Common Subsequence （lcs）【HDU】-1159

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                              Common Subsequence

 （公共子序列）

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         abfcabprogramming    contest abcd           mnp

Sample Output

420

例：

BDCABA    ABCBDAB

       可以看出：

F[i][j]=F[i-1][j-1]+1；（a[i]==b[j]）
F[i][j]=max(F[i-1][j],F[i][j-1])(a[i]!=b[j]);
n由于F(i,j)只和F(i-1,j-1), F(i-1,j)和F(i,j-1)有关, 
而在计算F(i,j)时, 只要选择一个合适的顺序, 就可以保证这三项都已经计算出来了, 
这样就可以计算出F(i,j). 这样一直推到f(len(a),len(b))就得到所要求的解了.

代码：

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;intf[1005][1005];int main(){char a[1005],b[1005];int i,j,le1,le2;while(scanf("%s%s",a,b)!=EOF){le1=strlen(a);le2=strlen(b);for(i=0;i<=le1;i++)        f[i][0]=0;for(i=0;i<=le2;i++)f[0][i]=0;for(i=1;i<=le1;i++){for(j=1;j<=le2;j++){if(a[i-1]==b[j-1])       //找到相等字符+1 {f[i][j]=f[i-1][j-1]+1;}else{//f[i][j]=f[i-1][j]>f[i][j-1]?f[i-1][j]:f[i][j-1];                     f[i][j]=max (f[i-1][j],f[i][j-1]);}}}printf("%d\n",f[le1][le2]);}return 0;}