Common Subsequence （dp)

Common Subsequence

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.

Input

abcfbc abfcabprogramming contest abcd mnp

Output

420

示意图：（有助于理解）

题意：找出两个字符串中的最长公共子序列

什么是最长公共子序列：点击打开链接

#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;char a[1000],b[1000];int dp[1000][1000];int main(){    while(~scanf("%s%s",a+1,b+1))    {        memset(dp,0,sizeof(dp));        int i,j;        int la=strlen(a+1),lb=strlen(b+1);        for(i=1; i<=lb; i++)        {            for(j=1; j<=la; j++)            {                if(a[j]==b[i])                    dp[i][j]=dp[i-1][j-1]+1;                else                    dp[i][j]=max(dp[i-1][j],dp[i][j-1]);            }        }        printf("%d\012",dp[lb][la]);        memset(a,0,sizeof(a));        memset(b,0,sizeof(b));    }    return 0;}