Simple packing algorithm for flat-ish things

packing.py

def side_by_side_simple(items):
    if max_height(items) > MAX_HEIGHT or max_width(items) > MAX_WIDTH:
        return False
    if total_depth(items) <= MAX_DEPTH:
        return True

    pairs = permutations(items, 2)
    stackable_pairs = []
    for a, b in pairs:
        stackable = False
        if a.height + b.height <= MAX_HEIGHT and max(a.width, b.width) <= MAX_WIDTH:
            stackable = True
        elif max(a.height, b.height) <= MAX_HEIGHT and a.width + b.width <= MAX_WIDTH:
            stackable = True
        elif max(a.height, b.height) <= MAX_WIDTH and a.width + b.width <= MAX_HEIGHT:
            stackable = True

        if stackable:
            stackable_pairs.append((max(a.depth, b.depth), a, b))

    if stackable_pairs:
        packed = []
        depth = 0

        for d, a, b in sorted(stackable_pairs):
            if a in packed or b in packed:
                break
            depth += d
            packed.append(a)
            packed.append(b)

        for i in items:
            if i not in packed:
                depth += i.depth

        if depth <= MAX_DEPTH:
            return True

    return False