检查给定的二维点是否形成 T 形

给定 5 个二维点的坐标，检查它们是否形成封闭的 T 形。如果它们形成 T 形，则打印“是”，否则打印“否”。注意：坐标应该是不同的和整数。
根据给定的条件，有 4 种可能的 T 形结构：

例子：

Input: [[7, 5], [8, 5], [6, 5], [7, 7], [7, 6]]
Output: Yes

Input: [[0, 0], [1, 0], [2, 0], [1, -1], [1, -2]]
Output: Yes

方法：

1. 将给定列表中的第一个点视为中心 (x, y)（即形成 T 形的两条线的交点）。
2. 然后检查形成以 (x, y) 为中心的 T 形所需的所有点是否存在于给定点的列表中。
3. 检查所有 4 种可能的 T 形图案。

下面是上述方法的实现：

Python3

# Python3 code to check if given 5
# 2-D points form T-shape or not
 
# Import the function to initialize the
# dictionary with a specific value
from collections import defaultdict
 
# This function checks if the points
# form T-shape pointing up
 
 
def isUpDirected(point, x, y):
 
    return (point[(x-1, y)] and
            point[(x, y)] and
            point[(x + 1, y)] and
            point[(x, y-1)] and
            point[(x, y-2)])
 
# This function checks if the points
# form T-shape pointing down
 
 
def isDownDirected(point, x, y):
 
    return (point[(x-1, y)] and
            point[(x, y)] and
            point[(x + 1, y)] and
            point[(x, y + 1)] and
            point[(x, y + 2)])
 
# This function checks if the points
# form T-shape pointing left
 
 
def isLeftDirected(point, x, y):
 
    return (point[(x, y + 1)] and
            point[(x, y)] and
            point[(x, y-1)] and
            point[(x + 1, y)] and
            point[(x + 2, y)])
 
# This function checks if the points
# form T-shape pointing right
 
 
def isRightDirected(point, x, y):
 
    return (point[(x, y + 1)] and
            point[(x, y)] and
            point[(x, y-1)] and
            point[(x-1, y)] and
            point[(x-2, y)])
 
 
# This function checks if given points
# form a T-shape or not
def solve(grid):
 
    # Initialize the dictionary with False value
    point = defaultdict(lambda: False)
    flag = False
 
    for i in range(len(grid)):
 
        # Assign True value to the points which
        # are present in the given list
        point[(grid[i][0], grid[i][1])] = True
 
    for i in range(len(grid)):
 
        # Check if the given points form any of the
        # 4 possible T-shaped formations
        if isUpDirected(point, grid[i][0], grid[i][1]) or
           isDownDirected(point, grid[i][0], grid[i][1]) or
            isLeftDirected(point, grid[i][0], grid[i][1]) or
            isRightDirected(point, grid[i][0], grid[i][1]):
 
            flag = True
            break
 
    if flag == True:
        return 'Yes'
    else:
        return 'No'
 
 
print(solve([[7, 5], [8, 5], [6, 5], [7, 7], [7, 6]]))
print(solve([[0, 0], [1, 0], [2, 0], [1, -1], [1, -2]]))

输出：

Yes
Yes

时间复杂度： O(1)