嵊州D3T2 福尔贝斯太太的快乐夏日 summer

嵊州D3T2

福尔贝斯太太的快乐夏日 summer

宗教，或是无节制的自由主义，是致人腐化的毒剂。

现在，一个人要经历 n 个事件，编号为 1 ∼ n。

经历 x 号事件，他的危险值就会增加 x。

一开始他的危险值是 0。

当一个人的危险值大于 0 且是 3 的倍数的时候，他会丧失生存的意义，而沉溺于享乐之中，不会再 去经历后面的事件。

那么，有多少种安排经历这 n 个事件的顺序，使得这个人能经历全部 n 个事件？

即有多少种 n 的全排列 A，满足以下条件：

请给出答案 %10000000000037 的结果。

Input

第一行一个整数 T，表示数据组数。

对于每组数据，一行一个整数 n 表示事件数。

Output

一行一个整数表示答案。

Examples

summer.in	summer.out
3 4 461350 946122	6 8077061242588 9686440545236

Notes

对于所有数据，满足 0 ≤ T ≤ 3 , 3 ≤ n ≤ 3 ∗ 10^9。

Subtask1[3pts]

T = 0

Subtask2[26pts]

n ≤ 8

Subtask3[24pts]

n ≤ 10^3

Subtask4[10pts]

n ≤ 3 ∗ 10^6

Subtask5[14pts]

n ≤ 3 ∗ 10^7

Subtask6[11pts]

n ≤ 3 ∗ 10^8

Subtask7[12pts]

无特殊限制

---

暴力法

假如n<10的话，我们就可以用这种方法（不想看就跳过吧）

#include<bits/stdc++.h>
using namespace std;
const int inf = 0x3f3f3f;
int per[inf];
int main(){
    freopen("summer.in","r",stdin);
    freopen("summer.out","w",stdout);
    int t;
    cin>>t;
    if(t==) return ;//3分！
    //输入与输出并存
    long long n;
    for(int i=;i<t;i++){
        cin>>n;
        long long out=,dan=;
        for(int j=;j<=n;j++)
            per[j]=j;
        while(next_permutation(per+,per+n+))
        {
            dan=;
            for(int j=;j<=n;j++){
                dan+=per[j];
                dan%=;
                if(dan==) break;
                    if(j==n) out++;
                out%=;
            }
        }
        cout<<out<<endl;
    }
    return ;
}
//请给出答案 %10000000000037 的结果
//思考：当t==0时，输出空白还是0？ 

这道题最大的敌人就是超时

要么，事先打表

要么，有公式

要么，3分。。。

而我呢

公式不会，

打表打错了

我是不是没救了？

解释一下代码：

其中有个

while(next_permutation(per+1,per+n+1))

下一个排列函数。

请参考https://www.cnblogs.com/send-off-a-friend/p/11178134.html

我写的一篇博客，有关于next_permutation()的哟

---

std

就用公式就好了！

分类讨论三种（其实是两种）

 #include <cstdio>
 #define FOR(i, l, r) for(long long i = l; i <= r; ++i)

 using namespace std;

 const long long mod = 10000000000037ll;
 const long long FAC[] = 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 long long n, m;
 int T;

 long long mul(long long a, long long b)
 {
     long long tmp = (a * b - (long long)((long double)a / mod * b + 1e-) * mod);
     if (tmp < ) tmp += mod; return tmp;
 }
 long long sqr(long long x) {return mul(x, x);}

 long long pow(long long a, long long b)
 {
     a %= mod, b %= mod;
     long long ans = ;
     for(; b; b >>= )
     {
         if (b & ) ans = mul(ans, a);
         a = mul(a, a);
     }
     return ans;
 }
 long long inv(long long x) {return pow(x, mod - );}

 long long fac(long long x)
 {
     long long ans = FAC[x / ];
     FOR(i, x /  *  + , x) ans = mul(ans, i);
     return ans;
 }

 void work()
 {
     scanf("%long longd", &m); n = m / ;
     if (m %  == ) printf("%long longd\n", mul(mul(fac( * n - ), sqr(fac(n))), inv(fac( * n - ))) * 2ll % mod); else
     if (m %  == ) printf("%long longd\n", mul(mul(mul(fac( * n), sqr(fac(n))), inv(fac( * n))), n + )); else
         printf("%long longd\n", mul(2ll * sqr(n + ), mul(mul(fac( * n), sqr(fac(n))), inv(fac( * n)))));
 }

 int main()
 {
 //    freopen("summer.in", "r", stdin);
 //    freopen("summer.out", "w", stdout);

     scanf("%d", &T);
     while (T--) work();

     return ;
 } 

OK！