Find Rectangles Find Rectangles
Undefined
English

This mission is an adaptation of the "Rectangles" game (from Simon Tatham's Portable Puzzle Collection). If you are lost or just want to play, the game is available here.

You have to divide a rectangular grid into rectangles, so that each rectangle contains exactly one cell with a non-empty number and the rectangle area is equal to this number.

The grid will be represented by a list of list of integers.
A rectangle will be represented by a tuple or list of four integers:

  • the first two are the coordinates of the top left corner ;
  • the last two are the coordinates of the bottom right corner.

6x6 example image

[[3, 0, 0, 0, 0, 2],          {(0, 0, 0, 2), (1, 2, 3, 2),
 [2, 0, 0, 4, 0, 0],           (1, 1, 5, 1), (1, 0, 2, 0),
 [0, 5, 0, 0, 0, 0],   ===\    (3, 0, 5, 0), (2, 4, 4, 5),
 [3, 0, 3, 2, 0, 0],   ===/    (0, 5, 1, 5), (0, 3, 1, 4),
 [0, 0, 2, 0, 0, 6],           (2, 3, 3, 3), (4, 2, 4, 3),
 [0, 0, 0, 4, 0, 0]]           (5, 2, 5, 5)}              

Rectangle A starts at (0, 0) and ends at (0, 2).
Rectangle B starts at (1, 2) and ends at (3, 2).
Rectangle C starts at (1, 1) and ends at (5, 1).
...
Rectangle K starts at (5, 2) and ends at (5, 5).

Input: A list of list of integers.

Output: An iterable/list/set of tuple/list of four integers.

Example:

rectangles([[3, 0, 0, 0, 0, 2],
            [2, 0, 0, 4, 0, 0],
            [0, 5, 0, 0, 0, 0],
            [3, 0, 3, 2, 0, 0],
            [0, 0, 2, 0, 0, 6],
            [0, 0, 0, 4, 0, 0]]) == {(0, 0, 0, 2), (1, 2, 3, 2), (1, 1, 5, 1), (1, 0, 2, 0),
                                     (3, 0, 5, 0), (2, 4, 4, 5), (0, 5, 1, 5), (0, 3, 1, 4),
                                     (2, 3, 3, 3), (4, 2, 4, 3), (5, 2, 5, 5)}

To play the puzzles / tests yourself: 1 2 3 4 5 6 7 8 9 10 11 12 13

Preconditions:

  • All puzzles have one and only one solution.
  • 6 ≤ len(grid) ≤ 50 and 6 ≤ len(grid[0]) ≤ 50.
  • all(len(row) == len(grid[0]) for row in grid).