C++ algorithm for N! orderings

Question

I have a list of N items and I am wondering how I can loop through the list to get every combination. There are no doubles, so I need to get all N! orderings. Extra memory is no problem, I'm trying to think of the simplest algorithm but I'm having trouble.

Answer 1

See std::next_permutation   

Answer 2

Expanding on others' answers, here's an example of std::next_permutation adapted from cplusplus.com

#include <iostream>
#include <algorithm>
using namespace std;

void outputArray(int* array, int size)
{
  for (int i = 0; i < size; ++i) { cout << array[i] << " "; }
}

int main ()
{
  int myints[] = { 1, 2, 3, 4, 5 };
  const int size = sizeof(myints);

  cout << "The 5! possible permutations with 5 elements:\n";

  sort (myints, myints + size);

  bool hasMorePermutations = true;
  do
  {
    outputArray(myints, size);
    hasMorePermutations = next_permutation(myints, myints + size);
  }
  while (hasMorePermutations);

  return 0;
}

Answer 3

C++ STL has next_permutation for this purpose.

Answer 4

Simple algorithm using Recursion:

PSEUDOCODE

getPermutations(CurItemList , CurPermList)

if CurItemList.isempty()
    return CurPermList
else
    Permutations = {}

    for i = 1 to CurItemList.size() 
        CurPermList.addLast(CurItemList.get(i))

        NextItemList = CurItemList.copy()
        NextItemList.remove(i)

        Permutations.add(getPermutations(NextItemList, CurPermList))

        CurPermList.removeLast()


return Permutations

// To make it look better
Permutations(ItemList) 
    return getPermutations(ItemList, {})

I didnt test it, but should work. Maybe its not the smartest way to do it, but its an easy way. If something is wrong please let me know!

Answer 5

Try building up the set of combinations recursively with a fixed count of possible elements. The set of all possible combinations will be the union of the sets of combinations of 1 element, 2 elements, ... up to N elements.

Then you can attack each fixed sized combination individually.