Search matrix for all rectangles of given dimensions (select blocks of seats)

Question

All,

I have been trying to work out how to select say 15 tickets within a single block of seats.

EDIT: the problem is - how to find all rect

Answer 1

I came here looking for a Python solution. Here is mine, which returns all positions:

import numpy

s = '''0 0 0 0 1 0 0 0 1 0 0
0 0 0 0 0 0 1 0 1 0 1
0 1 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0'''

area = 15
nrows = 6
ncols = 11
skip = 1

a = numpy.fromstring(s, dtype=int, sep=' ').reshape(nrows, ncols)
w = numpy.zeros(dtype=int, shape=a.shape)
h = numpy.zeros(dtype=int, shape=a.shape)
for r in range(nrows):
    for c in range(ncols):
        if a[r][c] == skip:
            continue
        if r == 0:
            h[r][c] = 1
        else:
            h[r][c] = h[r-1][c]+1
        if c == 0:
            w[r][c] = 1
        else:
            w[r][c] = w[r][c-1]+1
        minw = w[r][c]
        for dh in range(h[r][c]):
            minw = min(minw, w[r-dh][c])
            if (dh+1)*minw == area:
                print(
                    'area', area, 'row', r, 'col', c,
                    'height', dh+1, 'width', minw)

Output:

area 15 row 4 col 8 height 3 width 5
area 15 row 5 col 10 height 3 width 5