Given two string **X** and **Y**. The task is to find the length of longest subsequence of string X which is substring in sequence Y.

Examples:

Input : X = "ABCD", Y = "BACDBDCD" Output : 3 "ACD" is longest subsequence of X which is substring of Y. Input : X = "A", Y = "A" Output : 1

**Method 1 (Brute Force):**

Use brute force to find all the subsequence of X and for each subsequence check whether it is substring of Y or not. If it is substring of Y, maintain a maximum length varible and compare length with it.

**Method 2: (Dynamic Programming):**

Let n be length of X and m be length of Y. Create a 2D array ‘dp[][]’ of m + 1 rows and n + 1 columns. Value **dp[i][j]** is maximum length of subsequence of X[0….j] which is substring of Y[0….i]. Now for each cell of dp[][] fill value as :

for (i = 1 to m) for (j = 1 to n) if (x[i-1] == y[j - 1]) dp[i][j] = dp[i-1][j-1] + 1; else dp[i][j] = dp[i][j-1];

And finally, the length of the longest subsequence of x which is substring of y is max(dp[i][n]) where 1 <= i <= m.

Below is implementation this approach:

## C/C++

// C++ program to find maximum length of // subsequence of a string X such it is // substring in another string Y. #include <bits/stdc++.h> #define MAX 1000 using namespace std; // Return the maximum size of substring of // X which is substring in Y. int maxSubsequenceSubstring(char x[], char y[], int n, int m) { int dp[MAX][MAX]; // Initialize the dp[][] to 0. for (int i = 0; i <= m; i++) for (int j = 0; j <= n; j++) dp[i][j] = 0; // Calculating value for each element. for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { // If alphabet of string X and Y are // equal make dp[i][j] = 1 + dp[i-1][j-1] if (x[j - 1] == y[i - 1]) dp[i][j] = 1 + dp[i - 1][j - 1]; // Else copy the previous value in the // row i.e dp[i-1][j-1] else dp[i][j] = dp[i][j - 1]; } } // Finding the maximum length. int ans = 0; for (int i = 1; i <= m; i++) ans = max(ans, dp[i][n]); return ans; } // Driver Program int main() { char x[] = "ABCD"; char y[] = "BACDBDCD"; int n = strlen(x), m = strlen(y); cout << maxSubsequenceSubstring(x, y, n, m); return 0; }

## Java

// Java program to find maximum length of // subsequence of a string X such it is // substring in another string Y. public class GFG { static final int MAX = 1000; // Return the maximum size of substring of // X which is substring in Y. static int maxSubsequenceSubstring(char x[], char y[], int n, int m) { int dp[][] = new int[MAX][MAX]; // Initialize the dp[][] to 0. for (int i = 0; i <= m; i++) for (int j = 0; j <= n; j++) dp[i][j] = 0; // Calculating value for each element. for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { // If alphabet of string X and Y are // equal make dp[i][j] = 1 + dp[i-1][j-1] if (x[j - 1] == y[i - 1]) dp[i][j] = 1 + dp[i - 1][j - 1]; // Else copy the previous value in the // row i.e dp[i-1][j-1] else dp[i][j] = dp[i][j - 1]; } } // Finding the maximum length. int ans = 0; for (int i = 1; i <= m; i++) ans = Math.max(ans, dp[i][n]); return ans; } // Driver Method public static void main(String[] args) { char x[] = "ABCD".toCharArray(); char y[] = "BACDBDCD".toCharArray(); int n = x.length, m = y.length; System.out.println(maxSubsequenceSubstring(x, y, n, m)); } }

Output:

3

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