Find permutations of numbers 1..N with each successive pair summing to a square

nsum.py

# pylint: disable=C0103, R1728
#                 invalid-name, consider-using-generator
""" blacked and pylinted; https://mersenneforum.org/showthread.php?t=22915 """
import sys
from sys import argv, stderr
from math import isqrt

N = 15 if len(argv) < 2 else int(argv[1])
a = [[] for i in range(N + 1)]
stop = len(argv) >= 3


def is_square(i):
    """silence pylint"""
    return i == isqrt(i) ** 2


def populate(A):
    """poulate adjacency list"""
    for sq in range(2, 2 * N):
        if is_square(sq):
            for v in range(max(sq - N, 1), min(N + 1, sq)):
                if v != sq - v:
                    A[v].append(sq - v)


def srch(A, seen, v, cnt, sol):
    """recursive search at nove v"""
    seen[v] = True
    cnt[0] += 1
    sol.append(v)
    if cnt[0] == N:
        print(sol)
        if stop:
            sys.exit()
    else:
        for w in A[v]:
            if not seen[w]:
                srch(A, seen, w, cnt, sol)
    cnt[0] -= 1
    seen[v] = False
    sol.pop()


populate(a)
print("average vertex degree:", sum([len(l) for l in a]) / N, file=stderr)

for s in range(N + 1):
    if a[s] != []:
        srch(a, [False for i in range(N + 1)], s, [0], [])

https://mersenneforum.org/showthread.php?p=638895#post638895

$ black nsum.py 
All done! ✨ 🍰 ✨
1 file left unchanged.
$ pylint nsum.py 

--------------------------------------------------------------------
Your code has been rated at 10.00/10 (previous run: 10.00/10, +0.00)

$ python nsum.py 
average vertex degree: 2.0
[8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9]
[9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 1, 8]
$ python nsum.py 23
average vertex degree: 2.4347826086956523
[2, 23, 13, 12, 4, 21, 15, 10, 6, 19, 17, 8, 1, 3, 22, 14, 11, 5, 20, 16, 9, 7, 18]
[9, 16, 20, 5, 11, 14, 22, 3, 1, 8, 17, 19, 6, 10, 15, 21, 4, 12, 13, 23, 2, 7, 18]
[18, 7, 2, 23, 13, 12, 4, 21, 15, 10, 6, 19, 17, 8, 1, 3, 22, 14, 11, 5, 20, 16, 9]
[18, 7, 9, 16, 20, 5, 11, 14, 2, 23, 13, 12, 4, 21, 15, 10, 6, 19, 17, 8, 1, 3, 22]
[18, 7, 9, 16, 20, 5, 11, 14, 22, 3, 1, 8, 17, 19, 6, 10, 15, 21, 4, 12, 13, 23, 2]
[22, 3, 1, 8, 17, 19, 6, 10, 15, 21, 4, 12, 13, 23, 2, 14, 11, 5, 20, 16, 9, 7, 18]
$ time python nsum.py 45 stop
average vertex degree: 3.5555555555555554
[1, 3, 6, 10, 15, 21, 28, 8, 17, 32, 4, 5, 11, 14, 35, 29, 20, 44, 37, 12, 13, 36, 45, 19, 30, 34, 2, 7, 18, 31, 33, 16, 9, 27, 22, 42, 39, 25, 24, 40, 41, 23, 26, 38, 43]

real	0m1.430s
user	0m1.424s
sys	0m0.003s
$