We will use a very simple approach to do it.
Take out first character of String and insert into different places of permutations of remaining String recursively.
Lets say you have String as ABC.
So we take out A from ABC
First character =A and RemainingString = BCÂ
As we are applying recursion here, we will find permutations of BC.
Take out B from BC.
First character= B and RemainingString = CÂ
As we are applying recursion here, we will find permutations of C.
When we take out C, our String size becomes 0 and that is our base case here.
First character = C and RemainingString = “”Â
We insert C to differences indexes of Permutations  of RemainingString(“”), so we get permutation of C as C.
We insert B to different indexes of Permutations of remainingString(C), so we get BC and CB.
C: BC, CB
Now we insert A to different indexes in BC and CB.
BC : ABC , BAC , BCA
CB : ACB, CAB, CBA
so thats how we got all permutations of ABC.
It may look tricky but once you practice the solution, you will be able to understand it better.
Java program to find all Permutations of String in java:
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package org.arpit.java2blog; import java.util.HashSet; import java.util.Iterator; import java.util.Set; public class PermutationOfStringJava { public static void main(String[] args) { Set set=permutationOfString("ABC"); System.out.println("Permutations of String ABC are:"); for (Iterator iterator = set.iterator(); iterator.hasNext();) { String string = (String) iterator.next(); System.out.println(string); } } public static Set permutationOfString(String str) { Set permutationSet=new HashSet(); if(str.length()==0) { permutationSet.add(""); return permutationSet; } // take out first character of String char c=str.charAt(0); // Remaining String String rem=str.substring(1); Set permutatedSetForRemainingString=permutationOfString(rem); for (String permutedString: permutatedSetForRemainingString) { for (int j = 0; j <= permutedString.length(); j++) { String permutation=insertFirstCharAtDiffPlaces(permutedString,c,j); permutationSet.add(permutation); } } return permutationSet; } public static String insertFirstCharAtDiffPlaces(String perm,char firstChar,int index) { // Inserting firstCharacter of orig String at difference places based on index return perm.substring(0,index)+firstChar+perm.substring(index); } } |
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Permutations of String ABC are: ACB ABC BCA CBA CAB BAC |
