std::next_permutation Implementation Explanation seeming little inefficient?

Question

I was curious how std:next_permutation was implemented so I extracted the the gnu libstdc++ 4.7 version and sanitized the identifiers and formatting to produce the following demo...

#include <vector>
#include <iostream>
#include <algorithm>

using namespace std;

template<typename It>
bool next_permutation(It begin, It end)
{
    if (begin == end)
            return false;

    It i = begin;
    ++i;
    if (i == end)
            return false;

    i = end;
    --i;

    while (true)
    {
            It j = i;
            --i;

            if (*i < *j)
            {
                    It k = end;

                    while (!(*i < *--k))
                            /* pass */;

                    iter_swap(i, k);
                    reverse(j, end);
                    return true;
            }

            if (i == begin)
            {
                    reverse(begin, end);
                    return false;
            }
    }

}

  int main()
 {
             vector<int> v = { 1, 2, 3, 4 };

    do
    {
            for (int i = 0; i < 4; i++)
            {
                    cout << v[i] << " ";
            }
            cout << endl;
    }
    while (::next_permutation(v.begin(), v.end()));

}

My question is :

while (!(*i < *--k))
  /* Iterating linearly */;

Why cant we do a binary search instead of a naive linear iteration as the sequence from [i+1 , end) is in decreasing order ? That will increase the efficiency of search. How can a standard function in "algorithm.h" neglect such a thing which leads to better performance and efficiency ? Pls somebody explain ...

Answer 1

You will rarely have an array you want to permute with more than 15 elements (and actually even less), because it would require you to process 15! > 10^12 different permutations. And for arrays with such a small size binary search is less efficient than simple linear search.