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Check if a string is a scrambled form of another string

  • Difficulty Level : Hard
  • Last Updated : 13 Jul, 2021

Given two strings S1 and S2 of equal length, the task is to determine if S2 is a scrambled form of S1.
Scrambled string: 
Given string str, we can represent it as a binary tree by partitioning it into two non-empty substrings recursively.
Note: Scrambled string is not same as an Anagram
Below is one possible representation of str = “coder”:
 

    coder
   /    \
  co    der
 / \    /  \
c   o  d   er
           / \
          e   r

To scramble the string, we may choose any non-leaf node and swap its two children. 
Suppose, we choose the node “co” and swap its two children, it produces a scrambled string “ocder”.
 

    ocder
   /    \
  oc    der
 / \    /  \
o   c  d   er
           / \
          e   r

Thus, “ocder” is a scrambled string of “coder”.
Similarly, if we continue to swap the children of nodes “der” and “er”, it produces a scrambled string “ocred”.
 

    ocred
   /    \
  oc    red
 / \    /  \
o   c  re  d
       / \
      r   e

Thus, “ocred” is a scrambled string of “coder”.
Examples:

Input: S1=”coder”, S2=”ocder” 
Output: Yes 
Explanation: 
“ocder” is a scrambled form of “coder”
Input: S1=”abcde”, S2=”caebd” 
Output: No 
Explanation: 
“caebd” is not a scrambled form of “abcde”



Approach 
In order to solve this problem, we are using Divide and Conquer approach. 
Given two strings of equal length (say n+1), S1[0…n] and S2[0…n]. If S2 is a scrambled form of S1, then there must exist an index i such that at least one of the following conditions is true: 
 

  • S2[0…i] is a scrambled string of S1[0…i] and S2[i+1…n] is a scrambled string of S1[i+1…n].
  • S2[0…i] is a scrambled string of S1[n-i…n] and S2[i+1…n] is a scrambled string of S1[0…n-i-1].

Note: An optimization step to consider here is to check beforehand if the two strings are anagrams of each other. If not, it indicates that the strings contain different characters and can’t be a scrambled form of each other.
Below is the implementation of the above approach:
 

C++




// C++ Program to check if a
// given string is a scrambled
// form of another string
 
#include <bits/stdc++.h>
using namespace std;
 
bool isScramble(string S1, string S2)
{
    // Strings of non-equal length
    // cant' be scramble strings
    if (S1.length() != S2.length()) {
        return false;
    }
 
    int n = S1.length();
 
    // Empty strings are scramble strings
    if (n == 0) {
        return true;
    }
 
    // Equal strings are scramble strings
    if (S1 == S2) {
        return true;
    }
 
    // Check for the condition of anagram
    string copy_S1 = S1, copy_S2 = S2;
 
    sort(copy_S1.begin(), copy_S1.end());
    sort(copy_S2.begin(), copy_S2.end());
 
    if (copy_S1 != copy_S2) {
        return false;
    }
 
    for (int i = 1; i < n; i++) {
 
        // Check if S2[0...i] is a scrambled
        // string of S1[0...i] and if S2[i+1...n]
        // is a scrambled string of S1[i+1...n]
        if (isScramble(S1.substr(0, i), S2.substr(0, i))
            && isScramble(S1.substr(i, n - i),
                          S2.substr(i, n - i))) {
            return true;
        }
 
        // Check if S2[0...i] is a scrambled
        // string of S1[n-i...n] and S2[i+1...n]
        // is a scramble string of S1[0...n-i-1]
        if (isScramble(S1.substr(0, i),
                       S2.substr(n - i, i))
            && isScramble(S1.substr(i, n - i),
                          S2.substr(0, n - i))) {
            return true;
        }
    }
 
