51Nod－1186－质数检测 V2

ACM模版

描述

题解

伪随机素数检测，Miller-Rabin算法，如果用Java神马的有大数相关类型的话，就是一个模版题，套用一下这个算法模版就好了，然而如果用C++，那么这道题足够惨痛了，Miller-Rabin算法+大数算法……有点儿料！！！

代码

#include <cstdio> #include <cstring> #include <cstdlib> #define MAXL 4 #define M10 1000000000 #define Z10 9 const int zero[MAXL - 1] = {0}; struct bnum { int data[MAXL]; // 断成每截9个长度 // 读取字符串并转存 void read() { memset(data, 0, sizeof(data)); char buf[32]; scanf("%s", buf); int len = (int)strlen(buf); int i = 0, k; while (len >= Z10) { for (k = len - Z10; k < len; ++k) { data[i] = data[i] * 10 + buf[k] - '0'; } ++i; len -= Z10; } if (len > 0) { for (k = 0; k < len; ++k) { data[i] = data[i] * 10 + buf[k] - '0'; } } } bool operator == (const bnum &x) { return memcmp(data, x.data, sizeof(data)) == 0; } bnum & operator = (const int x) { memset(data, 0, sizeof(data)); data[0] = x; return *this; } bnum operator + (const bnum &x) { int i, carry = 0; bnum ans; for (i = 0; i < MAXL; ++i) { ans.data[i] = data[i] + x.data[i] + carry; carry = ans.data[i] / M10; ans.data[i] %= M10; } return ans; } bnum operator - (const bnum &x) { int i, carry = 0; bnum ans; for (i = 0; i < MAXL; ++i) { ans.data[i] = data[i] - x.data[i] - carry; if (ans.data[i] < 0) { ans.data[i] += M10; carry = 1; } else { carry = 0; } } return ans; } // assume *this < x * 2 bnum operator % (const bnum &x) { int i; for (i = MAXL - 1; i >= 0; --i) { if (data[i] < x.data[i]) { return *this; } else if (data[i] > x.data[i]) { break; } } return ((*this) - x); } bnum & div2() { int i, carry = 0, tmp; for (i = MAXL - 1; i >= 0; --i) { tmp = data[i] & 1; data[i] = (data[i] + carry) >> 1; carry = tmp * M10; } return *this; } bool is_odd() { return (data[0] & 1) == 1; } bool is_zero() { for (int i = 0; i < MAXL; ++i) { if (data[i]) { return false; } } return true; } }; void mulmod(bnum &a0, bnum &b0, bnum &p, bnum &ans) { bnum tmp = a0, b = b0; ans = 0; while (!b.is_zero()) { if (b.is_odd()) { ans = (ans + tmp) % p; } tmp = (tmp + tmp) % p; b.div2(); } } void powmod(bnum &a0, bnum &b0, bnum &p, bnum &ans) { bnum tmp = a0, b = b0; ans = 1; while (!b.is_zero()) { if (b.is_odd()) { mulmod(ans, tmp, p, ans); } mulmod(tmp, tmp, p, tmp); b.div2(); } } bool MillerRabinTest(bnum &p, int iter) { int i, small = 0, j, d = 0; for (i = 1; i < MAXL; ++i) { if (p.data[i]) { break; } } if (i == MAXL) { // small integer test if (p.data[0] < 2) { return false; } if (p.data[0] == 2) { return true; } small = 1; } if (!p.is_odd()) { return false; // even number } bnum a, s, m, one, pd1; one = 1; s = pd1 = p - one; while (!s.is_odd()) { s.div2(); ++d; } for (i = 0; i < iter; ++i) { a = rand(); if (small) { a.data[0] = a.data[0] % (p.data[0] - 1) + 1; } else { a.data[1] = a.data[0] / M10; a.data[0] %= M10; } if (a == one) { continue; } powmod(a, s, p, m); for (j = 0; j < d && !(m == one) && !(m == pd1); ++j) { mulmod(m, m, p, m); } if (!(m == pd1) && j > 0) { return false; } } return true; } int main() { bnum x; x.read(); puts(MillerRabinTest(x, 5) ? "Yes" : "No"); return 0; }

参考

《素数相关》