cities arrangement. Special arrangements for cultural, social and economic benefits have been created with these sister cities.

Vancouver () is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the most populous city in the province, the 2016 census recorded 631,486 people in the city, up from 603,502 in 2011. The Greater Vancouver area had a population of 2,463,431 in 2016, making it the third-largest metropolitan area in Canada. Vancouver has the highest population density in Canada, with over 5,400 people per square kilometre, which makes it the fifth-most densely populated city with over 250,000 residents in North America, behind New York City, Guadalajara, San Francisco, and Mexico City. Vancouver is one of the most ethnically and linguistically diverse cities in Canada: 52% of its residents are not native English speakers, 48.9% are native speakers of neither English nor French, and 50.6% of residents belong to visible minority groups.

温哥华市(英语:City of Vancouver)是加拿大不列颠哥伦比亚省低陆平原地区一沿岸城市,与最大城市多伦多约有4,200公里之遥,西南与不列颠哥伦比亚省省会维多利亚隔100公里的太平洋相望,北距不列颠哥伦比亚省北部最大城市乔治王子城约700公里,东距亚伯达省省会埃德蒙顿约900公里,南距美国西北大城西雅图约250公里。根据2016年加拿大统计局人口普查,温哥华市人口有63万人,而大温哥华地区的人口为246万,是不列颠哥伦比亚省以至加拿大西部最大的都会区,以及全国第三大都会区;市内人口则在全国排行第八。


History.

From the beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. Among the authors of early sorting algorithms around 1951 was Betty Holberton (née Snyder), who worked on ENIAC and UNIVAC. Bubble sort was analyzed as early as 1956. Comparison sorting algorithms have a fundamental requirement of Ω("n" log "n") comparisons (some input sequences will require a multiple of "n" log "n" comparisons); algorithms not based on comparisons, such as counting sort, can have better performance. Asymptotically optimal algorithms have been known since the mid-20th century—useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.  Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average case analysis, time–space tradeoffs, and upper and lower bounds.

Classification.

Sorting algorithms are often classified by:

Stability.

Stable sort algorithms sort repeated elements in the same order that they appear in the input. When sorting some kinds of data, only part of the data is examined when determining the sort order. For example, in the card sorting example to the right, the cards are being sorted by their rank, and their suit is being ignored. This allows the possibility of multiple different correctly sorted versions of the original list. Stable sorting algorithms choose one of these, according to the following rule: if two items compare as equal, like the two 5 cards, then their relative order will be preserved, so that if one came before the other in the input, it will also come before the other in the output.  Stability is important for the following reason: say that student records consisting of name and class section are sorted dynamically on a web page, first by name, then by class section in a second operation. If a stable sorting algorithm is used in both cases, the sort-by-class-section operation will not change the name order; with an unstable sort, it could be that sorting by section shuffles the name order. Using a stable sort, users can choose to sort by section and then by name, by first sorting using name and then sort again using section, resulting in the name order being preserved. (Some spreadsheet programs obey this behavior: sorting by name, then by section yields an alphabetical list of students by section.)  More formally, the data being sorted can be represented as a record or tuple of values, and the part of the data that is used for sorting is called the "key". In the card example, cards are represented as a record (rank, suit), and the key is the rank. A sorting algorithm is stable if whenever there are two records R and S with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list.  When equal elements are indistinguishable, such as with integers, or more generally, any data where the entire element is the key, stability is not an issue. Stability is also not an issue if all keys are different.  Unstable sorting algorithms can be specially implemented to be stable. One way of doing this is to artificially extend the key comparison, so that comparisons between two objects with otherwise equal keys are decided using the order of the entries in the original input list as a tie-breaker. Remembering this order, however, may require additional time and space.  One application for stable sorting algorithms is sorting a list using a primary and secondary key. For example, suppose we wish to sort a hand of cards such that the suits are in the order clubs (♣), diamonds (♦), hearts (♥), spades (♠), and within each suit, the cards are sorted by rank. This can be done by first sorting the cards by rank (using any sort), and then doing a stable sort by suit:  Within each suit, the stable sort preserves the ordering by rank that was already done. This idea can be extended to any number of keys and is utilised by radix sort. The same effect can be achieved with an unstable sort by using a lexicographic key comparison, which, e.g., compares first by suit, and then compares by rank if the suits are the same.

