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POJ 1458 Common Subsequence

时间:2014-03-18 05:29:58      阅读:510      评论:0      收藏:0      [点我收藏+]
Common Subsequence
Time Limit: 1000MS   Memory Limit: 10000K
Total Submissions: 35595   Accepted: 14185

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.

Input

The program input is from the std input. Each data set in the input contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct.

Output

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
2
0

-----------------------------------------------------------------------------
状态转移方程:
if(st1[i]==st2[j])
res[i+1][j+1]=res[i][j]+1;
else
res[i+1][j+1]= res[i][j+1]>res[i+1][j] ?res[i][j+1]:res[i+1][j] ;
res[i][j]表示字符串字串st1[0-i],st2[0-j]的公共子序列长度。


#include<stdio.h>
#include<stdlib.h> //最长公共子序列,别的不说了
#include<string.h>
#define MAX 1001    //唯一注意的是数组的大小
#define  Max(x,y)  (x)>(y)?(x):(y)
int main()
{
	char string1[MAX];
	char string2[MAX];
	//char string1a[26];
	//char string1b[26];
	int string[MAX][MAX];
	int max1,max2,i,j;
	
	while(scanf("%s%s",string1,string2)!=EOF)
	{
	memset(string, 0, sizeof(string));
	//gets(string1);
	//gets(string2);
	//memset(c,0,sizeof(string));
	max1=strlen(string1);
	max2=strlen(string2);
	
	
	for(i=1;i<=max1;i++)
	  for(j=1;j<=max2;j++)
	  {
	  	if(string1[i-1]==string2[j-1])
	  	  {
	  	  	string[i][j]=string[i-1][j-1]+1;//关键1
	  	  }
	  	else
	  	    string[i][j] = Max(string[i][j-1], string[i-1][j]);//关键2
	  }
	
	
	printf("%d\n",string[max1][max2]);
   }
	return 0;
} 

POJ 1458 Common Subsequence,布布扣,bubuko.com

POJ 1458 Common Subsequence

原文:http://blog.csdn.net/zzucsliang/article/details/21388517

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