matrix_traverse.py

def chop(matrix, box, direction, results=None):
    if results is None:
        results = []
    x1, y1, x2, y2 = box
    w = x2 - x1 + 1
    h = y2 - y1 + 1
    if w <= 0 or h <= 0:
        return results
    else:
        if direction == 0:
            results.extend( [matrix[y1][x] for x in range(x1, x2+1)] )
            y1 += 1
        elif direction == 1:
            results.extend( [matrix[y][x2] for y in range(y1, y2+1)] )
            x2 -= 1
        elif direction == 2:
            results.extend( [matrix[y2][x] for x in range(x2, x1-1, -1)] )
            y2 -= 1
        elif direction == 3:
            results.extend( [matrix[y][x1] for y in range(y2, y1-1, -1)] )
            x1 += 1

        return chop(matrix, (x1, y1, x2, y2), (direction+1)%4, results=results)

def traverse(matrix):
    box = (0, 0, len(matrix[0])-1, len(matrix)-1)
    return chop(matrix, box, 0)\
    
    
# tests

assert traverse([[12, 32], [7, 34]]) \
    ==  [12, 32, 34, 7]

assert traverse([ [12, 17, 9], [19, 28, 11], [43, 7, 34] ]) \
    == [12, 17, 9, 11, 34, 7, 43, 19, 28]

assert traverse([ [12, 32, 9, 11], [8, 54, 76, 23], [27, 18, 25, 9], [11, 23, 78, 63] ]) \
    == [12, 32, 9, 11, 23, 9, 63, 78, 23, 11, 27, 8, 54, 76, 25, 18]

assert traverse([ [12, 32, 9, 11, 34], [8, 54, 76, 23, 7], [27, 18, 25, 9, 43], [11, 23, 78, 63, 19], [9, 22, 56, 31, 5] ]) \
    == [12, 32, 9, 11, 34, 7, 43, 19, 5, 31, 56, 22, 9, 11, 27, 8, 54, 76, 23, 9, 63, 78, 23, 18, 25]

assert traverse([ [12, 17], [9, 11], [19, 28] ]) \
    == [12, 17, 11, 28, 19, 9]

assert traverse([[12, 17, 9, 7, 21, 10], [19, 28, 11, 25, 2, 6], [10, 3, 8, 13, 4, 29], [5, 12, 9, 14, 31, 18]]) \
    == [12, 17, 9, 7, 21, 10, 6, 29, 18, 31, 14, 9, 12, 5, 10, 19, 28, 11, 25, 2, 4, 13, 8, 3]