    // If none of the above
    // conditions are satisfied
    return false;
}
 
// Driver Code
int main()
{
    string S1 = "coder";
    string S2 = "ocred";
 
    if (isScramble(S1, S2)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
 
    return 0;
}

Java




// Java program to check if a
// given string is a scrambled
// form of another string
import java.util.*;
 
class GFG{
     
static boolean isScramble(String S1,
                          String S2)
{
     
    // Strings of non-equal length
    // cant' be scramble strings
    if (S1.length() != S2.length())
    {
        return false;
    }
     
    int n = S1.length();
 
    // Empty strings are scramble strings
    if (n == 0)
    {
        return true;
    }
     
    // Equal strings are scramble strings
    if (S1.equals(S2))
    {
        return true;
    }
     
    // Converting string to
    // character array
    char[] tempArray1 = S1.toCharArray();
    char[] tempArray2 = S2.toCharArray();
     
    // Checking condition for Anagram
    Arrays.sort(tempArray1);
    Arrays.sort(tempArray2);
     
    String copy_S1 = new String(tempArray1);
    String copy_S2 = new String(tempArray2);
     
    if (!copy_S1.equals(copy_S2))
    {
        return false;
    }
         
    for(int i = 1; i < n; i++)
    {
         
        // Check if S2[0...i] is a scrambled
        // string of S1[0...i] and if S2[i+1...n]
        // is a scrambled string of S1[i+1...n]
        if (isScramble(S1.substring(0, i),
                       S2.substring(0, i)) &&
            isScramble(S1.substring(i, n),
                       S2.substring(i, n)))
        {
            return true;
        }
 
        // Check if S2[0...i] is a scrambled
        // string of S1[n-i...n] and S2[i+1...n]
        // is a scramble string of S1[0...n-i-1]
        if (isScramble(S1.substring(n - i, n),
                       S2.substring(0, i)) &&
            isScramble(S1.substring(0, n - i),
                       S2.substring(i, n)))
        {
            return true;
        }
    }
     
    // If none of the above
    // conditions are satisfied
    return false;
}
 
// Driver Code
public static void main(String[] args)
{
    String S1 = "coder";
    String S2 = "ocred";
     
    if (isScramble(S1, S2))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by dadi madhav

Python3




# Python3 program to check if a
# given string is a scrambled
# form of another string
def isScramble(S1: str, S2: str):
     
    # Strings of non-equal length
    # cant' be scramble strings
    if len(S1) != len(S2):
        return False
 
    n = len(S1)
 
    # Empty strings are scramble strings
    if not n:
        return True
 
    # Equal strings are scramble strings
    if S1 == S2:
        return True
 
    # Check for the condition of anagram
    if sorted(S1) != sorted(S2):
        return False
 
    for i in range(1, n):
         
        # Check if S2[0...i] is a scrambled
        # string of S1[0...i] and if S2[i+1...n]
        # is a scrambled string of S1[i+1...n]
        if (isScramble(S1[:i], S2[:i]) and
            isScramble(S1[i:], S2[i:])):
            return True
 
        # Check if S2[0...i] is a scrambled
        # string of S1[n-i...n] and S2[i+1...n]
        # is a scramble string of S1[0...n-i-1]
        if (isScramble(S1[-i:], S2[:i]) and
            isScramble(S1[:-i], S2[i:])):
            return True
 
    # If none of the above
    # conditions are satisfied
    return False
 
# Driver Code
if __name__ == "__main__":
     
    S1 = "coder"
    S2 = "ocred"
     
    if (isScramble(S1, S2)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by sgshah2

C#




// C# program to check if a
// given string is a scrambled
// form of another string
using System;
using System.Collections.Generic;
class GFG {
     
    static bool isScramble(string S1, string S2)
    {
           
        // Strings of non-equal length
        // cant' be scramble strings
        if (S1.Length != S2.Length) 
        {
            return false;
        }
           
        int n = S1.Length;
       
        // Empty strings are scramble strings
        if (n == 0) 
        {
            return true;
        }
           
        // Equal strings are scramble strings
        if (S1.Equals(S2))
        {
            return true;
        }
           