Comparison of algorithms.

In this table, is the number of records to be sorted. The columns "Average" and "Worst" give the time complexity in each case, under the assumption that the length of each key is constant, and that therefore all comparisons, swaps, and other needed operations can proceed in constant time. "Memory" denotes the amount of auxiliary storage needed beyond that used by the list itself, under the same assumption. The run times and the memory requirements listed below should be understood to be inside big O notation, hence the base of the logarithms does not matter; the notation means.

Comparison sorts.

Below is a table of comparison sorts. A comparison sort cannot perform better than.

Non-comparison sorts.

The following table describes integer sorting algorithms and other sorting algorithms that are not comparison sorts. As such, they are not limited to. Complexities below assume items to be sorted, with keys of size, digit size, and the range of numbers to be sorted. Many of them are based on the assumption that the key size is large enough that all entries have unique key values, and hence that, where ≪ means "much less than". In the unit-cost random access machine model, algorithms with running time of formula_1, such as radix sort, still take time proportional to, because is limited to be not more than formula_2, and a larger number of elements to sort would require a bigger in order to store them in the memory.  Samplesort can be used to parallelize any of the non-comparison sorts, by efficiently distributing data into several buckets and then passing down sorting to several processors, with no need to merge as buckets are already sorted between each other.

Others.

Some algorithms are slow compared to those discussed above, such as the bogosort with unbounded run time and the stooge sort which has "O"("n") run time. These sorts are usually described for educational purposes in order to demonstrate how run time of algorithms is estimated. The following table describes some sorting algorithms that are impractical for real-life use in traditional software contexts due to extremely poor performance or specialized hardware requirements. Theoretical computer scientists have detailed other sorting algorithms that provide better than "O"("n" log "n") time complexity assuming additional constraints, including:

Popular sorting algorithms.

While there are a large number of sorting algorithms, in practical implementations a few algorithms predominate. Insertion sort is widely used for small data sets, while for large data sets an asymptotically efficient sort is used, primarily heap sort, merge sort, or quicksort. Efficient implementations generally use a hybrid algorithm, combining an asymptotically efficient algorithm for the overall sort with insertion sort for small lists at the bottom of a recursion. Highly tuned implementations use more sophisticated variants, such as Timsort (merge sort, insertion sort, and additional logic), used in Android, Java, and Python, and introsort (quicksort and heap sort), used (in variant forms) in some C++ sort implementations and in.NET.  For more restricted data, such as numbers in a fixed interval, distribution sorts such as counting sort or radix sort are widely used. Bubble sort and variants are rarely used in practice, but are commonly found in teaching and theoretical discussions.  When physically sorting objects (such as alphabetizing papers, tests or books) people intuitively generally use insertion sorts for small sets. For larger sets, people often first bucket, such as by initial letter, and multiple bucketing allows practical sorting of very large sets. Often space is relatively cheap, such as by spreading objects out on the floor or over a large area, but operations are expensive, particularly moving an object a large distance – locality of reference is important. Merge sorts are also practical for physical objects, particularly as two hands can be used, one for each list to merge, while other algorithms, such as heap sort or quick sort, are poorly suited for human use. Other algorithms, such as library sort, a variant of insertion sort that leaves spaces, are also practical for physical use.

Simple sorts.

Two of the simplest sorts are insertion sort and selection sort, both of which are efficient on small data, due to low overhead, but not efficient on large data. Insertion sort is generally faster than selection sort in practice, due to fewer comparisons and good performance on almost-sorted data, and thus is preferred in practice, but selection sort uses fewer writes, and thus is used when write performance is a limiting factor.

Insertion sort.

"Insertion sort" is a simple sorting algorithm that is relatively efficient for small lists and mostly sorted lists, and is often used as part of more sophisticated algorithms. It works by taking elements from the list one by one and inserting them in their correct position into a new sorted list similar to how we put money in our wallet. In arrays, the new list and the remaining elements can share the array's space, but insertion is expensive, requiring shifting all following elements over by one. Shellsort (see below) is a variant of insertion sort that is more efficient for larger lists.

Selection sort.

