Count of rectangles possible from N and M straight lines parallel to X and Y axis respectively
Given two integers N and M, where N straight lines are parallel to the X-axis and M straight lines are parallel to Y-axis, the task is to calculate the number of rectangles that can be formed by these lines.
Input: N = 3, M = 6
There are total 45 rectangles possible with 3 lines parallel to x axis and 6 lines parallel to y axis.
Input: N = 2, M = 4
There are total 6 rectangles possible with 2 lines parallel to x axis and 4 lines parallel to y axis.
To solve the problem mentioned above we need to observe that a rectangle is formed by 4 straight lines in which opposite sides are parallel and the angle between any two sides is 90. Hence, for every rectangle, two sides need to be parallel to X-axis and the other two sides need to be parallel to Y-axis.
- Number of ways to select two lines parallel to X axis = NC2 and the Number of ways to select two lines parallel to Y axis = MC2 .
- So the total number of rectangles = NC2 * MC2 = [ N * (N – 1) / 2 ] * [ M * (M – 1) / 2 ]
Below is implementation of above approach:
Time Complexity: O(1), as constant operations are being performed.
Auxiliary Space: O(1), as constant space is being used.