LeetCode #4 Longest Common Subsequence

Question

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.

动归经典问题，最长公共子序列，注意是子序列而不是子串 

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.

动态规划法

先确定状态（或最优子结构），c(i, j)表示str1中前i个字符和str2中前j个字符中的最长公共子序列的长度

可以以一个例子来写出状态转移方程：

　　当str1[

 

来源：https://www.cnblogs.com/sbj123456789/p/11565809.html