2020.7.8 --素数线性筛,欧拉函数模板

素数线性筛

const int maxn = 2e7; int n, m, prime[maxn], isnt_prime[maxn],tot;

void get_prime(int n) {
    isnt_prime[0] = isnt_prime[1] = 1;
    for (int i = 2; i <= n; ++i)
    { //当前数是所有数小于n的数而不只是素数，这是欧拉筛与埃氏筛的区别
        if (!isnt_prime[i])
            prime[++tot] = i;
        for (int j = 1; j <= tot && i * prime[j] <= n; ++j)
        { //当前数乘上的素数为prime[j]
            isnt_prime[i * prime[j]] = 1;
            if (i % prime[j] == 0)
                break;
        }
    } 
}
     

线性欧拉筛 O(n)

ll euler[maxn];
void eul() {
    for (int i = 2; i < maxn; i++)
    {
        if (!euler[i])
            for (int j = i; j < maxn; j += i)
            {
                if (!euler[j])
                    euler[j] = j;
                euler[j] = euler[j] / i * (i - 1);
            }
    } }

单一欧拉筛 O(sqrt(n))

ll eular(ll n)
{
    ll ans = n;
    for(int i=2; i*i <= n; ++i)
    {
        if(n%i == 0)
        {
            ans = ans/i*(i-1);
            while(n%i == 0)
                n/=i;
        }
    }
    if(n > 1) ans = ans/n*(n-1);
    return ans; }