Harmonic Number (II)
Description
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
11
1
2
3
4
5
6
7
8
9
10
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
思路:类似分块的思想最多有2sqrt（n）个数；
#include<bits/stdc++.h> using namespace std; #define ll long long #define esp 0.00000000001 #define pi 4*atan(1) const int N=1e3+10,M=1e7+10,inf=1e9+10,mod=1e9+7; int main() { int T,cas=1; scanf("%d",&T); while(T--) { ll x; scanf("%lld",&x); ll ans=0; for(ll i=1;i*i<=x;i++) { if(i!=x/i) ans+=x/i; ll len=(x/i)-x/(i+1); ans+=i*len; } printf("Case %d: %lld ",cas++,ans); } return 0; }