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题意:题目定义了Carmichael Numbers 即 a^p % p = a.并且p不是素数。之后输入p,a问p是否为Carmichael Numbers？
坑点:先是各种RE，因为poj不能用srand()...之后各种WA..因为里面(a,p) ?= 1不一定互素，即这时Fermat定理的性质并不能直接用欧拉定理来判定。。即 a^(p-1)%p = 1判断是错误的。。作的
#include<iostream> #include<cstdio> #include<cstring> #include<string.h> #include<algorithm> #include<map> #include<queue> #include<vector> #include<cmath> #include<stdlib.h> #include<time.h> using namespace std; template<typename T> void read1(T &m) { T x=0,f=1;char ch=getchar(); while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();} while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();} m = x*f; } template<typename T> void read2(T &a,T &b){read1(a);read1(b);} typedef long long ll; int T,kase = 1,i,j,k,n,m; ll mult(ll x,ll y,ll mod) // ·ÀÖ¹x*y±¬long long; { ll ans = 0;x %= mod; while(y){ if(y&1) ans += x, y--; if(ans >= mod) ans -= mod; y >>= 1; x <<= 1; if(x >= mod) x -= mod; } return ans; } ll pow(ll a,ll n,ll mod) { a %= mod; ll ans = 1; while(n){ if(n&1) ans = ans*a%mod; a = a*a%mod; n >>= 1; } return ans; } int p[16]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53}; bool Miller_Rabin(ll n) { if(n <= 2) return n == 2; if(n%2 == 0) return false; ll t = n - 1; while(t%2 == 0) t >>= 1; for(int i = 0;i < 16;i++){ if(p[i] >= n) return true; if(n % p[i] == 0) return false; ll tmp = t; ll x = pow(p[i],t,n); // p[i]^t % n; while(tmp < n){ ll y = mult(x,x,n); if(y == 1 && x != 1 && x != n-1) return false; x = y; tmp <<= 1; } if(x != 1) return false; // Fermat theory } return true; } int main() { ll x,y; while(read2(x,y), x + y){ if(Miller_Rabin(x) || pow(y,x,x) != y) puts("no"); else puts("yes"); } return 0; }
poj 3641 Pseudoprime numbers Miller_Rabin测素裸题
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原文地址：http://www.cnblogs.com/hxer/p/5369714.html
