Link to Question

MEDIUM

Longest Common Subsequence

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.

Example

Input:

text1 = "abcde", text2 = "ace"

Output:

3

Explanation: The longest common subsequence is "ace" and its length is 3.

---

Constraints

• 1 ≤ text1.length, text2.length ≤ 1000
• text1 and text2 consist only of lowercase English characters.

---

Solution: Dynamic Programming

• Time Complexity: O(mn)
• Space Complexity: O(mn)

C++

class Solution {
public:
    int longestCommonSubsequence(string text1, string text2) {
        int m = text1.size(), n = text2.size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (text1[i - 1] == text2[j - 1])
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                else
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
            }
        }
        return dp[m][n];
    }
};