HD 1159 Common Subsequence （最长公共子序列）

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#dp #数据结构 #最长公共子序列

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本文介绍了一个经典的计算机科学问题——寻找两个字符串之间的最长公共子序列，并提供了一种使用动态规划解决该问题的方法。通过构造一个二维数组，程序能够有效地找出给定字符串的最长公共子序列长度。

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题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1159

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

程序原理如下状态方程：

#include<stdio.h>
#include<string.h>
#include<iostream>
using namespace std;

int smax(int x,int y){
	return x >=y ? x : y;
}

int maxstr[20001][20001];
char str1[2000],str2[2000];

int main(){
	int len1,len2;
	while(scanf("%s%s",&str1, &str2)!=EOF){
		len1=strlen(str1);
		len2=strlen(str2);
		for(int i=0; i<=len1; ++i){
			maxstr[i][0]=0;//初始化边界，过滤掉0的情况
		}
		for(int i=0; i<=len2; ++i){
			maxstr[0][i]=0;
		}
		//填充矩阵
		for(int i=1; i<=len1; ++i){
			for(int j=1; j<=len2; ++j){
				if(str1[i-1]==str2[j-1])//相等的情况
					maxstr[i][j]=maxstr[i-1][j-1]+1;
				else if(maxstr[i-1][j] >= maxstr[i][j-1]){//比较“左边”和“上边“，根据其max来填充
					//maxstr[i][j]=smax(maxstr[i-1][j],maxstr[i][j-1]);
					maxstr[i][j]=maxstr[i-1][j];
				}else{
					maxstr[i][j]=maxstr[i][j-1];
				}
			
			}
		}
		printf("%d\n",maxstr[len1][len2]);
	}
	return 0;
}

资料链接：http://www.cnblogs.com/huangxincheng/archive/2012/11/11/2764625.html