CSUOJ 1525 Algebraic Teamwork

Problem A

Algebraic Teamwork

The great pioneers of group theory and linear algebra want to cooperate and join their theories. In group theory, permutations – also known as bijective functions – play an important role. For a finite set A, a function σ : A → A is called a permutation of A if and only if there is some function ρ : A → A with σ(ρ(a)) = a and ρ(σ(a)) = a   for all a ∈ A.

The other half of the new team – the experts on linear algebra – deal a lot with idempotent functions. They appear as projections when computing shadows in 3D games or as closure operators like the transitive closure, just to name a few examples. A function p : A → A is called idempotent if and only if p(p(a)) = p(a)      for all a ∈ A.

To continue with their joined research, they need your help. The team is interested in non-idempotent permutations of a given finite set A. As a first step, they discovered that the result only depends on the set’s size. For a concrete size 1 ≤ n ≤ 10⁵, they want you to compute the number of permutations on a set of cardinality n that are not idempotent.

Input

The input starts with the number t ≤ 100 of test cases. Then t lines follow, each containing the set’s size 1 ≤ n ≤ 10⁵.

Output

Output one line for every test case containing the number modulo 1000000007 = (10⁹ + 7) of non-idempotent permutations on a set of cardinality n.

Sample Input	Sample Output
3 1 2 2171	0 1 6425

 

解题：n!-1

 1 #include <bits/stdc++.h>

 2 #define LL long long

 3 using namespace std;

 4 const int maxn = 100010;

 5 const int md = 1e9+7;

 6 LL d[maxn];

 7 int main(){

 8     d[0] = 1;

 9     for(int i = 1; i < maxn; ++i)

10         d[i] = (i%md*d[i-1])%md;

11     int x,ks;

12     scanf("%d",&ks);

13     while(ks--){

14         scanf("%d",&x);

15         printf("%lld\n",(d[x]+md-1)%md);

16     }

17     return 0;

18 }

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