Check if one string can be converted to other using given operation

Given two strings S and T of same length. The task is to determine whether or not we can build a string A(initially empty) equal to string T by performing the below operations. 

1. Delete the first character of S and add it at the front of A. 
   
2. Delete the first character of S and add it at the back of A. 
   

Examples:

Input: S = “abab” T = “baab” 
Output: YES 
Explanation:
Add ‘a’ at front of A, then A = “a” and S = “bab” 
Add ‘b’ at front of A, then A = “ba” and S = “ab” 
Add ‘a’ at back of A, then A = “baa” and S = “b” 
Add ‘b’ at back of A, then A = “baab” and S = “” 
So we can make string A equal to string T 
Input: S = “geeks” T = “Teeks” 
Output: NO   

Approach: The idea is to use Dynamic Programming to solve this problem. 
There are two possible moves for every character( front move or back move ). So, for each character, we will check if it is possible to add the character in the front or back of the new string. If it’s possible, we will move to the next character. If it’s not possible, then the operation will stop at that point and No will be printed. 

1. Firstly we will make a 2D boolean array dp[][] having rows and columns equal to the length of string S, where dp[i][j] = 1 indicates that all characters of string S from index i to n-1 can be placed in the new string A with j front moves such that it becomes equal to string T. 
   
2. We can traverse string S from the back and for each character update dp[][] in two ways, if we take the (i-1)-th character as a front move or (i-1)-th character as a back move. 
   
3. Finally, we will check if any value at the 1st row is equal to one or not. 

Below is the implementation of the above approach  

C++

// C++ implementation of above
// approach
#include <bits/stdc++.h>
using namespace std;

// Function that prints whether
// is it possible to make a
// string equal to T by
// performing given operations
void twoStringsEquality(string s,
                        string t)
{
    int n = s.length();

    vector<vector<int> > dp(
        n, vector<int>(
               n + 1, 0));

    // Base case, if we put the
    // last character at front
    // of A
    if (s[n - 1] == t[0])
        dp[n - 1][1] = 1;

    // Base case, if we put the
    // last character at back
    // of A
    if (s[n - 1] == t[n - 1])
        dp[n - 1][0] = 1;

    for (int i = n - 1; i > 0; i--) {
        for (int j = 0; j <= n - i; j++) {

            // Condition if current
            // sequence is matchable
            if (dp[i][j]) {
                // Condition for front
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[j])
                    dp[i - 1][j + 1] = 1;

                // Condition for back
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[i + j - 1])
                    dp[i - 1][j] = 1;
            }
        }
    }

    bool ans = false;

    for (int i = 0; i <= n; i++) {
        // Condition if it is
        // possible to make
        // string A equal to
        // string T
        if (dp[0][i] == 1) {
            ans = true;
            break;
        }
    }

    // Print final
    // answer
    if (ans == true)
        cout << "Yes"
             << "\n";
    else
        cout << "No"
             << "\n";
}

// Driver Code
int main()
{
    string S = "abab";

    string T = "baab";

    twoStringsEquality(S, T);

    return 0;
}

Java

// Java implementation of above
// approach
import java.util.*;

class GFG{

// Function that prints whether
// is it possible to make a
// String equal to T by
// performing given operations
static void twoStringsEquality(String s,
                               String t)
{
    int n = s.length();

    int [][]dp = new int[n][n + 1];

    // Base case, if we put the
    // last character at front
    // of A
    if (s.charAt(n - 1) == t.charAt(0))
        dp[n - 1][1] = 1;

    // Base case, if we put the
    // last character at back
    // of A
    if (s.charAt(n - 1) == t.charAt(n - 1))
        dp[n - 1][0] = 1;

    for(int i = n - 1; i > 0; i--)
    {
       for(int j = 0; j <= n - i; j++)
       {

          // Condition if current
          // sequence is matchable
          if (dp[i][j] > 0)
          {

              // Condition for front
              // move to (i - 1)th
              // character
              if (s.charAt(i - 1) ==
                  t.charAt(j))
                  dp[i - 1][j + 1] = 1;

              // Condition for back
              // move to (i - 1)th
              // character
              if (s.charAt(i - 1) ==
                  t.charAt(i + j -1))
                  dp[i - 1][j] = 1;
          }
       }
    }

    boolean ans = false;

    for(int i = 0; i <= n; i++)
    {

       // Condition if it is possible
       // to make String A equal to
       // String T
       if (dp[0][i] == 1)
       {
           ans = true;
           break;
       }
    }

