String Permutations Algorithm with example code in C/C++ ~ code hackers blog

Monday, June 15, 2015

String Permutations Algorithm with example code in C/C++

TheUnknown Monday, June 15, 2015 Algorithms, C (programming language), C & C++, Data Structure, Programming, Programming Tutorials, Recursion, String Manipulations No comments

Permutations of 3 balls (Photo credit: Wikipedia)

Hello Everyone,

Today I will be telling you how to print all the possible permutations of a string provided by the user. I will show you the recursive way to do this. The programming paradigm that we use in case of Recursion is backtracking.

What do you mean by Permutations ?

A permutation, also called an “arrangement number” or “order,” is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. A string of length n has n! permutation.

For more info visit here --> http://mathworld.wolfram.com/Permutation.html

Recursion

This is a bad method for printing permutations since its time complex i.e. it takes more time to execute than the iterative method this is because of the extensive use of the call stack. Now the following image explains the recursion technique. The image presents the recursion tree of the method of permutations generation. We take the example string that we permute as "GOD".

In order to find all possible combinations for a given string, then start at a position i, then find and place all possible letters in position i. Every time we put a new letter in position i, we should then find all the possible combinations at position i+1 – this would be the recursive call that we make.

Here's the C++ implementation string permutation.

	#include <iostream>
	#include <cstring>

	void swap(char* src, char* dst)
	{
	char ch = *dst;
	dst = src;
	*src = ch;
	}

	void permuteString(char* s, int beg, int end)
	{
	int i;
	int range = end - beg;
	if (range == 1) {
	std::cout<<s<<std::endl;
	} else {
	for(i=0; i<range; i++) {
	swap(&s[beg], &s[beg+i]);
	permuteString(s, beg+1, end);
	swap(&s[beg], &s[beg+i]);
	}
	}
	}

	int main()
	{
	char str[] = "GOD";
	std::cout<<"The permutations are :- "<<std::endl;
	permuteString(str, 0, strlen(str));
	return 0;
	}

view raw StringPerm.cpp hosted with ❤ by GitHub

Now the above code will print all the permutations of the string "GOD" without repetition. But if you want to print them lexicographic manner i.e where the repetitions of the characters are included then read the matter below.

Since we are going in lexicographic order, so we have to do the following ,its pretty much understandable. (Note : the numbers represent index and 1 means the starting index , we will not use 0 for the first index as we do it in programming.)

Start with index '1' and then recurse over rest of the 'n - 1' numbers.
- Start with '2' and then recurse over rest of the 'n - 2' numbers.
- Start with '3' and then recurse over rest of the 'n - 2' numbers.
  :
  :
- Start with 'i' and then recurse over rest of the 'n - 2' numbers.
  :
  :
- Start with 'n' and then recurse over rest of the 'n - 2' numbers.
Start with a '2' and then recurse over rest of the 'n - 1' numbers.
- Start with '1' and then recurse over rest of the 'n - 2' numbers.
- Start with '3' and then recurse over rest of the 'n - 2' numbers.
  :
  :
- Start with 'i' and then recurse over rest of the 'n - 2' numbers.
  :
  :
- Start with 'n' and then recurse over rest of the 'n - 2' numbers.
:
:
Start with 'i' and then recurse over rest of the 'n - 1' numbers.
:
:
Start with 'n' and then recurse over rest of the 'n - 1' numbers.

Important thing to note is, in every recursion you start with the minimum numbers left, to be printed, and then keep picking the next minimum, and so on, till you exhaust all the 'n' numbers.

Here's the C Code for Lexicographical Permutations.

	#include<stdio.h>
	#include<stdlib.h>
	#include<string.h>

	/* Following function is used by the library qsort() function to sort an array of chars */
	int compare (const void * a, const void * b);

	/* this function recursively prints all repeated permutations of the given string.*/
	void LRecurse (char str, char data, int last, int index)
	{
	int i, len = strlen(str);

	// One by one fix all characters at the given index and recur for the subsequent indexes
	for ( i=0; i<len; i++ )
	{
	// Fix the ith character at index and if this is not the last index then recursively call for higher indexes
	data[index] = str[i] ;

	// If this is the last index then print the string stored in data
	if (index == last)
	printf("%s\n", data);
	else
	LRecurse (str, data, last, index+1);
	}
	}

	/* This function sorts input string, allocate memory and calls LRecurse() for printing all permutations */
	void LSort(char *str)
	{
	int len = strlen (str) ;

	char data = (char ) malloc (sizeof(char) * (len + 1)) ;
	data[len] = '\0';

	// Sort the input string so that we get all output strings in lexicographically sorted order
	qsort(str, len, sizeof(char), compare);
	LRecurse (str, data, len-1, 0);
	free(data);// Free data to avoid memory leak
	}

	// Needed for library function qsort()
	int compare (const void * a, const void * b)
	{
	return ( (char )a - (char )b );
	}

	int main()
	{
	char str[] = "GOD";
	printf("All permutations of %s in Lexicographic order are : \n", str);
	LSort(str);
	getchar();
	return 0;
	}