Question

void permute(string elems, int mid, int end)
{
    static int count;
    if (mid == end) {
        cout << ++count << " : " << elems << endl;
        return ;
    }
    else {
    for (int i = mid; i <= end; i++) {
            swap(elems, mid, i);
            permute(elems, mid + 1, end);
            swap(elems, mid, i);
        }
    }
}

The above function shows the permutations of str(with str[0..mid-1] as a steady prefix, and str[mid..end] as a permutable suffix). So we can use permute(str, 0, str.size() - 1) to show all the permutations of one string.

But the function uses a recursive algorithm; maybe its performance could be improved?

Are there any better methods to permute a string?

Answer 1

Here is a non-recursive algorithm in C++ from the Wikipedia entry for unordered generation of permutations. For the string s of length n, for any k from 0 to n! - 1 inclusive, the following modifies s to provide a unique permutation (that is, different from those generated for any other k value on that range). To generate all permutations, run it for all n! k values on the original value of s.

#include <algorithm>

void permutation(int k, string &s) 
{
    for(int j = 1; j < s.size(); ++j) 
    {
        std::swap(s[k % (j + 1)], s[j]); 
        k = k / (j + 1);
    }
}

Here swap(s, i, j) swaps position i and j of the string s.