                    ABCD
                    CABD
                    ACDB
                    DACB
                    BCDA
                    ACBD
                    ADCB
                    CDAB
                    DABC
                    BCAD
                    CADB
                    CDBA
                    CBAD
                    ABDC
                    ADBC
                    BDCA
                    DCBA
                    BACD
                    BADC
                    BDAC
                    CBDA
                    DBCA
                    DCAB

Listed above are   all-but-one   of the permutations of the symbols   A,   B,   C,   and   D,   except   for one permutation that's   not   listed.



Task

Find that missing permutation.



Methods

 Obvious method: 
        enumerate all permutations of   A,  B,  C,  and  D,  
        and then look for the missing permutation. 

 alternate method:
        Hint:  if all permutations were shown above,  how many 
        times would  A  appear in each position?     
        What is the  parity  of this number?

 another alternate method:
        Hint:  if you add up the letter values of each column, 
        does a missing letter   A,  B,  C,  and  D   from each
        column cause the total value for each column to be unique?



Related task

   Permutations)


#include <algorithm>
#include <vector>
#include <set>
#include <iterator>
#include <iostream>
#include <string>
 
static const std::string GivenPermutations[] = {
  "ABCD","CABD","ACDB","DACB",
  "BCDA","ACBD","ADCB","CDAB",
  "DABC","BCAD","CADB","CDBA",
  "CBAD","ABDC","ADBC","BDCA",
  "DCBA","BACD","BADC","BDAC",
  "CBDA","DBCA","DCAB"
};
static const size_t NumGivenPermutations = sizeof(GivenPermutations) / sizeof(*GivenPermutations);
 
int main()
{
    std::vector<std::string> permutations;
    std::string initial = "ABCD";
    permutations.push_back(initial);
 
    while(true)
    {
        std::string p = permutations.back();
        std::next_permutation(p.begin(), p.end());
        if(p == permutations.front())
            break;
        permutations.push_back(p);
    }
 
    std::vector<std::string> missing;
    std::set<std::string> given_permutations(GivenPermutations, GivenPermutations + NumGivenPermutations);
    std::set_difference(permutations.begin(), permutations.end(), given_permutations.begin(),
        given_permutations.end(), std::back_inserter(missing));
    std::copy(missing.begin(), missing.end(), std::ostream_iterator<std::string>(std::cout, "\n"));
    return 0;
}