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  • HDOJ -- 4632 区间DP

    Palindrome subsequence

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/65535 K (Java/Others)
    Total Submission(s): 1977    Accepted Submission(s): 822


    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
     

     思路:设dp[i][j]表示区间[i,j]的回文串的个数,那么有dp[i][j] = dp[j+1][i] + dp[j][i-1] - dp[j+1][i-1],如果str[i] == str[j],那么dp[i][j]还要加上dp[j+1][i-1] + 1;

     1 #include<iostream>
     2 #include<cstdio>
     3 #include<cstring>
     4 #define MAX 1010
     5 #define MOD 10007
     6 using namespace std;
     7 int dp[MAX][MAX];
     8 char str[MAX];
     9 int main(){
    10     int T, cnt = 0;
    11     //freopen("in.c", "r", stdin);
    12     scanf("%d", &T);
    13     while(T--){
    14         memset(str, 0, sizeof(str));
    15         memset(dp, 0, sizeof(dp));
    16         scanf("%s", str);
    17         int len = strlen(str);
    18         for(int i = 0; i< len;i ++) dp[i][i] = 1;
    19         for(int i = 0;i < len;i ++){
    20             for(int j = i-1;j >= 0;j --){
    21                 dp[j][i] = (dp[j][i-1] + dp[j+1][i] - dp[j+1][i-1] + MOD)%MOD;
    22                 if(str[i] == str[j]) dp[j][i] = (dp[j][i] + dp[j+1][i-1] + 1 + MOD)%MOD;
    23             }
    24         }
    25         printf("Case %d: %d
    ", ++cnt, dp[0][len-1]);
    26     }
    27     return 0;
    28 }
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  • 原文地址:https://www.cnblogs.com/anhuizhiye/p/3618702.html
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