問題
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.
制約
1 ≤ height, width ≤ 500. Rotation does not change the answer.
例
入力：
width = 3
height = 2
期待される出力：
expected = 2入力：
long long width = 3;
long long height = 2;
期待される出力：
long long expected = 2;入力：
long width = 3;
long height = 2;
期待される出力：
long expected = 2;解説
Cut off a 2 × 2 square, leaving a 2 × 1 rectangle. One more cut splits the remainder into two unit squares.
入力：
width = 4
height = 4
期待される出力：
expected = 0入力：
long long width = 4;
long long height = 4;
期待される出力：
long long expected = 0;入力：
long width = 4;
long height = 4;
期待される出力：
long expected = 0;解説
The starting rectangle is already a square.
解き方のヒント
まずは自分で考えてから、ヒントを 1 つずつ開いてみましょう。
ヒント 1
A rectangle can be solved by splitting it into two smaller rectangles and combining their best answers.
ヒント 2
Try every possible horizontal and vertical cut to find the minimum.
ヒント 3
Memoization or a table is helpful because many subrectangles repeat.
目安の計算量
O(h*w*(h+w)) time, O(h*w) extra space
参考資料
この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。