Algorithm: String Full Permutation

Suppose that we are going to display Permutation for ‘A’,’B’,’C’,’D’. So there should be have 4!=24 combinations.

Following is one algorithm to calculate these combinations.

1. Doing exchange the first character with each of rest characters.

We can get following combinations with header A, B, C, and D respectively.

ABCD

BACD

CABD

DABC

2. Lock first character and doing exchange the second character with each of rest.

Take ABCD for example, we lock A and will exchange B with the rest of characters respectively. We can get ABCD, ACBD and ADBC.

Likewise, we can do the same to BACD, CABD and DABC. And we can get following combinations.

3. Repeat Step2: Lock next character, third one, and exchange the third character with each of rest until locked character is the last one.

So, we can get the final combinations as below as well as what we want.

C++ Implement:

// AllPermutations2.cpp : Defines the entry point for the console application. // #include "stdafx.h" #include <iostream.h> void swap(char* left , char* right) { char temp = *left ; *left = *right ; *right = temp ; } void Perm(char str[], int k, int m) { if(k==m) { for(int i=0 ; i<=m ; i++) cout<<str[i] ; cout<<endl ; } else { for(int i=k ; i<=m ; i++) { swap(&str[k],&str[i]) ; Perm(str, k+1, m) ; swap(&str[k],&str[i]) ; } } } int main(int argc, char* argv[]) { char str[] = {'A','B','C','D'} ; Perm(str,0,3) ; return 0; }

 

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