You can build a spiral by starting near the center of the matrix and always turning right unless the element has been visited already:
#!/usr/bin/env python
NORTH, S, W, E = (0, -1), (0, 1), (-1, 0), (1, 0) # directions
turn_right = {NORTH: E, E: S, S: W, W: NORTH} # old -> new direction
def spiral(width, height):
if width < 1 or height < 1:
raise ValueError
x, y = width // 2, height // 2 # start near the center
dx, dy = NORTH # initial direction
matrix = [[None] * width for _ in range(height)]
count = 0
while True:
count += 1
matrix[y][x] = count # visit
# try to turn right
new_dx, new_dy = turn_right[dx,dy]
new_x, new_y = x + new_dx, y + new_dy
if (0 <= new_x < width and 0 <= new_y < height and
matrix[new_y][new_x] is None): # can turn right
x, y = new_x, new_y
dx, dy = new_dx, new_dy
else: # try to move straight
x, y = x + dx, y + dy
if not (0 <= x < width and 0 <= y < height):
return matrix # nowhere to go
def print_matrix(matrix):
width = len(str(max(el for row in matrix for el in row if el is not None)))
fmt = "{:0%dd}" % width
for row in matrix:
print(" ".join("_"*width if el is None else fmt.format(el) for el in row))
Example:
>>> print_matrix(spiral(5, 5))
21 22 23 24 25
20 07 08 09 10
19 06 01 02 11
18 05 04 03 12
17 16 15 14 13