数论专题小结：欧拉函数

1.n的欧拉函数

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);//注意要先除后乘while (n%i == 0)n /= i;}if (n > 1)//注意必须有这一步ans = ans / n*(n - 1);return ans;}

2.1~n的欧拉函数值

注：时间复杂度为O(N*loglogN)。

#define N 10000int phi[N];void phi_table(int n, int*phi){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);}}