LeetCode 1143. Longest Common Subsequence

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.

	class Solution {
	public:
	int longestCommonSubsequence(string text1, string text2) {
	// state var:
	// i: text1 index, j: text2 index
	// function:
	// dp(i, j): LCS of text1[0:i] text2[0:j] -> dp(len(t1), len(t2))
	// relation:
	// dp(i, j) = dp[i-1][j-1] + 1 (if text1[i] == text[j]) or max(dp[i-1][j], d[i][j-1])
	// base:
	// dp[0][x], dp[x][0] = 0
	// vars
	int n = text1.size();
	int m = text2.size();
	// memo
	vector<vector<int>> dp(n+1, vector<int>(m+1));
	// bottom-up
	for(int i = 1; i <= n; i++){
	for(int j = 1; j <= m; j++){
	// relation
	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]);
	}
	}
	// answer
	return dp[n][m];
	}
	};

view raw 1143. Longest Common Subsequence.cpp hosted with ❤ by GitHub