    // Print final answer
    if (ans == true)
        System.out.print("Yes" + "\n");
    else
        System.out.print("No" + "\n");
}

// Driver Code
public static void main(String[] args)
{
    String S = "abab";
    String T = "baab";

    twoStringsEquality(S, T);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 implementation of above
# approach

# Function that prints whether
# is it possible to make a
# equal to T by
# performing given operations
def twoStringsEquality(s, t):
    n = len(s)

    dp = [[0 for i in range(n + 1)]
             for i in range(n)]

    # Base case, if we put the
    # last character at front
    # of A
    if (s[n - 1] == t[0]):
        dp[n - 1][1] = 1

    # Base case, if we put the
    # last character at back
    # of A
    if (s[n - 1] == t[n - 1]):
        dp[n - 1][0] = 1

    for i in range(n - 1, -1, -1):
        for j in range(n - i + 1):

            # Condition if current
            # sequence is matchable
            if (dp[i][j]):

                # Condition for front
                # move to (i - 1)th
                # character
                if (s[i - 1] == t[j]):
                    dp[i - 1][j + 1] = 1

                # Condition for back
                # move to (i - 1)th
                # character
                if (s[i - 1] == t[i + j - 1]):
                    dp[i - 1][j] = 1

    ans = False

    for i in range(n + 1):

        # Condition if it is
        # possible to make
        # A equal to T
        if (dp[0][i] == 1):
            ans = True
            break

    # Print final answer
    if (ans == True):
        print("Yes")
    else:
        print("No")

# Driver Code
if __name__ == '__main__':

    S = "abab"
    T = "baab"

    twoStringsEquality(S, T)

# This code is contributed by mohit kumar 29

C#

// C# implementation of above
// approach
using System;
class GFG{

// Function that prints whether
// is it possible to make a
// String equal to T by
// performing given operations
static void twoStringsEquality(String s,
                               String t)
{
    int n = s.Length;

    int [,]dp = new int[n, n + 1];

    // Base case, if we put the
    // last character at front
    // of A
    if (s[n - 1] == t[0])
        dp[n - 1, 1] = 1;

    // Base case, if we put the
    // last character at back
    // of A
    if (s[n - 1] == t[n - 1])
        dp[n - 1, 0] = 1;

    for(int i = n - 1; i > 0; i--)
    {
        for(int j = 0; j <= n - i; j++)
        {

            // Condition if current
            // sequence is matchable
            if (dp[i, j] > 0)
            {

                // Condition for front
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[j])
                    dp[i - 1, j + 1] = 1;

                // Condition for back
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[i + j - 1])
                    dp[i - 1, j] = 1;
            }
        }
    }

    bool ans = false;

    for(int i = 0; i <= n; i++)
    {

        // Condition if it is possible
        // to make String A equal to
        // String T
        if (dp[0, i] == 1)
        {
            ans = true;
            break;
        }
    }

    // Print readonly answer
    if (ans == true)
        Console.Write("Yes" + "\n");
    else
        Console.Write("No" + "\n");
}

// Driver Code
public static void Main(String[] args)
{
    String S = "abab";
    String T = "baab";

    twoStringsEquality(S, T);
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript implementation of above
// approach

// Function that prints whether
// is it possible to make a
// string equal to T by
// performing given operations
function twoStringsEquality(s, t)
{
    var n = s.length;

    var dp = Array.from(Array(n), ()=>Array(n+1).fill(0));

    // Base case, if we put the
    // last character at front
    // of A
    if (s[n - 1] == t[0])
        dp[n - 1][1] = 1;

    // Base case, if we put the
    // last character at back
    // of A
    if (s[n - 1] == t[n - 1])
        dp[n - 1][0] = 1;

    for (var i = n - 1; i > 0; i--) {
        for (var j = 0; j <= n - i; j++) {

            // Condition if current
            // sequence is matchable
            if (dp[i][j]) {
                // Condition for front
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[j])
                    dp[i - 1][j + 1] = 1;

                // Condition for back
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[i + j - 1])
                    dp[i - 1][j] = 1;
            }
        }
    }

    var ans = false;

    for (var i = 0; i <= n; i++) {
        // Condition if it is
        // possible to make
        // string A equal to
        // string T
        if (dp[0][i] == 1) {
            ans = true;
            break;
        }
    }

    // Print final
    // answer
    if (ans == true)
        document.write( "Yes" + "<br>");
    else
        document.write( "No" + "<br>");
}

// Driver Code
var S = "abab";
var T = "baab";
twoStringsEquality(S, T);

// This code is contributed by rutvik_56.
</script>

Output

Yes

Time Complexity: O(N²)

Auxiliary Space: O(N²)

Efficient approach : Space optimization

In previous approach the current value dp[i][j] is only depend upon the current and previous row values of DP. So to optimize the space complexity we use a single 1D array to store the computations.

