LongestCommonSubsequence.java

/**
Given two strings text1 and text2, return the length of their longest common subsequence. If there is no common subsequence, return 0.
A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.
For example, "ace" is a subsequence of "abcde".
A common subsequence of two strings is a subsequence that is common to both strings.
 
Example 1:
Input: text1 = "abcde", text2 = "ace" 
Output: 3  
Explanation: The longest common subsequence is "ace" and its length is 3.
**/

class Solution {
    public int longestCommonSubsequence(String text1, String text2) {
        int m = text1.length(), n = text2.length();
        int mat[][] = new int[m+1][n+1];
        for(int i = 0 ;  i<=m;i++)
            mat[i][0] = 0;
        for(int i = 0 ;  i<=n;i++)
            mat[0][i] = 0;
        for(int i = 1 ;  i<=m;i++) {
            for(int j = 1 ;  j<=n;j++) {
                if(text1.charAt(i-1) == text2.charAt(j-1))
                    mat[i][j] = mat[i-1][j-1] + 1;
                else {
                    mat[i][j] = Math.max(mat[i-1][j],mat[i][j-1]);
                }
            }
        }
        return mat[m][n];
    }
}