Check if a string can be transformed to another by sorting substrings

Given two strings str1 and str2, each of length N and consisting of lowercase English alphabets only, the task is to check if string str1 can be transformed to string str2 by performing the following operations any number of times.

Examples : 

Input: str1 = “hdecb”, str2 = “cdheb”
Output: Yes
Explanation:
Sorting the substring “ec” in str1 modifies the string to “hdceb”
Sorting the substring “hdc” in str1 modifies the string to “cdheb”. 
Since, the modifed string is same as str2, the answer is Yes. 

Input: str1 = “abcdef”, str2 = “dacbfe”
Output: No

Approach: Follow the steps below to solve the problem:



  • Observe that, in the string str1, if there are two characters str1[i] and str2[j] such that str1[i] < str1[j], then these characters can be swapped.
  • In other words, it is possible to move a character freely to the left, until it encounters a smaller character. For example, “acdb” can be converted to either “acbd“, “abcd” as ‘b‘ can be moved freely to the left until ‘a‘ occurs.
  • Therefore, check if it is possible to move the required characters to the left, to their respective positions in the string str2.
  • Store the indices of every character of string str1 in an array.
  • Traverse the string str2, and for each character, check if the same character in str1 can be shifted to that position or not.

Below is the implementation of the above approach:

C++

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// C++ Program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if str1 can be
// transformed to t by sorting substrings
void canTransform(string& s, string& t)
{
    int n = s.length();
 
    // Occur[i] stores the indices
    // of char ('a'+i) in string s
    vector<int> occur[26];
    for (int x = 0; x < n; x++) {
        char ch = s[x] - 'a';
        occur[ch].push_back(x);
    }
 
    // idx[i] stores the next available
    // index of char ('a'+i) in occur[i]
    vector<int> idx(26, 0);
    bool poss = true;
    for (int x = 0; x < n; x++) {
        char ch = t[x] - 'a';
 
        // If this char is not available
        // anymore
        if (idx[ch] >= occur[ch].size()) {
 
            // Conversion not possible
            poss = false;
            break;
        }
        for (int small = 0; small < ch; small++) {
 
            // If one of the smaller characters
            // is available and occurs before
            if (idx[small] < occur[small].size()
                && occur[small][idx[small]]
                       < occur[ch][idx[ch]]) {
 
                // Conversion not possible
                poss = false;
                break;
            }
        }
        idx[ch]++;
    }
 
    // Print the answer
    if (poss) {
        cout << "Yes" << endl;
    }
    else {
        cout << "No" << endl;
    }
}
 
// Driver Code
int main()
{
    string s, t;
 
    s = "hdecb";
    t = "cdheb";
 
    canTransform(s, t);
    return 0;
}

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Java

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// Java Program to implement
// the above approach
import java.util.*;
class GFG{
 
// Function to check if str1
// can be transformed to t by
// sorting subStrings
static void canTransform(String s,
                         String t)
{
  int n = s.length();
 
  // Occur[i] stores the indices
  // of char ('a'+i) in String s
  Vector<Integer> occur[] = new Vector[26];
   
  for (int i = 0; i < occur.length; i++)
    occur[i] = new Vector<Integer>();
   
  for (int x = 0; x < n; x++)
  {
    char ch = (char)(s.charAt(x) - 'a');
    occur[ch].add(x);
  }
 
  // idx[i] stores the next available
  // index of char ('a'+i) in occur[i]
  int []idx = new int[26];
  boolean poss = true;
   
  for (int x = 0; x < n; x++)
  {
    char ch = (char)(t.charAt(x) - 'a');
 
    // If this char is
    // not available anymore
    if (idx[ch] >= occur[ch].size())
    {
      // Conversion not possible
      poss = false;
      break;
    }
    for (int small = 0; small < ch; small++)
    {
      // If one of the smaller characters
      // is available and occurs before
      if (idx[small] < occur[small].size() &&
          occur[small].get(idx[small]) <
          occur[ch].get(idx[ch]))
      {
        // Conversion not possible
        poss = false;
        break;
      }
    }
    idx[ch]++;
  }
 
  // Print the answer
  if (poss)
  {
    System.out.print("Yes" + "\n");
  }
  else
  {
    System.out.print("No" + "\n");
  }
}
 
// Driver Code
public static void main(String[] args)
{
  String s, t;
  s = "hdecb";
  t = "cdheb";
  canTransform(s, t);
}
}
 
// This code is contributed by Rajput-Ji

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Python3

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# Python3 program to implement
# the above approach
 
# Function to check if str1 can be
# transformed to t by sorting substrings
def canTransform(s, t):
     
    n = len(s)
 
    # Occur[i] stores the indices
    # of ('a'+i) in string s
    occur = [[] for i in range(26)]
     
    for x in range(n):
        ch = ord(s[x]) - ord('a')
        occur[ch].append(x)
 
    # idx[i] stores the next available
    # index of ('a'+i) in occur[i]
    idx = [0] * (26)
    poss = True
     
    for x in range(n):
        ch = ord(t[x]) - ord('a')
 
        # If this is not available
        # anymore
        if (idx[ch] >= len(occur[ch])):
 
            # Conversion not possible
            poss = False
            break
 
        for small in range(ch):
 
            # If one of the smaller characters
            # is available and occurs before
            if (idx[small] < len(occur[small]) and
                occur[small][idx[small]] <
                occur[ch][idx[ch]]):
 
                # Conversion not possible
                poss = False
                break
             
        idx[ch] += 1
 
    # Print the answer
    if (poss):
        print("Yes")
    else:
        print("No")
 
# Driver Code
if __name__ == '__main__':
 
    s = "hdecb"
    t = "cdheb"
 
    canTransform(s, t)
 
# This code is contributed by mohit kumar 29

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C#

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// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to check if str1
// can be transformed to t by
// sorting subStrings
static void canTransform(String s,
                         String t)
{
  int n = s.Length;
 
  // Occur[i] stores the indices
  // of char ('a'+i) in String s
  List<int> []occur = new List<int>[26];
   
  for(int i = 0; i < occur.Length; i++)
    occur[i] = new List<int>();
   
  for(int x = 0; x < n; x++)
  {
    char ch = (char)(s[x] - 'a');
    occur[ch].Add(x);
  }
 
  // idx[i] stores the next available
  // index of char ('a'+i) in occur[i]
  int []idx = new int[26];
  bool poss = true;
   
  for(int x = 0; x < n; x++)
  {
    char ch = (char)(t[x] - 'a');
 
    // If this char is
    // not available anymore
    if (idx[ch] >= occur[ch].Count)
    {
         
      // Conversion not possible
      poss = false;
      break;
    }
    for(int small = 0; small < ch; small++)
    {
         
      // If one of the smaller characters
      // is available and occurs before
      if (idx[small] < occur[small].Count &&
            occur[small][idx[small]] <
            occur[ch][idx[ch]])
      {
           
        // Conversion not possible
        poss = false;
        break;
      }
    }
    idx[ch]++;
  }
 
  // Print the answer
  if (poss)
  {
    Console.Write("Yes" + "\n");
  }
  else
  {
    Console.Write("No" + "\n");
  }
}
 
// Driver Code
public static void Main(String[] args)
{
  String s, t;
  s = "hdecb";
  t = "cdheb";
   
  canTransform(s, t);
}
}
 
// This code is contributed by Amit Katiyar

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Output: 

Yes








 

Time Complexity: O(N)
Auxiliary Space: O(N)

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