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.
Restricciones
1 ≤ height, width ≤ 500. Rotation does not change the answer.
Ejemplos
Entrada:
width = 3
height = 2
Salida esperada:
expected = 2Entrada:
long long width = 3;
long long height = 2;
Salida esperada:
long long expected = 2;Entrada:
long width = 3;
long height = 2;
Salida esperada:
long expected = 2;Explicación
Cut off a 2 × 2 square, leaving a 2 × 1 rectangle. One more cut splits the remainder into two unit squares.
Entrada:
width = 4
height = 4
Salida esperada:
expected = 0Entrada:
long long width = 4;
long long height = 4;
Salida esperada:
long long expected = 0;Entrada:
long width = 4;
long height = 4;
Salida esperada:
long expected = 0;Explicación
The starting rectangle is already a square.
Cómo abordarlo
Inténtalo primero por tu cuenta y luego abre las pistas una a una.
Pista 1
A rectangle can be solved by splitting it into two smaller rectangles and combining their best answers.
Pista 2
Try every possible horizontal and vertical cut to find the minimum.
Pista 3
Memoization or a table is helpful because many subrectangles repeat.
Complejidad esperada
O(h*w*(h+w)) time, O(h*w) extra space
Referencias
Este reto está adaptado para CodeUtility. Sigue el enunciado y las restricciones indicadas arriba.