江苏省赛 JSCPC2018 K. 2018

题目 K. 2018

Given a,b,c,d, find out the number of pairs of integers (x,y) where a ≤ x ≤ b,c ≤ y ≤ d and x·y is a multiple of 2018.

Input

The input consists of several test cases and is terminated by end-of-file. Each test case contains four integers a,b,c,d.

Output

For each test case, print an integer which denotes the result.
Constraint • 1≤ a ≤ b ≤109,1≤ c ≤ d ≤109 • The number of tests cases does not exceed 104.

Sample Input

1 2 1 2018
1 2018 1 2018
1 1000000000 1 1000000000

Sample Output

3
6051
1485883320325200

题解

• 给两个区间，分别在两个区间内选一个数x、y，满足x*y=2018
• 问：存在多少对这样的数

代码

#include 
#include 
using namespace std;

const int NUM[] = {1, 2, 1009, 2018};

void count(int n, int* cnt)
{
    cnt[3] = n / 2018;
    cnt[2] = n / 1009 - cnt[3];
    cnt[1] = n / 2 - cnt[3];
    cnt[0] = n - cnt[1] - cnt[2] - cnt[3];
}

long long solve(int n,  int m)
{
    static int a[4], b[4];
    count(n, a);
    count(m, b);
    long long result = 0;
    for (int i = 0; i < 4; ++ i) {
        for (int j = 0; j < 4; ++ j) {
            if (NUM[i] * NUM[j] % 2018 == 0) {
                result += 1LL * a[i] * b[j];
            }
        }
    }
    return result;
}

int main()
{
    int a, b, c, d;
    while (scanf("%d%d%d%d", &a, &b, &c, &d) == 4) {
        a --, c --;
        std::cout << solve(b, d) - solve(a, d) - solve(b, c) + solve(a, c) << std::endl;
    }
}