"Selection sort" is an in-place comparison sort. It has O("n") complexity, making it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity, and also has performance advantages over more complicated algorithms in certain situations.  The algorithm finds the minimum value, swaps it with the value in the first position, and repeats these steps for the remainder of the list. It does no more than "n" swaps, and thus is useful where swapping is very expensive.

Efficient sorts.

Practical general sorting algorithms are almost always based on an algorithm with average time complexity (and generally worst-case complexity) O("n" log "n"), of which the most common are heap sort, merge sort, and quicksort. Each has advantages and drawbacks, with the most significant being that simple implementation of merge sort uses O("n") additional space, and simple implementation of quicksort has O("n") worst-case complexity. These problems can be solved or ameliorated at the cost of a more complex algorithm.  While these algorithms are asymptotically efficient on random data, for practical efficiency on real-world data various modifications are used. First, the overhead of these algorithms becomes significant on smaller data, so often a hybrid algorithm is used, commonly switching to insertion sort once the data is small enough. Second, the algorithms often perform poorly on already sorted data or almost sorted data – these are common in real-world data, and can be sorted in O("n") time by appropriate algorithms. Finally, they may also be unstable, and stability is often a desirable property in a sort. Thus more sophisticated algorithms are often employed, such as Timsort (based on merge sort) or introsort (based on quicksort, falling back to heap sort).

Merge sort.

"Merge sort" takes advantage of the ease of merging already sorted lists into a new sorted list. It starts by comparing every two elements (i.e., 1 with 2, then 3 with 4...) and swapping them if the first should come after the second. It then merges each of the resulting lists of two into lists of four, then merges those lists of four, and so on; until at last two lists are merged into the final sorted list. Of the algorithms described here, this is the first that scales well to very large lists, because its worst-case running time is O("n" log "n"). It is also easily applied to lists, not only arrays, as it only requires sequential access, not random access. However, it has additional O("n") space complexity, and involves a large number of copies in simple implementations.  Merge sort has seen a relatively recent surge in popularity for practical implementations, due to its use in the sophisticated algorithm Timsort, which is used for the standard sort routine in the programming languages Python and Java (as of JDK7). Merge sort itself is the standard routine in Perl, among others, and has been used in Java at least since 2000 in JDK1.3.

Heapsort.

"Heapsort" is a much more efficient version of selection sort. It also works by determining the largest (or smallest) element of the list, placing that at the end (or beginning) of the list, then continuing with the rest of the list, but accomplishes this task efficiently by using a data structure called a heap, a special type of binary tree. Once the data list has been made into a heap, the root node is guaranteed to be the largest (or smallest) element. When it is removed and placed at the end of the list, the heap is rearranged so the largest element remaining moves to the root. Using the heap, finding the next largest element takes O(log "n") time, instead of O("n") for a linear scan as in simple selection sort. This allows Heapsort to run in O("n" log "n") time, and this is also the worst case complexity.

Quicksort.

"Quicksort" is a divide and conquer algorithm which relies on a "partition" operation: to partition an array, an element called a "pivot" is selected. All elements smaller than the pivot are moved before it and all greater elements are moved after it. This can be done efficiently in linear time and in-place. The lesser and greater sublists are then recursively sorted. This yields average time complexity of O("n" log "n"), with low overhead, and thus this is a popular algorithm. Efficient implementations of quicksort (with in-place partitioning) are typically unstable sorts and somewhat complex, but are among the fastest sorting algorithms in practice. Together with its modest O(log "n") space usage, quicksort is one of the most popular sorting algorithms and is available in many standard programming libraries.  The important caveat about quicksort is that its worst-case performance is O("n"); while this is rare, in naive implementations (choosing the first or last element as pivot) this occurs for sorted data, which is a common case. The most complex issue in quicksort is thus choosing a good pivot element, as consistently poor choices of pivots can result in drastically slower O("n") performance, but good choice of pivots yields O("n" log "n") performance, which is asymptotically optimal. For example, if at each step the median is chosen as the pivot then the algorithm works in O("n" log "n"). Finding the median, such as by the median of medians selection algorithm is however an O("n") operation on unsorted lists and therefore exacts significant overhead with sorting. In practice choosing a random pivot almost certainly yields O("n" log "n") performance.

Shellsort.

