Lintcode:Longest Common Subsequence 解题报告

Longest Common Subsequence

原题链接：http://lintcode.com/zh-cn/problem/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。

 public class Solution {
     /**
      * @param A, B: Two strings.
      * @return: The length of longest common subsequence of A and B.
      */
     public int longestCommonSubsequence(String A, String B) {
         // write your code here
         if (A == null || B == null) {
             return 0;
         }

         int lenA = A.length();
         int lenB = B.length();
         int[][] D = new int[lenA + 1][lenB + 1];

         for (int i = 0; i <= lenA; i++) {
             for (int j = 0; j <= lenB; j++) {
                 if (i == 0 || j == 0) {
                     D[i][j] = 0;
                 } else {
                     if (A.charAt(i - 1) == B.charAt(j - 1)) {
                         D[i][j] = D[i - 1][j - 1] + 1;
                     } else {
                         D[i][j] = Math.max(D[i - 1][j], D[i][j - 1]);
                     }
                 }
             }
         }

         return D[lenA][lenB];
     }
 }

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