Generating Permutations in Lexicographic Order vs Sorting?

algorithm, lexicographic, permutation, sorting

Solution

These are two different things. There are `N!` permutations, but there is only one sorted order (the sorted permutation is the smallest lexicographically).

Here is an example of a sorted permutation:

brown fox quick

Here is a list of permutations in lexicographic order:

brown fox quick
brown quick fox
fox brown quick
fox quick brown
quick brown fox
quick fox brown

Here is a program in C++ to generate permutations in lexicographic order:

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

using namespace std;

int main() {
    vector<string> s;
    s.push_back("quick");
    s.push_back("brown");
    s.push_back("fox");
    sort(s.begin(), s.end());
    do {
        for(int i = 0 ; i != s.size() ; i++) {
            cout << s[i] << " ";
        }
        cout << endl;
    } while (next_permutation(s.begin(), s.end()));
    return 0;
}

Problem

I'm a little bit confused. How is the problem of generating permutations in Lexicographic Order any different from the problem of sorting? Can someone please explain it to me with an example? Thanks

Original source