        // Converting string to 
        // character array
        char[] tempArray1 = S1.ToCharArray();
        char[] tempArray2 = S2.ToCharArray();
           
        // Checking condition for Anagram
        Array.Sort(tempArray1);
        Array.Sort(tempArray2);
           
        string copy_S1 = new string(tempArray1);
        string copy_S2 = new string(tempArray2);
           
        if (!copy_S1.Equals(copy_S2)) 
        {
            return false;
        }
               
        for(int i = 1; i < n; i++)
        {
               
            // Check if S2[0...i] is a scrambled
            // string of S1[0...i] and if S2[i+1...n]
            // is a scrambled string of S1[i+1...n]
            if (isScramble(S1.Substring(0, i), 
                           S2.Substring(0, i)) && 
                isScramble(S1.Substring(i, n - i),
                           S2.Substring(i, n - i)))
            {
                return true;
            }
       
            // Check if S2[0...i] is a scrambled
            // string of S1[n-i...n] and S2[i+1...n]
            // is a scramble string of S1[0...n-i-1]
            if (isScramble(S1.Substring(0, i),
                           S2.Substring(n - i, i)) && 
                isScramble(S1.Substring(i, n - i),
                           S2.Substring(0, n - i))) 
            {
                return true;
            }
        }
           
        // If none of the above
        // conditions are satisfied
        return false;
    }
   
  // Driver code
  static void Main()
  {
        string S1 = "coder";
        string S2 = "ocred";
           
        if (isScramble(S1, S2)) 
        {
            Console.WriteLine("Yes");
        }
        else
        {
            Console.WriteLine("No");
        }
  }
}
 
// This code is contributed by divyeshrabadiya07

Javascript




<script>
    // Javascript program to check if a
    // given string is a scrambled
    // form of another string
     
    function isScramble(S1, S2)
    {
 
        // Strings of non-equal length
        // can't be scramble strings
        if (S1.length != S2.length)
        {
            return false;
        }
 
        let n = S1.length;
 
        // Empty strings are scramble strings
        if (n == 0)
        {
            return true;
        }
 
        // Equal strings are scramble strings
        if (S1 == S2)
        {
            return true;
        }
 
        // Converting string to
        // character array
        let tempArray1 = S1.split('');
        let tempArray2 = S2.split('');
 
        // Checking condition for Anagram
        tempArray1.sort();
        tempArray2.sort();
 
        let copy_S1 = tempArray1.join("");
        let copy_S2 = tempArray2.join("");
 
        if (copy_S1 != copy_S2)
        {
            return false;
        }
 
        for(let i = 1; i < n; i++)
        {
 
            // Check if S2[0...i] is a scrambled
            // string of S1[0...i] and if S2[i+1...n]
            // is a scrambled string of S1[i+1...n]
            if (isScramble(S1.substring(0, i),
                           S2.substring(0, i)) &&
                isScramble(S1.substring(i, i + n),
                           S2.substring(i, i + n)))
            {
                return true;
            }
 
            // Check if S2[0...i] is a scrambled
            // string of S1[n-i...n] and S2[i+1...n]
            // is a scramble string of S1[0...n-i-1]
            if (isScramble(S1.substring(n - i, n - i + n),
                           S2.substring(0, i)) &&
                isScramble(S1.substring(0, n - i),
                           S2.substring(i, i + n)))
            {
                return true;
            }
        }
 
        // If none of the above
        // conditions are satisfied
        return false;
    }
     
    let S1 = "coder";
    let S2 = "ocred";
      
    if (isScramble(S1, S2))
    {
        document.write("Yes");
    }
    else
    {
        document.write("No");
    }
 
// This code is contributed by decode2207.
</script>
Output
Yes

Dynamic Programming Solution: The above recursive Code can be optimized by storing Boolean values of substrings in an unordered map, so if the same substrings have to be checked again we can easily just get value from the map instead of performing function calls.

