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Longest Common Subsequence

Problem​

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.

Solution Approach​

Expected Time complexity: O(n2)O(n^2)

Click - to see solution code
class Solution {
   public:
    int longestCommonSubsequence(string text1, string text2) {
        int n = text1.size();
        int m = text2.size();

        vector<vector<int>> dp(n + 1, vector<int>(m + 1));
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (text1[i - 1] == text2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                }
                dp[i][j] = max(dp[i][j], dp[i - 1][j]);
                dp[i][j] = max(dp[i][j], dp[i][j - 1]);
            }
        }
        return dp[n][m];
    }
};