[CSP-S Simulation Test]: palindrome (hash + prefix and two-dimensional)

Title Description

　　After the idle boredom of $ YGH $ seconds off the above two questions, start thinking about interesting palindrome string problem.
　　Before he had a floating string. Apparently $ YGH $ will $ manacher $, so he readily obtained a number of palindromic substring of this string. However, the number palindromic substring in question he is not satisfied, he intends to come up with a data structure to quickly determine the subscript string $ [l, r] $ substrings (the same palindromic repeat substring count). But this is too simple matter, he intends to test to $ YYR $ spicy chicken, spicy chicken but extremely $ YYR $ absolutely no idea.
　　So, $ YGH $ sped away, in a small piece of dust brought up the sleeves, contemplative $ YYR $ still there.

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Input Format

The first line of a string $ S $.
The second line an integer $ T $, represents the number of inquiries.
Then $ T $ lines of two integers $ l $, $ r $, $ query string indicates the subscript S $ $ [l, r] $ substring answers.

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Output Format

$ T $ output lines, each represents an integer answer to this inquiry.

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Sample

Sample input:

Ababaab
2
L 3
3 7

Sample output:

4
8

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Data range and tips

For $ 20 \% $ of the data, to ensure that $ | S |, T \ leqslant 500 $
for the data $ 40 \% $ ensure $ | S |, T 5,000 $ \ leqslant
data for $ 100 \% $ ensure $ | S | \ leqslant 5,000, T \ leqslant 100,000 $

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answer

I wish you all a happy National Day, Happy training!

The first question to be more abstract, the definition of a two-dimensional array $ Map $, if the interval $ [l, r] $ string is a palindrome, then $ Map [l] [r] = 1 $, otherwise $ 0 $.

So, all we need is the required point $ (l, l) $ the point $ (r, r) $ direct a few $ 1 $.

Palindrome sequence is not required in front of the hash $ $ process can achieve, the number of seek $ 1 $ prefix and can be used later.

Time complexity: $ \ Theta (n ^ 2 + T) $.

Expectations score: $ 100 $ points.

Actual score: $ 100 $ points.

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Code time

#include<bits/stdc++.h>
using namespace std;
int n;
char ch[5001];
int S[5001];
int Map[5001][5001];
unsigned long long flag[5001];
unsigned long long hash1[5001],hash2[5001];
void pre_work()
{
	flag[0]=1;
	for(int i=1;i<=n;i++)
	{
		flag[i]=flag[i-1]*131;
		hash1[i]=hash1[i-1]*131+S[i];
	}
	for(int i=n;i;i--)hash2[i]=hash2[i+1]*131+S[i];
	for(int i=1;i<=n;i++)
		for(int j=i;j<=n;j++)
			if(hash1[j]-hash1[i-1]*flag[j-i+1]==hash2[i]-hash2[j+1]*flag[j-i+1])
				Map[i][j]=1;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			Map[i][j]+=Map[i-1][j]+Map[i][j-1]-Map[i-1][j-1];
}
int main()
{
	scanf("%s",ch+1);
	n=strlen(ch+1);
	for(int i=1;i<=n;i++)
		S[i]=ch[i]-'a'+1;
	pre_work();
	int T;scanf("%d",&T);
	while(T--)
	{
		int l,r;
		scanf("%d%d",&l,&r);
		printf("%d\n",Map[r][r]-Map[l-1][r]-Map[r][l-1]+Map[l-1][l-1]);
	}
	return 0;
}

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rp ++