hdu 1159 最长公共子序列

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最新推荐文章于 2024-08-22 20:10:34 发布

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分类专栏：动态规划经典（最大子段和）动态规划经典（最长公共子序列）

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本文介绍了如何使用动态规划算法解决最长公共子序列问题，并提供了具体实现代码。

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1、http://acm.hdu.edu.cn/showproblem.php?pid=1159

2、题目大意：

给定两个字符串，求公共子串的大小，注意不是；连续的子串，相当于将来那个字符串去掉某些字符后剩余的子串相同的最大长度dp[i][j]表示的是a串中前i个字符中和b串中前j个字符中最长公共子序列的长度

3、题目：

Common Subsequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 15205 Accepted Submission(s): 6305

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 abfcab
programming contest 
abcd mnp

Sample Output

4、代码：

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
char a[1000];
char b[1000];
int dp[1000][1000];
int main()
{
	int i,j;
	while(scanf("%s%s",a,b)!=EOF)//注意如果写成while（1）则会超时，循环出不去
	{


		int len1=strlen(a);
		int len2=strlen(b);
		int len=len1>len2?len1:len2;
		for(i=0;i<=len;i++)
		{
			dp[i][0]=0;
			dp[0][i]=0;
		}
		for(i=1;i<=len1;i++)
		{
			for(j=1;j<=len2;j++)
			{
			    if(a[i-1]==b[j-1])//ij指的是
前ij个字符中，要判断第i个那么下标则是i-1

			    dp[i][j]=dp[i-1][j-1]+1;
			    else
				dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
			}
		}
		printf("%d\n",dp[len1][len2]);
		 memset(a,0,sizeof(a));
	    memset(b,0,sizeof(b));
	}
	return 0;

}
/*
abcfbc abfcab
programming contest
abcd mnp
*/