0
点赞
收藏
分享

微信扫一扫

Codeforces 245H H Queries for Number of Palindromes(DP)

逸省 2023-03-22 阅读 97


H. Queries for Number of Palindromes


time limit per test



memory limit per test



input



output



You've got a string s = s1s2... s|s| of length |s|, consisting of lowercase English letters. There also are q queries, each query is described by two integers li, ri (1 ≤ li ≤ ri ≤ |s|). The answer to the query is the number of substrings of string s[li... ri], which are palindromes.

String s[l... r] = slsl + 1... sr (1 ≤ l ≤ r ≤ |s|) is a substring of string s = s1s2... s|s|.

String t is called a palindrome, if it reads the same from left to right and from right to left. Formally, if t = t1t2... t|t| = t|t|t|t| - 1... t1.



Input



The first line contains string s (1 ≤ |s| ≤ 5000). The second line contains a single integer q (1 ≤ q ≤ 106) — the number of queries. Next q lines contain the queries. The i-th of these lines contains two space-separated integers li, ri (1 ≤ li ≤ ri ≤ |s|) — the description of the i-th query.

It is guaranteed that the given string consists only of lowercase English letters.



Output



Print q



Sample test(s)



Input



caaaba
5
1 1
1 4
2 3
4 6
4 5



Output


1
7
3
4
2



Note



Consider the fourth query in the first test case. String  s[4... 6] = «aba». Its palindrome substrings are: «a», «b», «a», «aba».

 

思路:DP,用个二维布尔数组判断是否回文。在用个二维数组存最优值

         初始化,当只有一个字符时是回文,并且最优值是1

         状态方程:is_palin[j][j+i]=is_palin[j+1][j+i-1]&s[j]==s[j+i];
    dp[j][j+i]=dp[j+1][j+i]+dp[j][j+i-1]-dp[j+1][i+j-1]+is_palin[j][j+i];

 

#include<iostream>
#include<cstring>
using namespace std;
const int mm=5005;
char s[mm];
int dp[mm][mm];
bool is_palin[mm][mm];
int main()
{
cin>>s;
int len=strlen(s);
memset(is_palin,0,sizeof(is_palin));
memset(dp,0,sizeof(dp));
for(int i=0;i<len;i++)
{
dp[i][i]=1;
is_palin[i][i]=true;
is_palin[i+1][i]=true;
}
for(int i=1;i<=len;i++)
for(int j=0;j<=len-i;j++)
{
is_palin[j][j+i]=is_palin[j+1][j+i-1]&s[j]==s[j+i];
dp[j][j+i]=dp[j+1][j+i]+dp[j][j+i-1]-dp[j+1][i+j-1]+is_palin[j][j+i];
}
int m,a,b;
cin>>m;
for(int i=0;i<m;i++)
{
cin>>a>>b;
cout<<dp[a-1][b-1]<<"\n";
}
}

 



举报

相关推荐

0 条评论