# Find length of longest subsequence of one string which is substring of another string in C++

C++Server Side ProgrammingProgramming

Suppose, we have two strings X and Y, and we have to find the length of longest subsequence of string X, which is substring in sequence Y. So if X = “ABCD” and Y = “BACDBDCD”, then output will be 3. As “ACD” is the longest sub-sequence of X, which is substring of Y.

Here we will use the dynamic programming approach to solve this problem. So if the length of X is n, and length of Y is m, then create DP array of order (m+1)x(n+1). Value of 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, it will follow like below:

• for i in range 1 to m:
• for j in range 1 to n
• when X[i – 1] is same as Y[j – i], then DP[i, j] := 1 + DP[i – 1, j – 1]
• Otherwise DP[i, j] := 1 + DP[i, j – 1]

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

## Example

Live Demo

#include<iostream>
#define MAX 100
using namespace std;
int maxSubLength(string x, string y) {
int table[MAX][MAX];
int n = x.length();
int m = y.length();
for (int i = 0; i <= m; i++)
for (int j = 0; j <= n; j++)
table[i][j] = 0;
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
if (x[j - 1] == y[i - 1])
table[i][j] = 1 + table[i - 1][j - 1];
else
table[i][j] = table[i][j - 1];
}
}
int ans = 0;
for (int i = 1; i <= m; i++)
ans = max(ans, table[i][n]);
return ans;
}
int main() {
string x = "ABCD";
string y = "BACDBDCD";
cout << "Length of Maximum subsequence substring is: " << maxSubLength(x, y);
}

## Output

Length of Maximum subsequence substring is: 3