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

#include <bits/stdc++.h>
#define LL long long
using namespace std;
const int maxn = 100010;
const int md = 1e9+7;
LL d[maxn];
int main(){
    d[0] = 1;
    for(int i = 1; i < maxn; ++i)
        d[i] = (i%md*d[i-1])%md;
    int x,ks;
    scanf("%d",&ks);
    while(ks--){
        scanf("%d",&x);
        printf("%lld
",(d[x]+md-1)%md);
    }
    return 0;
}