HDU 2620 - Ice Rain (数学)
题意
求 $ \sum _{i = 1}^{n} k \bmod i$
思路
$a \bmod b = a - b* \lfloor \frac {a}{b} \rfloor$
所以$ans = kn - 1 * \lfloor \frac {k}{1} \rfloor - 2 \lfloor \frac {k}{2} \rfloor - … - n * \lfloor \frac {k}{n} \rfloor$
可以成段统计。
计算出某个 $ \lfloor \frac {k}{a} \rfloor = \lfloor \frac {k}{b} \rfloor$的区间$a~b$
代码
#include <stack>
#include <cstdio>
#include <list>
#include <cassert>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <cstring>
#include <algorithm>
#include <cctype>
#include <string>
#include <map>
#include <cmath>
using namespace std;
#define LL long long
#define ULL unsigned long long
#define SZ(x) (int)x.size()
#define Lowbit(x) ((x) & (-x))
#define MP(a, b) make_pair(a, b)
#define MS(arr, num) memset(arr, num, sizeof(arr))
#define PB push_back
#define X first
#define Y second
#define ROP freopen("input.txt", "r", stdin);
#define MID(a, b) (a + ((b - a) >> 1))
#define LC rt << 1, l, mid
#define RC rt << 1|1, mid + 1, r
#define LRT rt << 1
#define RRT rt << 1|1
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const int MAXN = 2e3 + 10;
const int MOD = 1e9 + 7;
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
const int hash_size = 4e5 + 10;
int cases = 0;
typedef pair<int, int> pii;
int main()
{
LL n, k;
while (cin >> n >> k)
{
LL ans = n*k;
if (n > k) n = k;
for (int i = 1; i <= n; )
{
LL a = k / i;
LL ed = k / a;
if (ed > n) ed = n;
ans -= (i + ed) * (ed - i + 1) / 2 * a;
i = ed+1;
}
cout << ans << endl;
}
return 0;
}