Common Subsequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 18332 Accepted Submission(s): 7742

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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//78MS    4180K    653 B    C++    //dp，最长公共子序列  #include
     
      #include
      
       int dp[1005][1005];int Max(int a,int b){    return a>b?a:b;}int main(void){    char a[1005],b[1005];    while(scanf("%s %s",a,b)!=EOF)    {        int lena=strlen(a);        int lenb=strlen(b);        memset(dp,0,sizeof(dp));        int maxn=0;        for(int i=1;i<=lena;i++)            for(int j=1;j<=lenb;j++){                if(a[i-1]==b[j-1]) dp[i][j]=dp[i-1][j-1]+1; //状态转移方程                 else dp[i][j]=Max(dp[i][j-1],dp[i-1][j]);                if(dp[i][j]>maxn) maxn=dp[i][j];            }        printf("%d\n",maxn);    }    return 0;}