hdoj-1159-Common Subsequence【动态规划求最长公共子序列】

Common Subsequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 28152 Accepted Submission(s): 12556

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
2
0
  

Source

Southeastern Europe 2003

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#include<stdio.h> 
#include<string.h>
#include<algorithm>
using namespace std;
int lcs[1000][1000];
char s1[1001],s2[1001];
int len1,len2;
void f(){
	lcs[0][0]=s1[0]==s2[0]?1:0;
	for(int i=1;i<len1;++i){
		if(lcs[i-1][0]==0) 
		    lcs[i][0]=s1[i]==s2[0]?1:0;
		else  
		    lcs[i][0]=1;
	}
	for(int i=1;i<len2;++i){
		if(lcs[0][i-1]==0)
		    lcs[0][i]=s1[0]==s2[i]?1:0;
		else
		    lcs[0][i]=1;
	}
}
int main(){
	while(~scanf("%s%s",s1,s2)){
		int i,j;
		len1=strlen(s1),len2=strlen(s2);
		memset(lcs,0,sizeof(lcs));
		f();
        for(i=1;i<len1;++i){
			for(j=1;j<len2;++j){
				if(s1[i]==s2[j]) lcs[i][j]=lcs[i-1][j-1]+1;
				else lcs[i][j]=max(lcs[i-1][j],lcs[i][j-1]);
			}
		}
		printf("%d\n",lcs[len1-1][len2-1]);
	}
	return 0;
}

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
char s1[1000],s2[1000];
int c[1001][1001];
int main(){
	while(~scanf("%s%s",s1,s2)){
		int len1=strlen(s1),len2=strlen(s2);
		memset(c,0,sizeof(c));
		for(int i=0;i<len1;++i){
			for(int j=0;j<len2;++j){
				if(s1[i]==s2[j]){
					c[i+1][j+1]=c[i][j]+1;  //技巧：i+1，j+1
				}
				else c[i+1][j+1]=max(c[i][j+1],c[i+1][j]);
			}
		}
		printf("%d\n",c[len1][len2]);
	}
	return 0;
}