Doing zigzag 'My Way' ...

zigzag.py

'''
Created on 2 Jul 2016

@author: Josy

a question by Merkourios Katsimpris on gitter:myhdl triggered me to look at
    http://paddy3118.blogspot.nl/2008/08/zig-zag.html

    while the solution presented there is (very probably) very pythonic
    you need to read the explanation to understand what or why it is doing

    so I took a shot to deliver some 'annotated' code ...

    a zigzag of 4:
    
    0 - 1   5 - 6
      /   /   /
    2   4   7  12
    | /  [o]
    3   8  11  13

    9  10  14  15
    
    and 5:
    0 - 1   5 - 6  14
      /   /   /
    2   4   7  13  15
    | /  /
    3   8 [12] 16  21
      /  /
    9  11  17  20  22
    | /
    10 18  19  23  24

    the [] is our centre or 'pivot' point

'''

from __future__ import print_function

import math


def zigzag( dimension):
    ''' generate the zigzag indexes for a square array
        I exploit the fact that an array is symmetrical around its
        centre
    '''
    NUMBER_INDEXES = dimension ** 2
    HALFWAY = NUMBER_INDEXES // 2
    KERNEL_ODD = dimension & 1

    xy = [0 for _ in range(NUMBER_INDEXES)]
    # start at 0,0
    ix = 0
    iy = 0
    # 'fake' that we are going up and right
    direction = 1
    # the first index is always 0, so start with the second
    # until halfway 
    for i in range(1, HALFWAY + KERNEL_ODD):
        if direction > 0:
            # going up and right
            if iy == 0:
                # are at top
                ix += 1
                direction = -1
            else:
                ix += 1
                iy -= 1 
        else:
            # going down and left
            if ix == 0:
                # are at left
                iy += 1
                direction = 1
            else:
                ix -= 1
                iy += 1
        # update the index position
        xy[iy * dimension + ix] = i

    # have first half, but they are scattered over the list
    # so find the zeros to replace
    for i in range(1, NUMBER_INDEXES):
        if xy[i] == 0 :
            xy[i] = NUMBER_INDEXES - 1 - xy[NUMBER_INDEXES - 1 - i]

    return xy


def main(dim):
    zz = zigzag(dim)
    print( 'zigzag of {}:'.format(dim))
    width = int(math.ceil(math.log10(dim**2)))
    for j in range(dim):
        for i in range(dim):
            print('{:{width}}'.format(zz[j * dim + i], width=width), end=' ')
        print()


if __name__ == '__main__':
    main(4)