Check if the given 2-D points form T-shape or not

Given the coordinates of 5 2-dimensional points, check if they form a closed T shape. Print ‘Yes’ if they form T shape and ‘No’ otherwise. Note: Coordinates should be distinct and integers.

There are 4-types of T shaped formations possible according to the given conditions:

Examples:

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


Approach:

  1. Consider the first point in the given list as the centre (x, y) (i.e intersection of the two lines that form T-shape).
  2. Then check if all the points which are needed to form T-shape of which (x, y) is the centre are present in the list of given points or not.
  3. Check this for all the 4 possible patterns of T-shape.
  4. Repeat this process from step-1 for all points in the list until a solution is found.

Below is the implementation of the above approach:

# 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]]))

Output:

Yes
Yes

Time Complexity: O(1)



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I am currently pursuing BTech in ICT (Information and Communication Technology) I like competitive programming and solving algorithmic problems I am always excited about learning new technologies and have recently developed interest in Machine Learning I love to share my knowledge with others

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