qstates.py

import sys
 
limit = 5 if not len(sys.argv) > 1 else int(sys.argv[1])
 
found = {}
toler = 10 ** -5
energy = 1
while not set(found.keys()) >= set(range(1, limit + 1)):
    states = []
    for nx in range(1, int(energy ** .5) + 1):
        ny = (energy - nx ** 2) ** .5
        if abs(int(ny) - ny) < toler and not ny < toler:
            states.append((nx, int(ny)))
    nstates = len(states)
    if nstates not in found and nstates is not 0:
        found[nstates] = states
        print('%5.2f%%    %s: %s - %s' % (float(len(set(found.keys()) & set(range(1, limit)))) / limit * 100, nstates, energy, states))
    energy += 1
 
print('\n%s' % found)
 
'''
from collections import defaultdict
from itertools import product
 
states = defaultdict(list)
minstates = {}
 
for nx, ny in product(range(1, limit), range(1, limit)):
    states[nx ** 2 + ny ** 2].append((nx, ny))
    for state in range(1, min(nx ** 2, ny ** 2)):
        n = len(states[state])
        if n not in minstates or state < minstates[n]:
            minstates[n] = state
        del states[state]
 
print(minstates)
 
'''
 
'''
states = sorted(states.items(), key=lambda t: (len(t[1]), t[0]))
 
found = []
 
for state in states:
    n = len(state[1])
    if n not in found:
        print('%s - %s: %s' % (n, state[0], state[1]))
        found.append(n)
'''