HDU-1159 Common Subsequence（最长公共子序列附带输出序列代码）

HDU-1159 Common Subsequence（动态规划）

 

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, x ij = 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

 

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int main()
{ 
    char a[1000],b[1000];
   int dp[1000][1000];          //dp[i][j]表示一条长度为i,另一条长度为j,且以a[i],b[j]为结尾的的
                                //最长公共子序列                
 while(scanf("%s%s",a,b)!=EOF)
 {
     memset(dp,0,sizeof(dp));
   int la=strlen(a);
   int lb=strlen(b);
     for(int i=1;i<=la;i++)  
     for(int j=1;j<=lb;j++)
            {
             if(a[i-1]==b[j-1])            //a是从0开始，而dp是从1开始 
             dp[i][j]=dp[i-1][j-1]+1;      //dp表示最大的公共子串 
             else
             dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
               }
 printf("%d\n",dp[la][lb]);
}
 return 0;
} 

 

输出序列代码

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
char a[1000],b[1000];
int dp[1000][1000],flag[1000][1000];
void LCS()
{
        int i,j;
        int len1=strlen(a);
        int len2=strlen(b);
        for(i=1;i<=len1;i++)
        for(j=1;j<=len2;j++)
        {
            if(a[i-1]==b[j-1])  {dp[i][j]=dp[i-1][j-1]+1,flag[i][j]=0;}
            else
            {
                if(dp[i-1][j]>=dp[i][j-1])     {dp[i][j]=dp[i-1][j],  flag[i][j]=1;}
                else if(dp[i-1][j]<dp[i][j-1]) {dp[i][j]=dp[i][j-1],  flag[i][j]=-1;}
            }
        }
}
void PrintLCS(int i,int j)
{
    if(i==0||j==0) return ;
    if(flag[i][j]==0)
    {
        PrintLCS(i-1,j-1);   //因为有先后顺序。。。
        printf("%c",a[i-1]);
    }
    else if(flag[i][j]==1)
    PrintLCS(i-1,j);
    else if(flag[i][j]==-1)
    PrintLCS(i,j-1);
}
int main()
{

    while(scanf("%s%s",a,b)!=EOF)
    {
        memset(dp,0,sizeof(dp));
        memset(flag,0,sizeof(flag));
        LCS();
        PrintLCS(strlen(a),strlen(b));
    }
    return 0;
}