"Shellsort" was invented by Donald Shell in 1959. It improves upon insertion sort by moving out of order elements more than one position at a time. The concept behind Shellsort is that insertion sort performs in time, where k is the greatest distance between two out-of-place elements. This means that generally, they perform in "O"("n"), but for data that is mostly sorted, with only a few elements out of place, they perform faster. So, by first sorting elements far away, and progressively shrinking the gap between the elements to sort, the final sort computes much faster. One implementation can be described as arranging the data sequence in a two-dimensional array and then sorting the columns of the array using insertion sort.  The worst-case time complexity of Shellsort is an open problem and depends on the gap sequence used, with known complexities ranging from "O"("n") to "O"("n") and Θ("n" log "n"). This, combined with the fact that Shellsort is in-place, only needs a relatively small amount of code, and does not require use of the call stack, makes it is useful in situations where memory is at a premium, such as in embedded systems and operating system kernels.

Bubble sort and variants.

Bubble sort, and variants such as the shell sort and cocktail sort, are simple, highly-inefficient sorting algorithms. They are frequently seen in introductory texts due to ease of analysis, but they are rarely used in practice.

Bubble sort.

"Bubble sort" is a simple sorting algorithm. The algorithm starts at the beginning of the data set. It compares the first two elements, and if the first is greater than the second, it swaps them. It continues doing this for each pair of adjacent elements to the end of the data set. It then starts again with the first two elements, repeating until no swaps have occurred on the last pass. This algorithm's average time and worst-case performance is O("n"), so it is rarely used to sort large, unordered data sets. Bubble sort can be used to sort a small number of items (where its asymptotic inefficiency is not a high penalty). Bubble sort can also be used efficiently on a list of any length that is nearly sorted (that is, the elements are not significantly out of place). For example, if any number of elements are out of place by only one position (e.g. 0123546789 and 1032547698), bubble sort's exchange will get them in order on the first pass, the second pass will find all elements in order, so the sort will take only 2"n" time.

Comb sort.

"Comb sort" is a relatively simple sorting algorithm based on bubble sort and originally designed by Włodzimierz Dobosiewicz in 1980. It was later rediscovered and popularized by Stephen Lacey and Richard Box with a "Byte" Magazine article published in April 1991. The basic idea is to eliminate "turtles", or small values near the end of the list, since in a bubble sort these slow the sorting down tremendously. ("Rabbits", large values around the beginning of the list, do not pose a problem in bubble sort) It accomplishes this by initially swapping elements that are a certain distance from one another in the array, rather than only swapping elements if they are adjacent to one another, and then shrinking the chosen distance until it is operating as a normal bubble sort. Thus, if Shellsort can be thought of as a generalized version of insertion sort that swaps elements spaced a certain distance away from one another, comb sort can be thought of as the same generalization applied to bubble sort.

Distribution sort.

"Distribution sort" refers to any sorting algorithm where data is distributed from their input to multiple intermediate structures which are then gathered and placed on the output. For example, both bucket sort and flashsort are distribution based sorting algorithms. Distribution sorting algorithms can be used on a single processor, or they can be a distributed algorithm, where individual subsets are separately sorted on different processors, then combined. This allows external sorting of data too large to fit into a single computer's memory.

Counting sort.

Counting sort is applicable when each input is known to belong to a particular set, "S", of possibilities. The algorithm runs in O(|"S"| + "n") time and O(|"S"|) memory where "n" is the length of the input. It works by creating an integer array of size |"S"| and using the "i"th bin to count the occurrences of the "i"th member of "S" in the input. Each input is then counted by incrementing the value of its corresponding bin. Afterward, the counting array is looped through to arrange all of the inputs in order. This sorting algorithm often cannot be used because "S" needs to be reasonably small for the algorithm to be efficient, but it is extremely fast and demonstrates great asymptotic behavior as "n" increases. It also can be modified to provide stable behavior.

Bucket sort.

Bucket sort is a divide and conquer sorting algorithm that generalizes counting sort by partitioning an array into a finite number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm.  A bucket sort works best when the elements of the data set are evenly distributed across all buckets.

Radix sort.

