题意:素性测试和大整数分解, N (2 <= N < 254)。
分析:没啥好讲的,套个模板,POJ上C++提交
收获:写完这题得到模板
代码:
/************************************************ * Author :Running_Time * Created Time :2015-8-28 13:02:38 * File Name :POJ_1811.cpp ************************************************/ #include <cstdio> #include <algorithm> #include <iostream> #include <sstream> #include <cstring> #include <cmath> #include <string> #include <vector> #include <queue> #include <deque> #include <stack> #include <list> #include <map> #include <set> #include <bitset> #include <cstdlib> #include <ctime> using namespace std; #define lson l, mid, rt << 1 #define rson mid + 1, r, rt << 1 | 1 typedef long long ll; const int N = 1e5 + 10; const int S = 20; const int INF = 0x3f3f3f3f; const int MOD = 1e9 + 7; /* 素性测试,Miller_Rabin 随机算法 可以判断< 2^63的数 素数:true,合数:false */ const int S = 20; //随机算法判定次数,S越大,判错概率越小 //非递归写法,递归写法可能会爆栈 ll GCD(ll a, ll b) { if (a == 0) return 1; if (a < 0) a = -a; while (b) { ll c = a % b; a = b; b = c; } return a; } //计算 (a * b) % p,a,b是long long数,直接相乘可能会溢出 ll multi_mod(ll a, ll b, ll p) { ll ret = 0; a %= p; b %= p; while (b) { if (b & 1) { ret += a; if (ret >= p) ret -= p; } a <<= 1; if (a >= p) a -= p; b >>= 1; } return ret; } //计算 a ^ x % p ll pow_mod(ll a, ll x, ll p) { ll ret = 1; a %= p; while (x) { if (x & 1) ret = multi_mod (ret, a, p); a = multi_mod (a, a, p); x >>= 1; } return ret; } /* 以a为基,n-1=x*2^t,a^(n-1) = 1(mod n) 验证n是不是合数 一定是合数返回true, 不一定返回false */ bool check(ll a, ll n, ll x, int t) { ll ret = pow_mod (a, x, n); ll last = ret; for (int i=1; i<=t; ++i) { ret = multi_mod (ret, ret, n); if (ret == 1 && last != 1 && last != n - 1) return true; //合数 last = ret; } if (ret != 1) return true; return false; } bool Miller_Rabin(ll n) { if (n == 2) return true; if (n < 2 || ! (n & 1)) return false; //偶数或1 ll x = n - 1; int t = 0; while (! (x & 1)) { x >>= 1; t++; } for (int i=1; i<=S; ++i) { ll a = rand () % (n - 1) + 1; //需要cstdlib头文件 if (check (a, n, x, t)) return false; //合数 } return true; } /* 大整数分解,Pollard_rho 随机算法 factorize ()保存质因数在vector */ ll Pollard_rho(ll x, ll c) { ll i = 1, k = 2; ll a = rand () % x; ll b = a; while (1) { i++; a = (multi_mod (a, a, x) + c) % x; ll d = GCD (b - a, x); if (d != 1 && d != x) return d; if (b == a) return x; if (i == k) b = a, k += k; } } void factorize(ll n, vector<ll> &ret) { if (Miller_Rabin (n)) { //素数 ret.push_back (n); return ; } ll p = n; while (p >= n) p = Pollard_rho (p, rand () % (n - 1) + 1); factorize (p, ret); factorize (n / p, ret); } int main(void) { srand (time (NULL)); int T; scanf ("%d", &T); while (T--) { ll n; scanf ("%I64d", &n); if (Miller_Rabin (n)) puts ("Prime"); else { if (n <= 1) { puts ("-1"); continue; } vector<ll> ans; factorize (n, ans); sort (ans.begin (), ans.end ()); printf ("%I64d\n", ans[0]); // for (int i=0; i<ans.size (); ++i) { // printf ("%I64d%c", ans[i], (i == ans.size ()-1) ? ‘\n‘ : ‘ ‘); // } } } return 0; }
时间: 2024-10-29 22:12:29