1143. Longest Common Subsequence

Given two strings text1 and text2, return the length of their longest common subsequence.

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. (eg, “ace” is a subsequence of “abcde” while “aec” is not). A common subsequence of two strings is a subsequence that is common to both strings.

If there is no common subsequence, return 0.

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 <= 1000
• 1 <= text2.length <= 1000
• The input strings consist of lowercase English characters only.

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最长公共子序列问题，直接DP，完整代码如下：

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

本代码提交AC，用时92MS。