Longest Common Subsequence

2024-05-05 23:18:10

1、题目描述：

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.

Constraints:

1 <= text1.length, text2.length <= 1000
text1 and text2 consist of only lowercase English characters.

2、解答：

求最长公共子序列LCS的长度，考虑动态规划。有如下的动态规划策略：

如果a[i] == b[j]，那么对于LCS(i, j ) = 1 + LCS(i - 1, j - 1);
如果a[i] != b[j]，那么LCS(i, j) = max(LCS(i, j - 1), LCS(i - 1, j))。

其中LCS(i, j)代表序列a的前i部分和序列b的前j部分的最长公共子序列的长度。

代码如下：

class Solution {
public:int longestCommonSubsequence(string &a, string& b) {short m[1001][1001];for (auto i = 0; i < a.size(); ++i) for (auto j = 0; j < b.size(); ++j) {m[i+1][j+1] = a[i] == b[j] ? m[i][j] + 1 : max(m[i+1][j], m[i][j+1]);}return m[a.size()][b.size()];    }
};

3、题目链接及相关题目

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