1245-harmonic Number (II) (law problem)

1245-harmonic Number (II)

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Time Limit:3 second (s)

Memory limit:32 MB

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 is that I was using the the integer divisionsonly. However, you were given n, you had to find H (n) as in Mycode.

Input

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

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

Output

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

Sample Input	Output for Sample Input
11 1 2 3 4 5 6 7 8 9 10 2147483647	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 11:46,475,828,386

The solution, own ideas, but can not write out, read the answer, it is quite simple;

First look at two examples 1.N =   &NBSP;SQRT (Ten) = 3     10/SQRT (x) = 3i        1   2   3 &NB Sp       4   5   6   7   8   9   10n/i    10  5   3   & nbsp     2   2   1   1   1   1    1 m =  n/isum + = M;m = 1 Number 10/1-10/2 = 5;m = 2 the number of 10/2-10/3 = 2;m = 3 10/3-10/4 = 1;&NBSP;2.N =   &NBSP;&NBSP;SQRT (4     20/SQRT (20) = 5i        1   2   3   4       5   6   7   8   9 &nbs P               ( ), 20n/i   &NBSP;20 &NBSP;10 6   5       4   3   2   2   2    2     1   &nbsp ; 1     1     1     1     1     1     1    1   &N Bsp;1&nbsP;m =  n/isum + = M;m = 1 Number 20/1-20/2 = 10;m = 2 Number 20/2-20/3 = 4;m = 3 Number 20/3-20/4 = 1;m = 4 Number 20/4-20/5 = 1;...M = i Number 20/i-20/(i + 1) (1<= i <= sqrt (n))   So we can conclude that the number of sqrt (n) before we can directly use the For loop to find the sum + + + (sqrt-n/i (i + 1)) * I; When sqrt (n) = N/sqrt (n) (such as the first example 10,sum added a 3), Sum added a sqrt (n), minus the words, here output%i64d unexpectedly wa ... Code:

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <cmath>5#include <algorithm>6 #defineMem (x, y) memset (x,y,sizeof (x))7 using namespacestd;8typedefLong LongLL;9 Const intinf=0x3f3f3f3f;Ten  One intMain () { A     intT; -     intN,cnt=0; - LL Res; thescanf"%d",&T); -      while(t--){ -res=0; -scanf"%d",&n); +         intm=sqrt (n); -          for(intI=1; i<=m;i++) res+=n/i; +          for(intI=1; i<=m;i++) Ares+= (n/i-n/(i+1))*i; at             if(m==n/m) res-=m; -printf"Case %d:%lld\n",++cnt,res); -     } -     return 0; -}

1245-harmonic Number (II) (law problem)