Find Four points such that they form a square whose sides are parallel to x and y axes
Given ‘n’ pair of points, the task is to find four points such that they form a square whose sides are parallel to x and y axes or print “No such square” otherwise. If more than one square is possible then choose the one with the maximum area.
Input : n = 6, points = (1, 1), (4, 4), (3, 4), (4, 3), (1, 4), (4, 1)
Output : side of the square is : 3, points of the square are 1, 1 4, 1 1, 4 4, 4
Explanation: The points 1, 1 4, 1 1, 4 4, 4 form a square of side 3
Input :n= 6, points= (1, 1), (4, 5), (3, 4), (4, 3), (7, 4), (3, 1)
Output :No such square
Simple approach: Choose all possible pairs of points with four nested loops and then see if the points form a square which is parallel to principal axes. If yes then check if it is the largest square so far in terms of the area and store the result, and then display the result at the end of the program. Time Complexity: O(N^4) Efficient Approach: Create a nested loop for the top right and bottom left corner of the square and form a square with those two points, then check if the other two points were assumed actually exist. To check if a point exists or not, create a map and store the points on the map to reduce the time to check whether the points exist. Also, keep in check the largest square by area so far and print it in the end.
Below is the implementation of the above approach:
Side of the square is : 3, points of the square are 1, 1 4, 1 1, 4 4, 4
Time Complexity: O(N^2)
Auxiliary Space: O(N)