数论模板

#include <cstdio>
#include <cmath>
#include <cstring>

using namespace std;

const int maxn = 105;

int n;

int vis[maxn], prime[maxn], phi[maxn];

void sieve(int n)
{
    int m = (int) sqrt(n + 0.5);
    memset(vis, 0, sizeof vis);
    for (int i = 2; i <= m; i++) if (!vis[i])
        for (int j = i * i; j <= n; j += i) vis[j] = 1;
}

int get_primes(int n)
{
    sieve(n);
    int c = 0;
    for (int i = 2; i <= n; i++) if (!vis[i])
        prime[++c] = i;
    return c;
}

int gcd(int a, int b)
{
    return b == 0 ? a : gcd(b, a % b);
}

void ex_gcd(int a, int b, int d, int& x, int& y)
{
    if (!b) 
    {
        d = a;
        x = 1;
        y = 0;
    }else
    {
        ex_gcd(b, a % b, d, y, x);
        y -= x * (a / b);
    }
}

int ksm(int a, int b, int M)
{
    int ans = 1, base = a;
    while (b)
    {
        if (b & 1)
            ans = (ans *  base) % M;
        base = (base * base) % M;
        b >>= 1;
    } 
    return ans % M;
}

int euler_phi(int n)
{
    int m = (int)sqrt(n + 0.5);
    int ans = n;
    for (int i = 2; i <= m; i++) if (n % i == 0)
    {
        ans = ans / i * (i - 1);
        while (n % i == 0) n /= i;
    }
    if (n > 1) ans = ans / n * (n - 1);
}

void phi_table(int n)
{
    for (int i = 2; i <= n; i++) phi[i] = 0;
    phi[1] = 1;
    for (int i = 2; i <= n; i++) if (!phi[i])
    {
        for (int j = i; j <= n; j += i)
        {
            if (!phi[j]) phi[j] = j;
            phi[j] = phi[j] / i * (i - 1);
        }
    }
} 

int main()
{
    scanf("%d", &n);
    printf("%d
", get_primes(n));//求质数 
    for (int i = 2; i <= n; i++)
        if (!vis[i])
            printf("%d ", i);
    int x, y;
    printf("
");
    scanf("%d%d", &x, &y);
    printf("%d
",gcd(x, y));//求gcd 
    int a, b, d;
    x = y = 0;
    scanf("%d%d", &a, &b);
    ex_gcd(a, b, d, x, y);//求ex_gcd 
    printf("%d %d
", x, y);
    int M;
    scanf("%d%d%d", &a, &b, &M);//求a^b mod M; 
    printf("%d
", ksm(a, b, M));
    scanf("%d", &n);
    printf("%d
", euler_phi(n));
    phi_table(n);
    for (int i = 1; i <= n; i++)
        printf("%d ", phi[i]);
    return 0;
}