Problem
On each move, choose one rectangle and cut all the way across it, parallel to a side, making two rectangles with positive integer side lengths. Continue until every piece is a square. Squares may have different sizes. Count cuts, not pieces.
Implement rectangle_cutting(height, width).
Input
height: The starting rectangle height.
width: The starting rectangle width.
Output
Return the minimum number of cuts.
Constraints
1 ≤ height, width ≤ 500. Rotation does not change the answer.
Examples
Input:
width = 3
height = 2
Expected output:
expected = 2Input:
long long width = 3;
long long height = 2;
Expected output:
long long expected = 2;Input:
long width = 3;
long height = 2;
Expected output:
long expected = 2;Explanation
Cut off a 2 × 2 square, leaving a 2 × 1 rectangle. One more cut splits the remainder into two unit squares.
Input:
width = 4
height = 4
Expected output:
expected = 0Input:
long long width = 4;
long long height = 4;
Expected output:
long long expected = 0;Input:
long width = 4;
long height = 4;
Expected output:
long expected = 0;Explanation
The starting rectangle is already a square.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
A rectangle can be solved by splitting it into two smaller rectangles and combining their best answers.
Hint 2
Try every possible horizontal and vertical cut to find the minimum.
Hint 3
Memoization or a table is helpful because many subrectangles repeat.
Expected complexity
O(h*w*(h+w)) time, O(h*w) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.