Longest Common Subsequence

Problem

Given two strings text1 and text2, return the length of their longest common subsequence.

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. (eg, “ace” is a subsequence of “abcde” while “aec” is not). A common subsequence of two strings is a subsequence that is common to both strings.

If there is no common subsequence, return 0.

Example 1

Input: text1 = "abcde", text2 = "ace" 
Output: 3  
Explanation: The longest common subsequence is "ace" and its length is 3.

Example 2

Input: text1 = "abc", text2 = "abc"
Output: 3
Explanation: The longest common subsequence is "abc" and its length is 3.

Example 3

Input: text1 = "abc", text2 = "def"
Output: 0
Explanation: There is no such common subsequence, so the result is 0.

Constraints

• 1 <= text1.length <= 1000
• 1 <= text2.length <= 1000
• The input strings consist of lowercase English characters only.

Optimal Solution

Complexity

• Time: O(nm)
• Space: O(nm)

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