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==0) return 0;//3分！
    //输入与输出并存 
    long long n;
    for(int i=0;i<t;i++){
        cin>>n;
        long long out=0,dan=0;
        for(int j=1;j<=n;j++)
            per[j]=j;
        while(next_permutation(per+1,per+n+1))
        {
            dan=0;
            for(int j=1;j<=n;j++){
                dan+=per[j];
                dan%=3;
                if(dan==0) break;
                    if(j==n) out++;
                out%=10000000000037;
            }
        }
        cout<<out<<endl;
    }
    return 0;
}
//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[3010] = 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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-8) * mod);
    if (tmp < 0) 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 = 1;
    for(; b; b >>= 1)
    {
        if (b & 1) ans = mul(ans, a);
        a = mul(a, a);
    }    
    return ans;
}
long long inv(long long x) {return pow(x, mod - 2);}

long long fac(long long x)
{
    long long ans = FAC[x / 1000000];
    FOR(i, x / 1000000 * 1000000 + 1, x) ans = mul(ans, i);
    return ans;
}

void work()
{
    scanf("%long longd", &m); n = m / 3;
    if (m % 3 == 0) printf("%long longd\n", mul(mul(fac(3 * n - 2), sqr(fac(n))), inv(fac(2 * n - 2))) * 2ll % mod); else
    if (m % 3 == 1) printf("%long longd\n", mul(mul(mul(fac(3 * n), sqr(fac(n))), inv(fac(2 * n))), n + 1)); else
        printf("%long longd\n", mul(2ll * sqr(n + 1), mul(mul(fac(3 * n), sqr(fac(n))), inv(fac(2 * n)))));    
}

int main()
{
//    freopen("summer.in", "r", stdin);
//    freopen("summer.out", "w", stdout);
    
    scanf("%d", &T);
    while (T--) work();
    
    return 0;
} 

 OK！