Fansblog
Time Limit: 2000/2000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 3170 Accepted Submission(s): 671
Problem Description
Farmer John keeps a website called ‘FansBlog’ .Everyday , there are many people visited this blog.One day, he find the visits has reached P , which is a prime number.He thinks it is a interesting fact.And he remembers that the visits had reached another prime number.He try to find out the largest prime number Q ( Q < P ) ,and get the answer of Q! Module P.But he is too busy to find out the answer. So he ask you for help. ( Q! is the product of all positive integers less than or equal to n: n! = n * (n-1) * (n-2) * (n-3) *… * 3 * 2 * 1 . For example, 4! = 4 * 3 * 2 * 1 = 24 )
Input
First line contains an number T(1<=T<=10) indicating the number of testcases.
Then T line follows, each contains a positive prime number P (1e9≤p≤1e14)
Output
For each testcase, output an integer representing the factorial of Q modulo P.
Sample Input
1
1000000007
Sample Output
328400734
题意
给出一个素数P，找出小于P的最小素数Q，并计算Q的阶乘对P取模的结果
解决
从P-1开始进行素数检测，因为素数的分布是比较密集的，所以可以用试除法来判断素数。
在找到Q之后，由威尔逊定理可知：当P是素数的情况下，(P-1)! Ξ -1(mod P)
因为求的是Q! mod P，所以我们可以先将(P-1)! mod P求出来的，然后利用除法来计算Q! mod P
Code
1 #include <bits/stdc++.h> 2 #define ll long long 3 #define ull unsigned long long 4 #define ms(a,b) memset(a,b,sizeof(a)) 5 const int inf=0x3f3f3f3f; 6 const ll INF=0x3f3f3f3f3f3f3f3f; 7 const int maxn=1e6+10; 8 const int mod=1e9+7; 9 const int maxm=1e3+10; 10 using namespace std; 11 bool check(ll n) 12 { 13 for(ll i=2;i*i<=n;i++) 14 if(n%i==0) 15 return false; 16 return true; 17 } 18 ll modmul(ll A,ll B,ll Mod) 19 { 20 return (A*B-(ll)((long double)A*B/Mod)*Mod+Mod)%Mod; 21 } 22 ll Pow(ll a,ll b,ll c) 23 { 24 ll ans=1; 25 while(b) 26 { 27 if(b&1) 28 ans=modmul(ans,a,c); 29 b>>=1; 30 a=modmul(a,a,c); 31 } 32 return ans; 33 } 34 ll inv(ll a,ll b) 35 { 36 return Pow(a,b-2,b); 37 } 38 int main(int argc, char const *argv[]) 39 { 40 #ifndef ONLINE_JUDGE 41 freopen("in.txt", "r", stdin); 42 freopen("out.txt", "w", stdout); 43 srand((unsigned int)time(NULL)); 44 #endif 45 ios::sync_with_stdio(false); 46 cin.tie(0); 47 int t; 48 ll p; 49 cin>>t; 50 while(t--) 51 { 52 cin>>p; 53 ll num; 54 for(ll i=p-1;;i--) 55 if(check(i)) 56 { 57 num=i; 58 break; 59 } 60 ll ans=p-1; 61 for(ll i=num+1;i<=p-1;i++) 62 ans=modmul(ans,inv(i,p),p); 63 cout<<ans<<endl; 64 } 65 #ifndef ONLINE_JUDGE 66 cerr<<"Time elapsed: "<<1.0*clock()/CLOCKS_PER_SEC<<" s."<<endl; 67 #endif 68 return 0; 69 }