PathFinderCircleOfSquares.py

#!/usr/bin/python3

# Usage: First commandline argument is max.
#
# This script finds all possible paths that make a circle of squares
# and prints them.
#
# The output still contains duplicates and mirrors.
#

import sys

high = int( sys.argv[1] )
ring = tuple([ x+1 for x in range(high) ])
squares = set([ x**2 for x in range(1, high) if x**2 < 2*high ])
final = []



# Create dict of possible squares.
possq = dict()

for base in ring:
    possq[base] = []
    for num in ring:
        if num + base in squares and num != base:
            possq[base].append(num)

for key in possq.keys():
    possq[key] = tuple(possq[key])

firstkey = possq[1]

# Print dictionary with possible squares.
for i, j in possq.items():
#   print(i, j)
    pass

# Find circle

path = [1]
a = 0
x = 1
error = []
term = len(possq[1])

while not (len(path) == 1 and a == term):
#   print(path)
    while a < len(possq[path[-1]]):
        if possq[path[-1]][a] not in path:
            path.append(possq[path[-1]][a])
            a = 0
            if len(path) == high:
                print(*path, sep=' ')
            break
        a += 1
    else:
        b = path.pop()
        a = possq[path[-1]].index(b) + 1


# Print result

Final = []
[ Final.append(i) for i in final if i not in Final ]