题目意思:
http://poj.org/problem?id=1458
给出两个字符串,求出这两个字符串的最长子序列的长度,最长子序列的定义如下:
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.
题目分析:
此题为《算法导论》上的DP一节的经典题目。这里只给出动态转移方程:dp[i][j]:表示字符串x和字符串y,x的长度为i和y的长度j的最长子序列。
dp[i-1][j-1]+1 x[i]=y[j]
dp[i][j]={
max(dp[i-1[j],dp[i][j-1]]) x[i]!=x[j]
AC代码:
#include<iostream> #include<cstdio> #include<string> #include<cstring> using namespace std; int dp[1001][1001]; int DpCon(string s1,string s2){ for(int i=1;i<=s1.size();i++){ for(int j=1;j<=s2.size();j++){ if(s1[i-1]==s2[j-1]) dp[i][j]=dp[i-1][j-1]+1; else dp[i][j]=max(dp[i-1][j],dp[i][j-1]); } } return dp[s1.size()][s2.size()]; } int main() { string s1,s2; while(cin>>s1>>s2){ memset(dp,0,sizeof(dp)); cout<<DpCon(s1,s2)<<endl; } return 0; }
poj1458 Common Subsequence(经典DP)
原文地址:http://blog.csdn.net/fool_ran/article/details/40930301