Python 检查四个线段是否形成一个矩形(Check if four segments form a rectangle)_判断给定的 4 4个坐标能否组成矩形。 python-优快云博客

我们有四条线段作为其端点的一对坐标。我们需要判断这四条线段是否构成矩形。
示例：

输入：segment[] = [(4, 2), (7, 5),
(2, 4), (4, 2),
(2, 4), (5, 7),
(5, 7), (7, 5)]
输出：
是给定这些线段，可以组成一个长度为 3X2 的矩形。

输入：segment[] = [(7, 0), (10, 0),
(7, 0), (7, 3),
(7, 3), (10, 2),
(10, 2), (10, 0)]
输出：否
这些线段不能组成矩形。

上述示例如下所示：
这个问题主要是：如何检查给定的四个点是否形成一个正方形
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我们可以通过使用矩形的属性来解决这个问题。首先，我们检查线段的唯一端点总数，如果这些点的数量不等于 4，则线段不能构成矩形。然后我们检查所有点对之间的距离，最多应该有 3 个不同的距离，一个用于对角线，两个用于边，最后我们将检查这三个距离之间的关系，对于构成矩形的线段，这些距离应该满足勾股关系，因为矩形的边和对角线构成直角三角形。如果它们满足上述条件，那么我们将线段构成的多边形标记为矩形，否则不是。

示例代码：

# Python program to check whether it is possible
# to make a rectangle from 4 segments
N = 4

# Utility method to return square of distance
# between two points
def getDis(a, b):
return (a[0] - b[0])*(a[0] - b[0]) + (a[1] - b[1])*(a[1] - b[1])

# method returns true if line Segments make
# a rectangle
def isPossibleRectangle(segments):

st = set()

# putting all end points in a set to
# count total unique points
for i in range(N):
st.add((segments[i][0], segments[i][1]))
st.add((segments[i][2], segments[i][3]))

# If total unique points are not 4, then
# they can't make a rectangle
if len(st) != 4:
return False

# dist will store unique 'square of distances'
dist = set()

# calculating distance between all pair of
# end points of line segments
for it1 in st:
for it2 in st:
if it1 != it2:
dist.add(getDis(it1, it2))

# if total unique distance are more than 3,
# then line segment can't make a rectangle
if len(dist) > 3:
return False

# copying distance into array. Note that set maintains
# sorted order.
distance = []
for x in dist:
distance.append(x)

# Sort the distance list, as set in python, does not sort the elements by default.
distance.sort()

# If line seqments form a square
if len(dist) ==2 :
return (2*distance[0] == distance[1])

# distance of sides should satisfy pythagorean
# theorem
return (distance[0] + distance[1] == distance[2])

# Driver code to test above methods
segments = [
[4, 2, 7, 5],
[2, 4, 4, 2],
[2, 4, 5, 7],
[5, 7, 7, 5]
]

if(isPossibleRectangle(segments) == True):
print("Yes")
else:
print("No")

# The code is contributed by Nidhi goel.