嵊州D3T2 福尔贝斯太太的快乐夏日 summer
作者：互联网
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）
1 #include <cstdio>
2 #define FOR(i, l, r) for(long long i = l; i <= r; ++i)
3
4 using namespace std;
5
6 const long long mod = 10000000000037ll;
7 const long long FAC[3010] = 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8
9 long long n, m;
10 int T;
11
12 long long mul(long long a, long long b)
13 {
14 long long tmp = (a * b - (long long)((long double)a / mod * b + 1e-8) * mod);
15 if (tmp < 0) tmp += mod; return tmp;
16 }
17 long long sqr(long long x) {return mul(x, x);}
18
19 long long pow(long long a, long long b)
20 {
21 a %= mod, b %= mod;
22 long long ans = 1;
23 for(; b; b >>= 1)
24 {
25 if (b & 1) ans = mul(ans, a);
26 a = mul(a, a);
27 }
28 return ans;
29 }
30 long long inv(long long x) {return pow(x, mod - 2);}
31
32 long long fac(long long x)
33 {
34 long long ans = FAC[x / 1000000];
35 FOR(i, x / 1000000 * 1000000 + 1, x) ans = mul(ans, i);
36 return ans;
37 }
38
39 void work()
40 {
41 scanf("%long longd", &m); n = m / 3;
42 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
43 if (m % 3 == 1) printf("%long longd\n", mul(mul(mul(fac(3 * n), sqr(fac(n))), inv(fac(2 * n))), n + 1)); else
44 printf("%long longd\n", mul(2ll * sqr(n + 1), mul(mul(fac(3 * n), sqr(fac(n))), inv(fac(2 * n)))));
45 }
46
47 int main()
48 {
49 // freopen("summer.in", "r", stdin);
50 // freopen("summer.out", "w", stdout);
51
52 scanf("%d", &T);
53 while (T--) work();
54
55 return 0;
56 }
OK！
标签：summer,嵊州,int,ans,long,mul,fac,贝斯 来源： https://www.cnblogs.com/send-off-a-friend/p/11182024.html