"Radix sort" is an algorithm that sorts numbers by processing individual digits. "n" numbers consisting of "k" digits each are sorted in O("n" · "k") time. Radix sort can process digits of each number either starting from the least significant digit (LSD) or starting from the most significant digit (MSD). The LSD algorithm first sorts the list by the least significant digit while preserving their relative order using a stable sort. Then it sorts them by the next digit, and so on from the least significant to the most significant, ending up with a sorted list. While the LSD radix sort requires the use of a stable sort, the MSD radix sort algorithm does not (unless stable sorting is desired). In-place MSD radix sort is not stable. It is common for the counting sort algorithm to be used internally by the radix sort. A hybrid sorting approach, such as using insertion sort for small bins, improves performance of radix sort significantly.

Memory usage patterns and index sorting.

When the size of the array to be sorted approaches or exceeds the available primary memory, so that (much slower) disk or swap space must be employed, the memory usage pattern of a sorting algorithm becomes important, and an algorithm that might have been fairly efficient when the array fit easily in RAM may become impractical. In this scenario, the total number of comparisons becomes (relatively) less important, and the number of times sections of memory must be copied or swapped to and from the disk can dominate the performance characteristics of an algorithm. Thus, the number of passes and the localization of comparisons can be more important than the raw number of comparisons, since comparisons of nearby elements to one another happen at system bus speed (or, with caching, even at CPU speed), which, compared to disk speed, is virtually instantaneous.  For example, the popular recursive quicksort algorithm provides quite reasonable performance with adequate RAM, but due to the recursive way that it copies portions of the array it becomes much less practical when the array does not fit in RAM, because it may cause a number of slow copy or move operations to and from disk. In that scenario, another algorithm may be preferable even if it requires more total comparisons.  One way to work around this problem, which works well when complex records (such as in a relational database) are being sorted by a relatively small key field, is to create an index into the array and then sort the index, rather than the entire array. (A sorted version of the entire array can then be produced with one pass, reading from the index, but often even that is unnecessary, as having the sorted index is adequate.) Because the index is much smaller than the entire array, it may fit easily in memory where the entire array would not, effectively eliminating the disk-swapping problem. This procedure is sometimes called "tag sort".  Another technique for overcoming the memory-size problem is using external sorting, for example one of the ways is to combine two algorithms in a way that takes advantage of the strength of each to improve overall performance. For instance, the array might be subdivided into chunks of a size that will fit in RAM, the contents of each chunk sorted using an efficient algorithm (such as quicksort), and the results merged using a "k"-way merge similar to that used in mergesort. This is faster than performing either mergesort or quicksort over the entire list.  Techniques can also be combined. For sorting very large sets of data that vastly exceed system memory, even the index may need to be sorted using an algorithm or combination of algorithms designed to perform reasonably with virtual memory, i.e., to reduce the amount of swapping required.

Related algorithms.

Related problems include partial sorting (sorting only the "k" smallest elements of a list, or alternatively computing the "k" smallest elements, but unordered) and selection (computing the "k"th smallest element). These can be solved inefficiently by a total sort, but more efficient algorithms exist, often derived by generalizing a sorting algorithm. The most notable example is quickselect, which is related to quicksort. Conversely, some sorting algorithms can be derived by repeated application of a selection algorithm; quicksort and quickselect can be seen as the same pivoting move, differing only in whether one recurses on both sides (quicksort, divide and conquer) or one side (quickselect, decrease and conquer).  A kind of opposite of a sorting algorithm is a shuffling algorithm. These are fundamentally different because they require a source of random numbers. Shuffling can also be implemented by a sorting algorithm, namely by a random sort: assigning a random number to each element of the list and then sorting based on the random numbers. This is generally not done in practice, however, and there is a well-known simple and efficient algorithm for shuffling: the Fisher–Yates shuffle.

In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order. The most frequently used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output. More formally, the output of any sorting algorithm must satisfy two conditions:

在计算机科学与数学中,一个排序算法(英语:Sorting algorithm)是一种能将一串资料依照特定排序方式进行排列的一种算法。最常用到的排序方式是数值顺序以及字典顺序。有效的排序算法在一些算法(例如搜寻算法与合并算法)中是重要的,如此这些算法才能得到正确解答。排序算法也用在处理文字资料以及产生人类可读的输出结果。基本上,排序算法的输出必须遵守下列两个原则: