Check if it is possible to transform one string to another

Given two strings s1 and s2(all letters in uppercase). Check if it is possible to convert s1 to s2 by performing following operations.

1.  Make some lowercase letters uppercase. 
2. Delete all the lowercase letters. 

Examples:

Input : s1 = daBcd s2 = ABC 
Output : yes
Explanation : daBcd -> dABCd -> ABC  
Convert a and b at index 1 and 3 to 
upper case, delete the rest those are 
lowercase. We get the string s2. 

Input : s1 = argaju    s2 = RAJ
Output : yes 
Explanation : argaju -> aRgAJu -> RAJ  
convert index 1, 3 and 4 to uppercase 
and then delete. All lowercase letters

Input : s1 = ABcd s2= BCD 
Output : NO

Approach: 

Let DP_{i, j} be 1 if it is possible to convert 1st i characters of s1 to j characters of s2, else DP_{i, j}=0. Close observations gives us two conditions to deal with. 
Initially DP_{0, 0}=1, if DP_{i, j}=1 then it is possible to check for next sets using following conditions. 

1. If s1[i] in upper case is equal to s2[j] then it is possible to convert i+1 characters of s1 to j+1 characters of s2, hence DP_{i+1, j+1}=1.
2. If s1[i] is in lower case, then it is possible to delete that element and hence i+1 characters can be converted to j characters of s2. Hence DP_{i+1, j}=1. 

If DP_{n, m}=1, then it is possible to convert s1 to s2 by following conditions. 

Below is the CPP illustration of the above approach.  

C++

// cpp program to check if a string can
// be converted to another string by
// performing operations
#include <bits/stdc++.h>
using namespace std;

// function to check if a string can be
// converted to  another string by
// performing following operations
bool check(string s1, string s2)
{
    // calculates length
    int n = s1.length();
    int m = s2.length();

    bool dp[n + 1][m + 1];
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= m; j++) {
            dp[i][j] = false;
        }
    }
    // mark 1st position as true
    dp[0][0] = true;

    // traverse for all DPi, j
    for (int i = 0; i < s1.length(); i++) {
        for (int j = 0; j <= s2.length(); j++) {

            // if possible for to convert i
            // characters of s1 to j characters
            // of s2
            if (dp[i][j]) {

                // if upper_case(s1[i])==s2[j]
                // is same
                if (j < s2.length() &&
                    (toupper(s1[i]) == s2[j]))
                    dp[i + 1][j + 1] = true;

                // if not upper then deletion is
                // possible
                if (!isupper(s1[i]))
                    dp[i + 1][j] = true;
            }
        }
    }

    return (dp[n][m]);
}

// driver code
int main()
{
    string s1 = "daBcd";
    string s2 = "ABC";

    if (check(s1, s2))
        cout << "YES";
    else
        cout << "NO";

    return 0;
}

Java

// Java program to check if a string can
// be converted to another string by
// performing operations
import java.io.*;

class GFG {

    // function to check if a string can be
    // converted to another string by
    // performing following operations
    static boolean check(String s1, String s2)
    {
        // calculates length
        int n = s1.length();
        int m = s2.length();

        boolean dp[][]=new boolean[n + 1][m + 1];
        for (int i = 0; i <= n; i++)
        {
            for (int j = 0; j <= m; j++)
            {
                dp[i][j] = false;
            }
        }
        // mark 1st position as true
        dp[0][0] = true;

        // traverse for all DPi, j
        for (int i = 0; i < s1.length(); i++)
        {
            for (int j = 0; j <= s2.length(); j++)
            {

                // if possible for to convert i
                // characters of s1 to j characters
                // of s2
                if (dp[i][j]) {

                    // if upper_case(s1[i])==s2[j]
                    // is same
                    if (j < s2.length() &&
                        (Character.toUpperCase(s1.charAt(i)) == s2.charAt(j)))
                        dp[i + 1][j + 1] = true;

                    // if not upper then deletion is
                    // possible
                    if (!Character.isUpperCase(s1.charAt(i)))
                        dp[i + 1][j] = true;
                }
            }
        }

        return (dp[n][m]);
    }

    // driver code
    public static void main(String args[])
    {
        String s1 = "daBcd";
        String s2 = "ABC";

        if (check(s1, s2))
            System.out.println("YES");
        else
            System.out.println("NO");

    }
}

// This code is contributed by Nikita Tiwari.

Python3

# Python3 program to check if a string can
# be converted to another string by
# performing operations


# function to check if a string can be
# converted to another string by
# performing following operations
def check(s1,s2):

    # calculates length
    n = len(s1)
    m = len(s2)
    dp=([[False for i in range(m+1)]
       for i in range(n+1)])

    # mark 1st position as true
    dp[0][0] = True

    # traverse for all DPi, j
    for i in range(len(s1)):
        for j in range(len(s2)+1):

            # if possible for to convert i
            # characters of s1 to j characters
            # of s2
            if (dp[i][j]):

                # if upper_case(s1[i])==s2[j]
                # is same
                if ((j < len(s2) and
                   (s1[i].upper()== s2[j]))):
                    dp[i + 1][j + 1] = True

                # if not upper then deletion is
                # possible
                if (s1[i].isupper()==False):
                    dp[i + 1][j] = True
    return (dp[n][m])

# driver code
if __name__=='__main__':

    s1 = "daBcd"
    s2 = "ABC"
    if (check(s1, s2)):
        print("YES")
    else:
        print("NO")

# this code is contributed by
# sahilshelangia

C#

// C# program to check if a string can
// be converted to another string by
// performing operations
using System;

class GFG
{

// function to check if a string can be
// converted to another string by
// performing following operations
static bool check(string s1, string s2)
{
    // calculates length
    int n = s1.Length;
    int m = s2.Length;

    bool[,] dp = new bool[n + 1, m + 1];
    for (int i = 0; i <= n; i++)
    {
        for (int j = 0; j <= m; j++)
        {
            dp[i, j] = false;
        }
    }

    // mark 1st position as true
    dp[0, 0] = true;

    // traverse for all DPi, j
    for (int i = 0; i < s1.Length; i++)
    {
        for (int j = 0; j <= s2.Length; j++)
        {

            // if possible for to convert i
            // characters of s1 to j characters
            // of s2
            if (dp[i, j])
            {

                // if upper_case(s1[i])==s2[j]
                // is same
                if (j < s2.Length &&
                    (Char.ToUpper(s1[i]) == s2[j]))
                    dp[i + 1, j + 1] = true;

                // if not upper then deletion is
                // possible
                if (!Char.IsUpper(s1[i]))
                    dp[i + 1, j] = true;
            }
        }
    }

    return (dp[n, m]);
}

// Driver Code
public static void Main()
{
    string s1 = "daBcd";
    string s2 = "ABC";

    if (check(s1, s2))
        Console.Write("YES");
    else
        Console.Write("NO");
}
}

// This code is contributed
// by ChitraNayal

Javascript

<script>
// Javascript program to check if a string can
// be converted to another string by
// performing operations


    // function to check if a string can be
    // converted to another string by
    // performing following operations
    function check(s1,s2)
    {
        // calculates length
        let n = s1.length;
        let m = s2.length;

        let dp=new Array(n + 1);
        for (let i = 0; i <= n; i++)
        {
            dp[i]=new Array(m+1);
            for (let j = 0; j <= m; j++)
            {
                dp[i][j] = false;
            }
        }
        // mark 1st position as true
        dp[0][0] = true;

        // traverse for all DPi, j
        for (let i = 0; i < s1.length; i++)
        {
            for (let j = 0; j <= s2.length; j++)
            {


                // if possible for to convert i
                // characters of s1 to j characters
                // of s2
                if (dp[i][j]) {

                    // if upper_case(s1[i])==s2[j]
                    // is same
                    if (j < s2.length &&
                        (s1[i].toUpperCase() == s2[j]))
                        dp[i + 1][j + 1] = true;

                    // if not upper then deletion is
                    // possible

                    if (!(s1[i] == s1[i].toUpperCase()))
                        dp[i + 1][j] = true;
                }
            }
        }

        return (dp[n][m]);
    }

    // driver code
    let s1 = "daBcd";
    let s2 = "ABC";
    if (check(s1, s2))
        document.write("YES");
    else
        document.write("NO");



    // This code is contributed by avanitrachhadiya2155
</script>

Output

YES

Time Complexity: O(N*M) where N and M are the lengths of the strings.
Auxiliary Space: O(N*M)