G - Harmonic Number (II) （数列求和+找规律）

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最新推荐文章于 2024-08-17 23:39:22 发布

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G - Harmonic Number (II) （数列求和+找规律）

I was trying to solve problem '1234 - Harmonic Number', I wrote the following code

long long H( int n ) {
  long long res = 0;
  for( int i = 1; i <= n; i++ )
res = res + n / i;
  return res;
}

Yes, my error was that I was using the integer divisions only. However, you are given n, you have to find H(n) as in my code.

Input

Input starts with an integer T (≤ 1000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n < 231).

Output

For each case, print the case number and H(n) calculated by the code.

Sample Input

2147483647

Sample Output

Case 1: 1

Case 2: 3

Case 3: 5

Case 4: 8

Case 5: 10

Case 6: 14

Case 7: 16

Case 8: 20

Case 9: 23

Case 10: 27

Case 11: 46475828386

题意：给出一个数n，求n/1+n/2+n/3+...+n/n。

思路：都是正整数运算，但数据范围是从1到2^31，且一个点有1000个测试数据，暴力绝对t。我们发现，若是整数运算，则100/34=2,100/50=2，所以从34到50都是2，就可以进行分块处理。

代码：

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

int main()
{
    ll n,i,j,listt;
    cin >> listt;
    for ( int ji=1; ji<=listt; ji++ ) {
        cin >> n;
        ll ans = 0;
        for ( ll i=1; i<=n; i+=(j-i+1) ) {
            ll now = n/i;
            j = n/now;
            ans += now*(j-i+1);
        }

        cout << "Case " << ji << ": ";
        cout << ans << endl;
    }

    return 0;
}