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:3Explanation:The longest common subsequence is "ace" and its length is 3.

**Example 2:**

Input:text1 = "abc", text2 = "abc"Output:3Explanation:The longest common subsequence is "abc" and its length is 3.

**Example 3:**

Input:text1 = "abc", text2 = "def"Output:0Explanation: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.

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。