[CSP-S simulation test]: W Small Magic (math or find the law)

Topic Portal (internal title 130)

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Input Format

　　A first line integer $ n $, represents the length of the string.
　　The second row contains only lowercase string $ s $.

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Output Format

　　A row of integer result of the answer to the $ 998,244,353 $ modulo.

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Sample

Sample input:

2 of
a

Sample output:

625

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Data range and tips

　　For $ 20 \% $ test data, $ n \ leqslant 4 $.
　　For $ 40 \% $ test data, $ n \ leqslant 100 $.
　　For $ 60 \% $ test data, $ n \ leqslant 10,000,000 $.
　　Further test data for $ 20 \% $ ensure $ s $ $ A $ consisting only of.
　　Test data for $ 100 \% of $, $ 2 \ leqslant n \ leqslant 10,1 \ leqslant | s | \ leqslant 1,000,000 $.
　　For $ 100 \% $ test data, $ | s | \ leqslant n $.

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answer

They told me that hit the table to find a law ......

Anyway, I did not find out.

The answer is:

$$26^n-26^{(n-s)}-s\times 25\times 26^{(n-s-1)}$$

Time complexity: $ \ Theta (\ log n) $.

Expectations score: $ 100 $ points.

Actual score: $ 100 $ points.

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Code time

#include<bits/stdc++.h>
using namespace std;
const int mod=998244353;
long long n,s;
char ch[1000001];
long long ans;
long long qpow(long long x,long long y)
{
	if(y<0)return 0;
	long long res=1;
	while(y)
	{
		if(y&1)res=res*x%mod;
		x=x*x%mod;
		y>>=1;
	}
	return res;
}
int main ()
{
	scanf("%lld%s",&n,ch+1);
	s=strlen(ch+1);
	ans = ((qpow (26, n) -qpow (26 ns) + v)% s on-* 25% * against qpow (26, ns-1)% v + v)% v;
	printf("%lld",ans);
	return 0;
}

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rp ++