Given the length L and breadth B of a sheet of paper, the task is to find the maximum number of rectangles with given length l and breadth b that can be cut from this sheet of paper.
Input: L = 5, B = 2, l = 14, b = 3
The sheet is smaller than the required rectangle. So, no rectangle of the given dimension can be cut from the sheet.
Input: L = 10, B = 7, l = 4, b = 3
- Try to cut the rectangles horizontally i.e. length of the rectangle is aligned with the length of the sheet and breadth of the rectangle is aligned with the breadth of the sheet and store the count of rectangles possible in horizontal.
- Repeat the same with vertical alignment i.e. when length of the rectangle is aligned with the breadth of the sheet and breadth of the rectangle is aligned with the length of the sheet and store the result in vertical. Print max(horizontal, vertical) as the result.
Below is the implementation of the above approach:
# Python3 implementation of the approach
# Function to return the maximum
# rectangles possible
def maxRectangles(L, B, l, b):
horizontal, vertical = 0, 0
# Cut rectangles horizontally if possible
if l <= L and b <= B: # One rectangle is a single cell columns = B // b rows = L // l # Total rectangles = total cells horizontal = rows * columns # Cut rectangles vertically if possible if l <= B and b <= L: columns = L // b rows = B // l vertical = rows * columns # Return the maximum possible rectangles return max(horizontal, vertical) # Driver code if __name__ == "__main__": L, B, l, b = 10, 7, 4, 3 print(maxRectangles(L, B, l, b)) # This code is contributed by Rituraj Jain [tabby title = "C#"]
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- Count the number of rectangles such that ratio of sides lies in the range [a,b]
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