#include<bits/stdc++.h>
using namespace std;
long long n;
int main()
{
	cin>>n;
	cout<<n-int(sqrt(n));
	return 0;
}
o(1)即可求解

思路

这道题看似很难，其实很~难~简单，只要我们算出 $\sqrt{n}$，对它向下取整，然后输出 $n-\sqrt{n}$ 即可！

代码

#include <bits/stdc++.h>
using namespace std;
int n;//定义
int main() {
	cin >> n;//输入
	cout << n - int(sqrt(n));//计算并输出
	return 0;//程序拜拜
}

#include<bits/stdc++.h>
using namespace std;
int a[1005],n;
int main(){
	cin>>n;
	cout<<int(n-sqrt(n))+(int(sqrt(n))*sqrt(n)!=n);
    return 0;
}

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n;
signed main(){
cin>>n;
cout<<n-(long long)sqrt(n);
return 0;
}

• 每个数只会被它的因数翻转，一个数会被翻转它 $\leq n$ 的因数个数次。
• 这里最大数是 $n$ 且翻转 $n$ 次，也就是一个数会被翻转它的因数个数次。
• 那么由题意得被翻转偶数次才会黑色朝上，所以即求 $[1,n]$ 因数个数为偶数的数。
• 因数个数为偶数的数不好求，求因数个数为奇数的数。
• 因为因数是成对出现的，所以因数个数为奇数的数是一定完全平方数。
• $[1,n]$ 的完全平方数个数为 $\lfloor\sqrt{n}\rfloor$，所以答案为 $n-\lfloor\sqrt{n}\rfloor$。

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