Sieve prime number -------------------------------- number theory (template)

Given a positive integer n, please find the number of prime numbers in 1 ~ n.

The input format
consists of one line, including the integer n.

The output format
consists of one line and contains an integer representing the number of prime numbers in 1 ~ n.

Data range
1≤n≤106
Input sample:
8
Output sample:
4

Time complexity: O (nlogn)

#include<bits/stdc++.h>
using namespace std;
const int N=1e6+10000;
int prime[N];
int n;
bool st[N];
int main()
{
    scanf("%d",&n);
    int cnt=0;
    memset(st,false,sizeof st);
    for(int i=2;i<=n;i++)
    {
        if(!st[i]) prime[++cnt]=i;
        for(int j=1;prime[j]<=n/i&&j<=cnt;j++)
        {
            st[prime[j]*i]=true;
            if(i%prime[j]==0) break;
        }
    }
    
    cout<<cnt<<endl;
}