lightoj 1245 - Harmonic Number (II) 【数学 计数】

1245 - Harmonic Number (II)

PDF (English)

Statistics

Forum

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 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	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: 46475828386

 

PROBLEM SETTER: JANE ALAM JAN

题意：给你一个n，让你按照给出的程序求解结果。

太弱了，比赛时没找到规律。。。

令m = sqrt(n)。
ans = sigma( (n / i - n / (i+1)) * i) + n / i)。【1 <= i <= m】
ans -= n / m == m ? n / m : 0。

AC代码：

#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <vector>
#define INF 0x3f3f3f3f
#define eps 1e-8
#define MAXN (100000+10)
#define MAXM (50000000)
#define Ri(a) scanf("%d", &a)
#define Rl(a) scanf("%lld", &a)
#define Rf(a) scanf("%lf", &a)
#define Rs(a) scanf("%s", a)
#define Pi(a) printf("%d\n", (a))
#define Pf(a) printf("%lf\n", (a))
#define Pl(a) printf("%lld\n", (a))
#define Ps(a) printf("%s\n", (a))
#define W(a) while(a--)
#define CLR(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define LL long long
#define lson o<<1, l, mid
#define rson o<<1|1, mid+1, r
#define ll o<<1
#define rr o<<1|1
using namespace std;
int main()
{
int t; Ri(t);
int kcase = 1;
W(t)
{
LL n; Rl(n);
LL ans = 0;
LL m = sqrt(n);
for(LL i = 1; i <= m; i++)
ans += (n / i - n / (i+1)) * i + n / i;
if(m == n / m)
ans -= n / m;
printf("Case %d: %lld\n", kcase++, ans);
}
return 0;
}