Given a rectangle of height H and width W which has the bottom left corner at (0, 0). The task is to count the number of distinct Rhombi that have all points inside or on the border of the rectangle satisfying the following conditions exists:
- Have non-zero area.
- Have diagonals parallel to the x and y axes.
- Have integer coordinates.
Input: H = 2, W = 2
There is only one rhombus possible with coordinates (0, 1), (1, 0), (2, 1) and (1, 2).
Input: H = 4, W = 4
Approach: Since the diagonals are parallel to the axis, let’s try fixing the diagonals and creating rhombi on them. For the rhombus to have integer coordinates, the length of the diagonals must be even. Let’s fix the length of the diagonals to i and j, the number of rhombi we can form with these diagonal lengths inside the rectangle would be (H – i + 1) * (W – j + 1). Thus, we iterate over all possible values of i and j and update the count.
Below is the implementation of the above approach:
Time Complexity: O(H * W)
- Find the number of rectangles of size 2*1 which can be placed inside a rectangle of size n*m
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- Sum of Area of all possible square inside a rectangle
- Check if a point lies on or inside a rectangle | Set-2
- Check whether a given point lies inside a rectangle or not
- Check whether a given point lies on or inside the rectangle | Set 3
- Count number of squares in a rectangle
- Count Integral points inside a Triangle
- Number of visible boxes after putting one inside another
- Ratio of area of a rectangle with the rectangle inscribed in it
- Largest subset of rectangles such that no rectangle fit in any other rectangle
- Possible number of Rectangle and Squares with the given set of elements
- Number of squares of maximum area in a rectangle
- Number of squares of side length required to cover an N*M rectangle
- Count of sub-sets of size n with total element sum divisible by 3
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