UVA 10167 Birthday Cake

分析

对于一条直线Ax+By=0，如果一点(a,b)满足Aa+Bb>0则该点位于该直线上方，满足Aa+Bb<0则该点位于该直线下方，满足Aa+Bb=0则该点位于该直线上。
直接枚举所有可能的A、B，只要上方和下方的个数均等于N，枚举结束。

思路

因为如果存在一颗樱桃在这个切割线上，那么一定不能如此切割，所以如果存在一点在该线上，那么可以跳过这组(A,B)，适当剪枝。

代码

#include <cstdio>#define MAX_N 52int cherries[MAX_N<<1][2];int N;void solve(){    for (int A = -100; A <= 100; A++)        for (int B = -100; B <= 100; B++) {            int u = 0, d = 0;            for (int i = 0; i < (N<<1); i++)                if      (A*cherries[i][0] + B*cherries[i][1] > 0) u++;                else if (A*cherries[i][0] + B*cherries[i][1] < 0) d++;                else break;            if (u == N && d == N) {                printf("%d %d\n", A, B);                return;            }        }}int main(){    while (scanf("%d", &N), N) {        for (int i = 0; i < (N<<1); i++)            scanf("%d%d", &cherries[i][0], &cherries[i][1]);        solve();    }    return 0;}

题目

Description

Lucy and Lily are twins. Today is their birthday.Mother buys a birthday cake for them. Now we put the cake onto a Descartes coordinate. Its center is at (0, 0), and the cake’s length of radius is 100.

There are 2 N (N is a integer, 1 ≤ N ≤ 50) cherries on the cake. Mother wants to cut the cake into two halves with a knife (of course a beeline). The twins would like to be treated fairly, that means, the shape of the two halves must be the same (that means the beeline must go through the center of the cake) , and each half must have N cherrie(s). Can you help her?

Note: the coordinate of a cherry (x, y) are two integers. You must give the line as form two integers A, B (stands for Ax + By = 0) each number mustn’t in [−500, 500]. Cherries are not allowed lying on the beeline. For each data set there is at least one solution.

Input

The input file contains several scenarios. Each of them consists of 2 parts:
The first part consists of a line with a number N, the second part consists of 2 N lines, each line has two number, meaning (x, y). There is only one space between two border numbers. The input file is ended with N = 0.

Output

For each scenario, print a line containing two numbers A and B. There should be a space between them. If there are many solutions, you can only print one of them.

Sample Input

2
-20 20
-30 20
-10 -50
10 -5
0

Sample Output

0 1