Kattis - Tractor

最新推荐文章于 2022-06-07 14:00:04 发布

原创最新推荐文章于 2022-06-07 14:00:04 发布 · 490 阅读

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Bessie偷走了拖拉机，在坐标平面上的矩形农场内冒险。每次只能沿着正x轴或正y轴方向移动，且第n次移动会前进2^(n-1)个单位。本篇探讨了在给定农场尺寸的情况下，Bessie能够到达的所有可能位置。

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Bessie the Cow has stolen Farmer John’s tractor and is running wild on the coordinate plane! She, however, is a terrible driver, and can only move according to the following rules:

Each of her movements is in the same direction as either the positive x-axis or the positive y-axis.
Her nth movement takes her 2n−1 units forward in her chosen direction. (On her first movement, n=1, so she moves 1 unit.)

Farmer John’s farm is on the coordinate plane, in the shape of a rectangle with corners at (0,0), (A,0), (0,B) and (A,B). If Bessie starts at (0,0), how many points inside the farm, including the boundary, could she reach?

Input

The input begins with an integer N (1≤N≤100) on a line by itself, indicating the number of test cases that follow. Each of the following N lines contains two space separated integers A and B (1≤A,B≤108), describing the upper-right corner of Farmer John’s farm.

Output

Output N lines, with the Nth line containing the number of points that Bessie could possibly reach in the Nth test case.

In the first test case of the sample, Bessie can reach the following six points: (0,0), (0,1), (1,0), (1,2), (2,1) and (3,0).

Sample Input 1	Sample Output 1
2 2 3 7 7	6 15

一开始没看到数据大小是10^8，用bfs做结果超时了……后来想了一下大概是个数学问题

#include <iostream>
#include <string>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <stack>
#include <set>
#include <queue>
#include <map>
#include <algorithm>
using namespace std;
int t, a, b;
int main() {
    cin >> t;
    while (t--) {
        cin >> a >> b;
        int ans = 0;
        for (int i = 1; ; i = i * 2 + 1) {
            int y1 = max(0, i - b), y2 = min(a, i);
            if (y1 > a) break;
            ans += abs(y1 - y2) + 1;
        }
        cout << ans + 1 << endl;
    }
}