Memoized Code: 

C++




// C++ Program to check if a
// given string is a scrambled
// form of another string
 
#include <bits/stdc++.h>
using namespace std;
 
// map declaration for storing key value pair
// means for storing subproblem result
unordered_map<string, bool> mp;
 
bool isScramble(string S1, string S2)
{
    // Strings of non-equal length
    // cant' be scramble strings
    if (S1.length() != S2.length()) {
        return false;
    }
 
    int n = S1.length();
 
    // Empty strings are scramble strings
    if (n == 0) {
        return true;
    }
 
    // Equal strings are scramble strings
    if (S1 == S2) {
        return true;
    }
    // Check for the condition of anagram
    string copy_S1 = S1, copy_S2 = S2;
 
    sort(copy_S1.begin(), copy_S1.end());
    sort(copy_S2.begin(), copy_S2.end());
 
    if (copy_S1 != copy_S2) {
        return false;
    }
 
    // make key of type string for search in map
    string key = (S1 + " " + S2);
    // checking if both string are before calculated or not
    // if calculated means find in map then return it's
    // value
    if (mp.find(key) != mp.end()) {
        return mp[key];
    }
 
    // declaring flag variable to store result
    bool flag = false;
 
    for (int i = 1; i < n; i++) {
 
        // Check if S2[0...i] is a scrambled
        // string of S1[0...i] and if S2[i+1...n]
        // is a scrambled string of S1[i+1...n]
        if (isScramble(S1.substr(0, i), S2.substr(0, i))
            && isScramble(S1.substr(i, n - i),
                          S2.substr(i, n - i))) {
            flag = true;
            return true;
        }
 
        // Check if S2[0...i] is a scrambled
        // string of S1[n-i...n] and S2[i+1...n]
        // is a scramble string of S1[0...n-i-1]
        if (isScramble(S1.substr(0, i), S2.substr(n - i, i))
            && isScramble(S1.substr(i, n - i),
                          S2.substr(0, n - i))) {
            flag = true;
            return true;
        }
    }
 
    // add key & flag value to map (store for future use)
    // so next time no required to calculate it again
    mp[key] = flag;
 
    // If none of the above conditions are satisfied
    return false;
}
 
// Driver Code
int main()
{
    string S1 = "coder";
    string S2 = "ocred";
 
    if (isScramble(S1, S2)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
 
    return 0;
}

Python3




# Declaring unordered map globally
map={}
# Python3 program to check if a
# given string is a scrambled
# form of another string
def isScramble(S1: str, S2: str):
     
    # Strings of non-equal length
    # cant' be scramble strings
    if len(S1) != len(S2):
        return False
 
    n = len(S1)
 
    # Empty strings are scramble strings
    if not n:
        return True
 
    # Equal strings are scramble strings
    if S1 == S2:
        return True
 
    # Check for the condition of anagram
    if sorted(S1) != sorted(S2):
        return False
     
    # Checking if both Substrings are in
    # map or are already calculated or not
    if(S1+' '+S2 in map):
        return map[S1+' '+S2]
     
    # Declaring a flag variable
    flag = False
 
    for i in range(1, n):
         
        # Check if S2[0...i] is a scrambled
        # string of S1[0...i] and if S2[i+1...n]
        # is a scrambled string of S1[i+1...n]
        if (isScramble(S1[:i], S2[:i]) and
            isScramble(S1[i:], S2[i:])):
            flag = True
            return True
 
        # Check if S2[0...i] is a scrambled
        # string of S1[n-i...n] and S2[i+1...n]
        # is a scramble string of S1[0...n-i-1]
        if (isScramble(S1[-i:], S2[:i]) and
            isScramble(S1[:-i], S2[i:])):
            flag = True
            return True
     
    # Storing calculated value to map
    map[S1+" "+S2] = flag
     
    # If none of the above
    # conditions are satisfied
    return False
 
# Driver Code
if __name__ == "__main__":
     
    S1 = "great"
    S2 = "rgate"
     
    if (isScramble(S1, S2)):
        print("Yes")
    else:
        print("No")
Output
Yes

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