Longest Common Subsequence

Problem Statement - link #

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.

Examples #

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.

Solutions #

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

      for(int i=1; i<m+1; i++)
        for(int j=1; j<n+1; 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];
      
    }
};