算法：最长子序列1143. Longest Common Subsequence

Posted 2021-10-08 架构师易筋

# 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.

解法：升级为二维表格，动态规划解决

-	a(1)	c(2)	e(3)
a(1)	1 (1, 1)	1 (1, 2)	1
b(2)	1 (2, 1)	1	1
c(3)	1	2	2
d(4)	1	2	2
e (5)	1	2	3

class Solution {
    public int longestCommonSubsequence(String text1, String text2) {
        int rowLen = text1.length();
        int colLen = text2.length();
        char[] chars1 = text1.toCharArray();
        char[] chars2 = text2.toCharArray();
        
        int[][] dp = new int[rowLen + 1][colLen + 1];
        for (int r = 0; r < rowLen; r++) {
            for (int c = 0; c < colLen; c++) {
                if (chars1[r] == chars2[c]) {
                    dp[r + 1][c + 1] = 1 + dp[r][c];
                } else {
                    dp[r + 1][c + 1] = Math.max(dp[r + 1][c], dp[r][c + 1]);
                }
            }
        }
        
        return dp[rowLen][colLen];
    }
}