51nod 1186 质数检测 V2

1186 质数检测 V2

基准时间限制：1 秒 空间限制：131072 KB 分值: 40 难度：4级算法题

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给出1个正整数N，检测N是否为质数。如果是，输出"Yes"，否则输出"No"。

Input

输入一个数N(2 <= N <= 10^30)

Output

如果N为质数，输出"Yes"，否则输出"No"。

Input示例

17

Output示例

Yes

大数的素数测试，套上模板

#include<iostream>using namespace std;//#include<stdlib>#include<string>#include<string.h>#include<algorithm>#define MAXL 4#define M10 1000000000#define Z10 9const 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;}