題面
醫學界發現的新病毒因其蔓延速度和Internet上傳播的"紅色病毒"不相上下,被稱爲"紅色病毒",經研究發現,該病毒及其變種的DNA的一條單鏈中,胞嘧啶,腺嘧啶均是成對出現的。
現在有一長度爲N的字符串,滿足一下條件:
(1) 字符串僅由A,B,C,D四個字母組成;
(2) A出現偶數次(也可以不出現);
(3) C出現偶數次(也可以不出現);
計算滿足條件的字符串個數.
當N=2時,所有滿足條件的字符串有如下6個:BB,BD,DB,DD,AA,CC.
由於這個數據肯能非常龐大,你只要給出最後兩位數字即可.
Input
每組輸入的第一行是一個整數T,表示測試實例的個數,下面是T行數據,每行一個整數N(1<=N<2^64),當T=0時結束.
Output
對於每個測試實例,輸出字符串個數的最後兩位,每組輸出後跟一個空行.
題解
這題要用指數型母函數來推結論,出現隨意次對應的函數是,“出現偶數次”所對應的函數是,
最終的答案函數就是,因爲,所以第N項的係數乘N!即答案就是。
我們用unsigned long long 存N,然後用快速冪就行。
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")
//優化
*/
#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;
}