题目

暴力代码，官网过55%

#include <bits/stdc++.h>
using namespace std;
int main()
{int n;cin >> n;vector<bool> a(n + 1);a[1] = 1;int res = 1;for (int i = 2; i <= n; i++){if (a[i] == 0){for (int j = i; j <= n; j += i)a[j] = a[j] ^ 1;res++;}}cout << res;
}

代码

#include <iostream>
#include <unordered_map>
#include <cmath>
using namespace std;
using ll = long long;
const int N = 20000010;
int primes[N], cnt;
bool st[N];
int mu[N];
unordered_map<int, int> mp;void init(int n)
{mu[1] = 1;for (int i = 2; i <= n; i++){if (!st[i]){primes[cnt++] = i;mu[i] = -1;}for (int j = 0; j < cnt && primes[j] * i <= n; j++){int x = primes[j];st[i * x] = true;if (i % x == 0){break;}else{mu[i * x] = -mu[i]; // 利用积性 mu[i*x] = mu[x] * mu[i]，其中mu[x] = -1}}}for (int i = 1; i <= n; i++) // 求莫比乌斯函数的前缀和（<=2e7）mu[i] += mu[i - 1];
}int cal(int n) // 记忆化计算莫比乌斯函数的前缀和（>2e7）
{if (n <= 20000000)return mu[n];if (mp.count(n))return mp[n];ll res = 1;for (ll l = 2, r; l <= n; l = r + 1) // 杜教筛（不太懂QAQ）{r = n / (n / l);res -= (r - l + 1) * cal(n / l);}return mp[n] = res;
}int main()
{init(20000000);ll n;cin >> n;ll res = 0;for (ll l = 1, r; l <= n / l; l = r + 1) // 公式1简化+分块，注意权重形式是n/i/i{r = sqrt(n / (n / l / l));res += (cal(r) - cal(l - 1)) * (n / (l * l));}cout << res << '\n';return 0;
}