Question : Is the attached logic correct? I am asking since my code based on this logic failed.Here is the problem link. Reproducing here verbatim : The Shuseki Islands are an archipelago of 30001 small islands in the  Yutampo Sea. The islands are evenly spaced along a line, numbered from  0 to 30000 from the west to the east. These islands are known to  contain many treasures. There are n gems in the Shuseki Islands in  total, and the i-th gem is located on island pi.Mr. Kitayuta has just arrived at island 0. With his great jumping  ability, he will repeatedly perform jumps between islands to the east  according to the following process:First, he will jump from island 0 to island d. After that, he will  continue jumping according to the following rule. Let l be the length  of the previous jump, that is, if his previous jump was from island  prev to island cur, let l=cur-prev. He will perform a jump of  length l-1, l or l+1 to the east. That is, he will jump to island  (cur+l-1), (cur+l) or (cur+l+1) (if they exist). The length  of a jump must be positive, that is, he cannot perform a jump of  length 0 when l=1. If there is no valid destination, he will stop  jumping. Mr. Kitayuta will collect the gems on the islands visited  during the process. Find the maximum number of gems that he can  collect.Input The first line of the input contains two space-separated  integers n and d (1n,d30000), denoting the number of the gems  in the Shuseki Islands and the length of the Mr. Kitayuta's first  jump, respectively.The next n lines describe the location of the gems. The i-th of them  (1in) contains a integer pi (dp1p2...pn30000),  denoting the number of the island that contains the i-th gem.Output Print the maximum number of gems that Mr. Kitayuta can collect.My solution code is along the following lines : Create a Directed Acyclic Graph by creating edges from a vertex to all the next possible vertices (based on the previous jump length).Here weight(u,v) is number of gems on vertex v(island v).Now find the vertex with maximum distance from source vertex. Since it's a DAG, do topological sort and use this algorithm to find the longest path in a DAG.
Codeforces : 505C. Mr. Kitayuta, the Treasure Hunter
graph