Python Training Excercises

1.1 — Q1

Given an integer n, generate a matrix of size n*n that contains a spiral of incrementing values from the outside to the inside.

1.2 — A1.py

#!/usr/bin/env python
import sys
import math

def get_vector(theta=0.0):
    '''Get a vector for a radius on the unit circle with rotation theta'''
    return int(math.cos(theta)), int(math.sin(theta))

def spiral(n=1, start=0, inc=1):
    '''return a matrix of size n*n that increments 'start' by 'inc'
    starting at 0,0'''
    val = start
    loc = (0,0)
    _spiral = {}
    v = get_vector(0)
    quarter_turns = 0

    while True:
        _spiral[loc] = val
        val += inc
        # compute next location
        next_loc = tuple(sum(x) for x in zip(loc, v))
        # check if out of bounds
        if (_spiral.get(next_loc) is not None 
                or any(coord < 0 or coord >= n for coord in next_loc)):
            # rotate velocity vector
            quarter_turns = (quarter_turns + 1) % 4
            v = get_vector(float(quarter_turns) * math.pi / 2.0)
            # reapply velocity
            next_loc = tuple(sum(x) for x in zip(loc, v))
            # quit if next_loc still has a value, we're done
            if (_spiral.get(next_loc) is not None 
               or any(coord < 0 or coord >= n for coord in next_loc)):
                return _spiral
        loc = next_loc

if __name__ == '__main__':
    try:
        size = int(sys.argv[1])
        start = int(sys.argv[2])
        inc = int(sys.argv[3])
    except IndexError:
        print "Usage: %s size start increment" % __file__
    s = spiral(size, start, inc)
    width = len(str(start + (size**2 - 1) * inc))
    for y in xrange(size):
        for x in xrange(size):
            print "{val:<{width}d}".format(val=s[(x,y)], width=width),
        print "\n"