Common Subsequence(最长公共子序列)
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 abfcab programming contest abcd mnp
Sample Output
4 2 0
题解:动态规划
代码:
#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
int main()
{
char a[1005],b[1005];
int dp[1005][1005];
while(scanf("%s%s",a,b)!=EOF)
{
memset(dp,0,sizeof(dp));
for(int t=1;t<=strlen(a);t++)
{
for(int j=1;j<=strlen(b);j++)
{
if(a[t-1]==b[j-1])
{
dp[t][j]=max(dp[t-1][j-1]+1,dp[t][j]);
}
else
{
dp[t][j]=max(dp[t-1][j],dp[t][j-1]);
}
}
}
printf("%d\n",dp[strlen(a)][strlen(b)]);
}
}
-------------------------------------------
个性签名:独学而无友,则孤陋而寡闻。做一个灵魂有趣的人!
如果觉得这篇文章对你有小小的帮助的话,记得在右下角点个“推荐”哦,博主在此感谢!
万水千山总是情,打赏一分行不行,所以如果你心情还比较高兴,也是可以扫码打赏博主,哈哈哈(っ•̀ω•́)っ✎⁾⁾!