HDU 1159 Common Subsequence （最长公共子序列）

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Common Subsequence

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 40565    Accepted Submission(s): 18717

Problem Description

A subsequence of a given sequence is the given sequence with some elements (possible none) left out. Given a sequence X = <x1, x2, ..., xm> another sequence Z = <z1, z2, ..., zk> is a subsequence of X if there exists a strictly increasing sequence <i1, i2, ..., ik> of indices of X such that for all j = 1,2,...,k, xij = zj. For example, Z = <a, b, f, c> is a subsequence of X = <a, b, c, f, b, c> with index sequence <1, 2, 4, 6>. Given two sequences X and Y the problem is to find the length of the maximum-length common subsequence of X and Y. 
The program input is from a text file. Each data set in the file contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct. For each set of data the program prints on the standard output the length of the maximum-length common subsequence from the beginning of a separate line. 

 

Sample Input

abcfbc abfcabprogramming contest abcd mnp

 

Sample Output

420

题目要求求两个字符串的最长公共子序列。用dp[i][j]表示第一个串中前i个字符跟第二个串中前j个字符的相等数目。裸的模板题。

代码实现：

#include<iostream>#include<algorithm>#include<cstring>#define ll long longusing namespace std;const int maxn=1005;int dp[maxn][maxn];/*最长公共子串，dp[i][j]表示第一个串中前i个字符跟第二个串中前j个字符的相等数目*/ int main(){char s1[maxn],s2[maxn];int len1,len2,i,j,k;while(cin>>s1>>s2){len1=strlen(s1);len2=strlen(s2);memset(dp,0,sizeof(dp));for(i=1;i<=len1;i++){for(j=1;j<=len2;j++){if(s1[i-1]==s2[j-1])dp[i][j]=dp[i-1][j-1]+1;elsedp[i][j]=max(dp[i-1][j],dp[i][j-1]);}}cout<<dp[len1][len2]<<endl;}return 0;}