给定5个2维点的坐标,请检查它们是否形成闭合的T形。如果它们形成T形,则打印“是”,否则,则打印“否”。注意:坐标应该是不同的并且是整数。
根据给定条件,可能有4种类型的T形地层:
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:
- 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)。
- 然后检查在给定点列表中是否存在形成(x,y)为中心的T形所需的所有点。
- 选中所有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)
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