在一组数据中,如何用最小的边界范围选择出尽可能多的数据,用python实现一下
时间: 2024-01-21 17:16:06 浏览: 71
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这个问题可以通过求最小矩形边界框(Minimum Bounding Rectangle,MBR)来解决。MBR是一个矩形,它包含了所有数据点,且矩形的面积最小。
下面是用Python实现该算法的代码:
```python
import numpy as np
def minimum_bounding_rectangle(points):
"""
计算点集的最小边界矩形
:param points: 点集,每个点是一个二维坐标(x,y)
:return: 最小边界矩形,即左下角和右上角坐标
"""
# 将点集按x轴排序
points = sorted(points, key=lambda x: x[0])
# 初始化最小边界矩形
min_rect = None
for i in range(len(points)):
for j in range(i+1, len(points)):
# 计算矩形的左下角和右上角坐标
x1, y1 = points[i]
x2, y2 = points[j]
left = min(x1, x2)
bottom = min(y1, y2)
right = max(x1, x2)
top = max(y1, y2)
# 计算矩形的面积
area = (right - left) * (top - bottom)
# 更新最小边界矩形
if min_rect is None or area < min_rect[2]:
min_rect = (left, bottom, area)
# 计算最小边界矩形的右上角坐标
left, bottom, area = min_rect
for i in range(len(points)):
x, y = points[i]
if left <= x <= left + np.sqrt(area) and bottom <= y <= bottom + np.sqrt(area):
right = max(right, x)
top = max(top, y)
return (left, bottom, right, top)
```
下面是一个简单的测试:
```python
points = [(1, 2), (3, 4), (5, 6), (7, 8), (9, 10)]
min_rect = minimum_bounding_rectangle(points)
print(min_rect)
```
输出结果为:
```
(1, 2, 9, 10)
```
这表示点集最小边界矩形的左下角坐标为(1,2),右上角坐标为(9,10)。
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