Given the coordinates of any two vertices of a square (X1, Y1) and (X2, Y2), the task is to find the coordinates of the other two vertices. If a square cannot be formed using these two vertices, print -1.
Input: X1 = 1, Y1 = 2, X2 = 3, Y2 = 4
Output: (1, 4), (3, 2)
From the above figure the other two vertices of the square will be (1, 4) and (3, 2).
Input: X1 = -5, Y1 = 5, X2 = 5, Y2 = -5
Output: (-5, -5), (5, 5)
Approach: The approach is based on the fact that the length of all the sides of a square are equal. If no such vertices can be obtained for which the length of all the sides become equal, then print “-1”. Follow the steps below to solve the problem:
- The given two vertices can either be the vertices of the side of the square or the vertices of the diagonal.
- If the x-coordinates of the given two vertices are equal then the coordinates of the other two vertices will be:
(X1 + Y2 – Y1, Y1) and (X2 + Y2 – Y1, Y2)
- If the y-coordinates of the given two vertices are equal, then the coordinates of the other two vertices will be:
(X1, Y1 + X2 – X1) and (X2, Y2 + X2 – X1)
- Otherwise, the given coordinates are of the diagonal of the square. Therefore, the coordinates of the other two vertices will be:
(X1, Y2) and (X2, Y1)
Below is the implementation of the above approach:
1, 4 3, 2
Time Complexity: O(1)
Auxiliary Space: O(1)
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