Day1.cpp

/* Question
1143. 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.
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.*/

//Solution

class Solution {
 public:
  int longestCommonSubsequence(string text1, string text2) {
    const int m = text1.length();
    const int n = text2.length();
    // dp[i][j] := the length of LCS(text1[0..i), text2[0..j))
    vector<vector<int>> dp(m + 1, vector<int>(n + 1));

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        dp[i + 1][j + 1] = text1[i] == text2[j]
                               ? 1 + dp[i][j]
                               : max(dp[i][j + 1], dp[i + 1][j]);

    return dp[m][n];
  }
};