Implementation steps:

• Create a 1D vector dp of size large+1.
• Set a base case by initializing the values of DP .
• Now iterate over subproblems by the help of nested loop and get the current value from previous computations.
• Now Create a temporary 1d vector temp used to store the current values from previous computations.
• After every iteration assign the value of temp to dp for further iteration.
• Initialize a variable ans to store the final answer and update it by iterating through the Dp.
• At last return and print the final answer stored in ans .

Implementation: 

C++

// C++ implementation of above
// approach
#include <bits/stdc++.h>
using namespace std;

// Function that prints whether
// is it possible to make a
// string equal to T by
// performing given operations
void twoStringsEquality(string s,
                        string t)
{
    int n = s.length();

    vector<int> dp(n + 1, 0);

    // Base case, if we put the
    // last character at front
    // of A
    if (s[n - 1] == t[0])
        dp[1] = 1;

    // Base case, if we put the
    // last character at back
    // of A
    if (s[n - 1] == t[n - 1])
        dp[0] = 1;

    for (int i = n - 1; i > 0; i--) {
        vector<int> temp(n + 1, 0);
        for (int j = 0; j <= n - i; j++) {

            // Condition if current
            // sequence is matchable
            if (dp[j]) {
                // Condition for front
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[j])
                    temp[j + 1] = 1;

                // Condition for back
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[i + j - 1])
                    temp[j] = 1;
            }
        }
        dp = temp;
    }

    bool ans = false;

    for (int i = 0; i <= n; i++) {
        // Condition if it is
        // possible to make
        // string A equal to
        // string T
        if (dp[i] == 1) {
            ans = true;
            break;
        }
    }

    // Print final
    // answer
    if (ans == true)
        cout << "Yes"
            << "\n";
    else
        cout << "No"
            << "\n";
}

// Driver Code
int main()
{
    string S = "abab";

    string T = "baab";

    twoStringsEquality(S, T);

    return 0;
}

Java

import java.util.*;

class Main
{

    // Function that prints whether
    // is it possible to make a
    // string equal to T by
    // performing given operations
    static void twoStringsEquality(String s, String t) {
        int n = s.length();

        List<Integer> dp = new ArrayList<>(Collections.nCopies(n + 1, 0));

        // Base case, if we put the
        // last character at front
        // of A
        if (s.charAt(n - 1) == t.charAt(0))
            dp.set(1, 1);

        // Base case, if we put the
        // last character at back
        // of A
        if (s.charAt(n - 1) == t.charAt(n - 1))
            dp.set(0, 1);

        for (int i = n - 1; i > 0; i--) {
            List<Integer> temp = new ArrayList<>(Collections.nCopies(n + 1, 0));
            for (int j = 0; j <= n - i; j++) {

                // Condition if current
                // sequence is matchable
                if (dp.get(j) == 1) {
                    // Condition for front
                    // move to (i - 1)th
                    // character
                    if (s.charAt(i - 1) == t.charAt(j))
                        temp.set(j + 1, 1);

                    // Condition for back
                    // move to (i - 1)th
                    // character
                    if (s.charAt(i - 1) == t.charAt(i + j - 1))
                        temp.set(j, 1);
                }
            }
            dp = temp;
        }

        boolean ans = false;

        for (int i = 0; i <= n; i++) {
            // Condition if it is
            // possible to make
            // string A equal to
            // string T
            if (dp.get(i) == 1) {
                ans = true;
                break;
            }
        }

        // Print final
        // answer
        if (ans == true)
            System.out.println("Yes");
        else
            System.out.println("No");
    }

    // Driver Code
    public static void main(String[] args) {
        String S = "abab";

        String T = "baab";

        twoStringsEquality(S, T);
    }
}

Python3

# Function that prints whether
# is it possible to make a
# string equal to T by
# performing given operations
def twoStringsEquality(s, t):
    n = len(s)

    dp = [0] * (n + 1)

