题面
医学界发现的新病毒因其蔓延速度和Internet上传播的"红色病毒"不相上下,被称为"红色病毒",经研究发现,该病毒及其变种的DNA的一条单链中,胞嘧啶,腺嘧啶均是成对出现的。
现在有一长度为N的字符串,满足一下条件:
(1) 字符串仅由A,B,C,D四个字母组成;
(2) A出现偶数次(也可以不出现);
(3) C出现偶数次(也可以不出现);
计算满足条件的字符串个数.
当N=2时,所有满足条件的字符串有如下6个:BB,BD,DB,DD,AA,CC.
由于这个数据肯能非常庞大,你只要给出最后两位数字即可.
Input
每组输入的第一行是一个整数T,表示测试实例的个数,下面是T行数据,每行一个整数N(1<=N<2^64),当T=0时结束.
Output
对于每个测试实例,输出字符串个数的最后两位,每组输出后跟一个空行.
题解
这题要用指数型母函数来推结论，出现随意次对应的函数是，“出现偶数次”所对应的函数是，
最终的答案函数就是，因为，所以第N项的系数乘N!即答案就是。
我们用unsigned long long 存N，然后用快速幂就行。
ＣＯＤＥ
/*
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
//优化
*/
#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#include<algorithm>
#define LL long long
#define ULL unsigned long long
using namespace std;
inline int read() {
int f = 1,x = 0;char s = getchar();
while(s < '0' || s > '9') {if(s == '-') f = -1;s = getchar();}
while(s >= '0' && s <= '9') {x = x * 10 + s - '0';s = getchar();}
return x * f;
}
inline ULL readu() {
ULL x = 0;char s = getchar();
while(s < '0' || s > '9') {s = getchar();}
while(s >= '0' && s <= '9') {x = x * 10 + s - '0';s = getchar();}
return x;
}
int mod = 100;
int n,m,q,i,j,s,o,k;
ULL N;
LL qkpow(LL a,ULL b) {
LL res = 1;
while(b) {
if(b&1) res = 1ll*res*a % mod;
b >>= 1;
a=1ll*a*a%mod;
}
return res % mod;
}
int main() {
bool flag = 0;
int T;
while(T = read()) {
int tt = 0;
while(T --){
N = readu();
// printf("%llu\n",N);
LL ans = (qkpow(4ll,N-1) + qkpow(2ll,N-1)) % mod;
printf("Case %d: %lld\n",++tt,ans);
}
flag = 1;
if(flag) putchar('\n');
}
return 0;
}
