Problema
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.
Vincoli
1 ≤ height, width ≤ 500. Rotation does not change the answer.
Esempi
Input:
width = 3
height = 2
Output atteso:
expected = 2Input:
long long width = 3;
long long height = 2;
Output atteso:
long long expected = 2;Input:
long width = 3;
long height = 2;
Output atteso:
long expected = 2;Spiegazione
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
Output atteso:
expected = 0Input:
long long width = 4;
long long height = 4;
Output atteso:
long long expected = 0;Input:
long width = 4;
long height = 4;
Output atteso:
long expected = 0;Spiegazione
The starting rectangle is already a square.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
A rectangle can be solved by splitting it into two smaller rectangles and combining their best answers.
Suggerimento 2
Try every possible horizontal and vertical cut to find the minimum.
Suggerimento 3
Memoization or a table is helpful because many subrectangles repeat.
Complessità attesa
O(h*w*(h+w)) time, O(h*w) extra space
Riferimenti
Questa sfida è adattata per CodeUtility. Segui la traccia e i vincoli sopra.