1. Longest Common Subsequence.cpp

/*
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.

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, text2.length <= 1000
text1 and text2 consist of only lowercase English characters.
*/

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