HDU 4632 Palindrome subsequence 记忆化搜索
2015-10-24 21:27
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Palindrome subsequence
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/65535 K (Java/Others)Total Submission(s): 2735 Accepted Submission(s): 1105
Problem Description
In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence <A, B, D> is a subsequence of <A, B, C, D, E, F>.
(http://en.wikipedia.org/wiki/Subsequence)
Given a string S, your task is to find out how many different subsequence of S is palindrome. Note that for any two subsequence X = <Sx1, Sx2, ..., Sxk> and Y = <Sy1, Sy2, ..., Syk> , if there
exist an integer i (1<=i<=k) such that xi != yi, the subsequence X and Y should be consider different even if Sxi = Syi. Also two subsequences with different length should be considered different.
Input
The first line contains only one integer T (T<=50), which is the number of test cases. Each test case contains a string S, the length of S is not greater than 1000 and only contains lowercase letters.
Output
For each test case, output the case number first, then output the number of different subsequence of the given string, the answer should be module 10007.
Sample Input
4
a
aaaaa
goodafternooneveryone
welcometoooxxourproblems
Sample Output
Case 1: 1
Case 2: 31
Case 3: 421
Case 4: 960
Source
2013 Multi-University Training Contest 4
Recommend
zhuyuanchen520
给出一个串问区间有多少个回文子串
dp[i][j]表示第i个到第j个有dp[i][j]个子串
当str[i]==str[j]时候可以知道dp[i][j]=(dp(i,j-1)+dp(i+1,j)+)%mod
否则dp[i][j]=(dp[i][j-1]+dp[i+1][j]-dp[x+1][y+1]+mod)%mod可能出现负值
ACcode:
#pragma warning(disable:4786)//使命名长度不受限制 #pragma comment(linker, "/STACK:102400000,102400000")//手工开栈 #include <map> #include <set> #include <queue> #include <cmath> #include <stack> #include <cctype> #include <cstdio> #include <cstring> #include <stdlib.h> #include <iostream> #include <algorithm> #define rd(x) scanf("%d",&x) #define rd2(x,y) scanf("%d%d",&x,&y) #define rds(x) scanf("%s",x) #define rdc(x) scanf("%c",&x) #define ll long long int #define maxn 1001 #define mod 10007 #define INF 0x3f3f3f3f //int 最大值 #define FOR(i,f_start,f_end) for(int i=f_start;i<=f_end;++i) #define MT(x,i) memset(x,i,sizeof(x)) #define PI acos(-1.0) #define E exp(1) using namespace std; int loop,dp[maxn][maxn],cnt=1,len; char str[1010]; int DP(int x,int y){ if(x>y)return 0; if(x==y)return 1; if(dp[x][y])return dp[x][y]; if(str[x-1]==str[y-1]) return dp[x][y]=(DP(x,y-1)+DP(x+1,y)+1)%mod; return dp[x][y]=(DP(x,y-1)+DP(x+1,y)-DP(x+1,y-1)+mod)%mod; } int main(){ rd(loop); while(loop--){ rds(str);MT(dp,0); len=strlen(str); printf("Case %d: %d\n",cnt++,DP(1,len)); } return 0; } /* 4 a aaaaa goodafternooneveryone welcometoooxxourproblems */
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