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Longest Common Subsequence

Given two strings, find the longest comment subsequence (LCS).

Your code should return the length of LCS.

样例
For "ABCD" and "EDCA", the LCS is "A" (or D or C), return 1

For "ABCD" and "EACB", the LCS is "AC", return 2

说明
What‘s the definition of Longest Common Subsequence?

* The longest common subsequence (LCS) problem is to find the longest subsequence common to all sequences in a set of sequences (often just two). (Note that a subsequence is different from a substring, for the terms of the former need not be consecutive terms of the original sequence.) It is a classic computer science problem, the basis of file comparison programs such as diff, and has applications in bioinformatics.

* https://en.wikipedia.org/wiki/Longest_common_subsequence_problem

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SOLUTION 1:

DP. 

1. D[i][j] 定义为s1, s2的前i,j个字符串的最长common subsequence. 

2. D[i][j] 当char i == char j， D[i - 1][j - 1] + 1

    当char i != char j, D[i ][j - 1], D[i - 1][j] 里取一个大的（因为最后一个不相同，所以有可能s1的最后一个字符会出现在s2的前部分里，反之亦然。

 1 public class Solution {
 2     /**
 3      * @param A, B: Two strings.
 4      * @return: The length of longest common subsequence of A and B.
 5      */
 6     public int longestCommonSubsequence(String A, String B) {
 7         // write your code here
 8         if (A == null || B == null) {
 9             return 0;
10         }
11         
12         int lenA = A.length();
13         int lenB = B.length();
14         int[][] D = new int[lenA + 1][lenB + 1];
15         
16         for (int i = 0; i <= lenA; i++) {
17             for (int j = 0; j <= lenB; j++) {
18                 if (i == 0 || j == 0) {
19                     D[i][j] = 0;
20                 } else {
21                     if (A.charAt(i - 1) == B.charAt(j - 1)) {
22                         D[i][j] = D[i - 1][j - 1] + 1;
23                     } else {
24                         D[i][j] = Math.max(D[i - 1][j], D[i][j - 1]);
25                     }
26                 }
27             }
28         }
29         
30         return D[lenA][lenB];
31     }
32 }

View Code

 https://github.com/yuzhangcmu/LeetCode_algorithm/blob/master/lintcode/dp/longestCommonSubsequence.java

Lintcode:Longest Common Subsequence 解题报告

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原文地址：http://www.cnblogs.com/yuzhangcmu/p/4199531.html