如何用python解决
时间: 2023-07-19 16:43:32 浏览: 99
要用Python解决ZOJ2483这个计算几何问题,可以按照以下步骤进行:
1. 定义圆的类Circle,包含圆心坐标和半径信息,以及计算两个圆交点的方法intersect。
```python
class Circle:
def __init__(self, x, y, r):
self.x = x
self.y = y
self.r = r
def intersect(self, other):
d = ((self.x - other.x) ** 2 + (self.y - other.y) ** 2) ** 0.5
if d > self.r + other.r or d < abs(self.r - other.r):
return None
a = (self.r ** 2 - other.r ** 2 + d ** 2) / (2 * d)
h = (self.r ** 2 - a ** 2) ** 0.5
x2 = self.x + a * (other.x - self.x) / d
y2 = self.y + a * (other.y - self.y) / d
x3_1 = x2 + h * (other.y - self.y) / d
x3_2 = x2 - h * (other.y - self.y) / d
y3_1 = y2 - h * (other.x - self.x) / d
y3_2 = y2 + h * (other.x - self.x) / d
if x3_1 == x3_2 and y3_1 == y3_2:
return (x3_1, y3_1)
else:
return [(x3_1, y3_1), (x3_2, y3_2)]
```
2. 读入输入数据,创建两个圆的对象。
```python
x1, y1, r1 = map(float, input().split())
x2, y2, r2 = map(float, input().split())
c1 = Circle(x1, y1, r1)
c2 = Circle(x2, y2, r2)
```
3. 计算两个圆的交点,并判断是否有交点。
```python
inter_points = c1.intersect(c2)
if inter_points is None:
print(0)
exit()
```
4. 计算交点构成的图形的面积。
```python
if type(inter_points) == list:
x1, y1 = inter_points[0]
x2, y2 = inter_points[1]
area = abs((x1 - x2) * (y1 - y2))
else:
area = 0
print(round(area + c1.r ** 2 * math.acos((d ** 2 + r1 ** 2 - r2 ** 2) / (2 * d * r1)) + c2.r ** 2 * math.acos((d ** 2 + r2 ** 2 - r1 ** 2) / (2 * d * r2)) - 0.5 * ((-d + r1 + r2) * (d + r1 - r2) * (d - r1 + r2) * (d + r1 + r2)) ** 0.5, 2))
```
完整代码如下:
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