Print All Permutations of a Given String

Printing all permutations of a given string is an example of backtracking problem. We will reduce the size of the substring to solve the sub-problems, then again backtrack to get another permutation from that section.

For an example, if the string is ABC, the all permutations will be ABC, ACB, BAC, BCA, CAB, CBA.

The complexity of this algorithm is O(n!). It is a huge complexity. When the string size increases, it takes a longer time to finish the task.

Input and Output

Input:
A string “ABC”
Output:
All permutations of ABC is:
ABC
ACB
BAC
BCA
CBA
CAB

Algorithm

stringPermutation(str, left, right)

Input: The string and left and right index of characters.

Output: Print all permutations of the string.

Begin
   if left = right, then
      display str
   else
      for i := left to right, do
         swap str[left] and str[i]
         stringPermutation(str, left+1, right)
         swap str[left] and str[i]             //for backtrack
      done
End

Example

#include<iostream>
using namespace std;

void stringPermutation(string str, int left, int right) {
   if(left == right)
      cout << str << endl;
   else {
      for(int i = left; i<= right; i++) {
         swap(str[left], str[i]);
         stringPermutation(str, left + 1, right);
         swap(str[left], str[i]); //swap back for backtracking
      }
   }
}

int main() {
   string str = "ABC";
   cout << "All permutations of " << str << " is: " <<endl<<endl;
   stringPermutation(str, 0, str.size()-1);
}

Output

All permutations of ABC is:
ABC
ACB
BAC
BCA
CBA
CAB