    # Base case, if we put the
    # last character at front
    # of A
    if s[n - 1] == t[0]:
        dp[1] = 1

    # Base case, if we put the
    # last character at back
    # of A
    if s[n - 1] == t[n - 1]:
        dp[0] = 1

    for i in range(n - 1, 0, -1):
        temp = [0] * (n + 1)
        for j in range(0, n - i + 1):

            # Condition if current
            # sequence is matchable
            if dp[j]:
                # Condition for front
                # move to (i - 1)th
                # character
                if s[i - 1] == t[j]:
                    temp[j + 1] = 1

                # Condition for back
                # move to (i - 1)th
                # character
                if s[i - 1] == t[i + j - 1]:
                    temp[j] = 1
        dp = temp

    ans = False

    for i in range(0, n + 1):
        # Condition if it is
        # possible to make
        # string A equal to
        # string T
        if dp[i] == 1:
            ans = True
            break

    # Print final
    # answer
    if ans:
        print("Yes")
    else:
        print("No")

# Driver Code
if __name__ == "__main__":
    S = "abab"
    T = "baab"
    twoStringsEquality(S, T)

C#

using System;
using System.Collections.Generic;

public class GFG {
  // Function that prints whether
// is it possible to make a
// string equal to T by
// performing given operations
public static void TwoStringsEquality(string s, string t) {
    int n = s.Length;

    List<int> dp = new List<int>(new int[n + 1]);

    // Base case, if we put the
    // last character at front
    // of A
    if (s[n - 1] == t[0])
        dp[1] = 1;

    // Base case, if we put the
    // last character at back
    // of A
    if (s[n - 1] == t[n - 1])
        dp[0] = 1;

    for (int i = n - 1; i > 0; i--) {
        List<int> temp = new List<int>(new int[n + 1]);
        for (int j = 0; j <= n - i; j++) {

            // Condition if current
            // sequence is matchable
            if (dp[j] == 1) {
                // Condition for front
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[j])
                    temp[j + 1] = 1;

                // Condition for back
                // move to (i - 1)th
                // character
                if (s[i - 1] == t[i + j - 1])
                    temp[j] = 1;
            }
        }
        dp = temp;
    }

    bool ans = false;

    for (int i = 0; i <= n; i++) {
        // Condition if it is
        // possible to make
        // string A equal to
        // string T
        if (dp[i] == 1) {
            ans = true;
            break;
        }
    }

    // Print final
    // answer
    if (ans == true)
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}

// Driver Code
public static void Main() {
    string S = "abab";

    string T = "baab";

    TwoStringsEquality(S, T);
}

}

Javascript

// Function that prints whether
// it is possible to make a
// string equal to T by
// performing given operations
function twoStringsEquality(s, t) {
    const n = s.length;

    let dp = new Array(n + 1).fill(0);

    // Base case, if we put the
    // last character at front
    // of A
    if (s[n - 1] === t[0]) {
        dp[1] = 1;
    }

    // Base case, if we put the
    // last character at back
    // of A
    if (s[n - 1] === t[n - 1]) {
        dp[0] = 1;
    }

    for (let i = n - 1; i > 0; i--) {
        const temp = new Array(n + 1).fill(0);
        for (let j = 0; j <= n - i; j++) {

            // Condition if current
            // sequence is matchable
            if (dp[j]) {
                // Condition for front
                // move to (i - 1)th
                // character
                if (s[i - 1] === t[j]) {
                    temp[j + 1] = 1;
                }

                // Condition for back
                // move to (i - 1)th
                // character
                if (s[i - 1] === t[i + j - 1]) {
                    temp[j] = 1;
                }
            }
        }
        dp = temp;
    }

    let ans = false;

    for (let i = 0; i <= n; i++) {
        // Condition if it is
        // possible to make
        // string A equal to
        // string T
        if (dp[i] === 1) {
            ans = true;
            break;
        }
    }

    // Print final
    // answer
    if (ans) {
        console.log("Yes");
    } else {
        console.log("No");
    }
}

// Driver Code
const S = "abab";
const T = "baab";
twoStringsEquality(S, T);

// This code is contributed by Dwaipayan Bandyopadhyay

Output:

Yes

Time Complexity: O(N^2)

Auxiliary Space: O(N)