Popping Balloons 气球的问题

Question

Problem Description
John loves programming contests. There is just one problem: his team is not very good at programming. This usually doesn't bother him, but what does bother him is that everyone gets a balloon for every correct submission. John's team never gets any balloons, while other teams get one balloon after the other. This frustrates him, so John would like to see that all other teams have no balloons either.
This year he has a plan to achieve just that. John has hired a ninja to pop all balloons for him. At any time during the contest, he can call for the ninja to come down through a hole in the ceiling and pop all balloons by using his shurikens (ninja stars), before leaving through the hole in the ceiling again. Of course the ninja wants to use as few of his precious shurikens as possible. Therefore, John must write a program that computes how many shurikens are needed to pop all balloons. Because all balloons are usually at approximately the same height, he can model the problem as a 2-dimensional problem. He sets the location of the ninja (where he comes in) as the origin (0, 0) and uses circles to model the balloons. To be on the safe side, these circles can have different radii. Shurikens are assumed to be thrown from the origin and move in a straight line. Any circle/balloon crossed by this haline will be popped by this shuriken. The question then becomes: how many halines rooted at the origin are necessary to cross all circles?
Of course, as mentioned above, John is not a very good programmer, so he asks you to make this program for him. Can you help him out? You might get a balloon if you get it right...

Input
The first line of the input contains a single number: the number of test cases to follow. Each test case has the following format:
1.One line with a single integer n (0 <= n <= 1,000): the number of balloons.
2.n lines, each containing three integers xi,yi (-10^4 <= xi,yi <= 10^4), and ri (1 <= ri <= 10^4),describing the circle used to model the ith balloon, where (xi, yi) is the center of the circle and ri is the radius.
You can assume that two lines (rooted at the origin) that are tangent to two distinct circles make an angle of at least 10^-6 radians at the origin. Furthermore, the circles do not cross each other (but can touch) and do not contain the origin.

Output
For every test case in the input, the output should contain one integer on a single line: the minimum number of shurikens the ninja needs to pop all balloons.

Sample Input
2
5
2 0 1
5 0 2
0 3 2
-4 0 2
0 -2 1
5
4 1 3
5 -5 3
0 -4 2
-4 4 3
-10 3 3

Sample Output
4
3

Answer 1

以下回答参考 皆我百晓生、券券喵儿 等免费微信小程序相关内容作答，并由本人整理回复。

# 读取数据
input = readLines()

# 定义函数计算最小的shuriken数量
def calculate_min_shuriken(balloons):
    # 初始化最小shuriken数量为inf
    min_shuriken = float('inf')
    
    # 遍历每一个balloon
    for i in range(len(balloons)):
        # 计算当前balloon与origin的距离
        distance = sqrt((balloons[i][0])**2 + (balloons[i][1])**2)
        
        # 如果当前balloon距离origin小于等于shuriken的最大半径，则将最小shuriken数量更新为当前位置的shuriken数量
        if distance <= balloons[i][2]:
            min_shuriken = min(min_shuriken, i+1)
            
    return min_shuriken

# 遍历所有的测试案例
for i in range(1, len(input)+1):
    # 从输入中获取第i个测试案例的数据
    balloons = [list(map(int, line.split())) for line in input[i-1].split('\n')]
    
    # 调用calculate_min_shuriken函数并打印结果
    print(calculate_min_shuriken(balloons))

注意：这个程序可能会有一些问题。例如，如果两个或多个圆相交，那么它们可能无法通过相同的shuriken来穿过所有这些圆。此外，对于一些特定的情况（比如一个大圆和一个小圆相交），这个程序可能不会给出正确的答案。