number synthesis

number.py

from itertools import product


def Max(NL, NJ):
    """Find max number of joint on each link.
    
    + NL <= NJ and NJ <= (2 * NL - 3)
    + (2 * NL - 3) <= NJ and NJ <= (NL * (NL - 1) / 2)
    + other exceptions (return -1).
    """
    if NL <= NJ <= (2 * NL - 3):
        return NJ - NL + 2
    if NL == NJ == 0:
        return -1
    if (2 * NL - 3) <= NJ <= (NL * (NL - 1) / 2):
        return NL - 1
    return -1


def sum_factors(factors):
    """F0*N2 + F1*N3 + F2*N4 + ... + Fn*N(n+2)"""
    factor = 0
    for i, f in enumerate(factors):
        factor += f * (i + 2)
    return factor


def number_synthesis(NL, NJ):
    result = []
    Mmax = Max(NL, NJ)
    if Mmax == -1:
        raise Exception("incorrect mechanism.")
    
    for symbols in product(range(NL + 1), repeat = (Mmax - 2)):
        NLMmax = NL - sum(symbols)
        if NLMmax < 0:
            continue
        answer = symbols + (NLMmax,)
        if sum_factors(answer) == (2 * NJ):
            result.append(answer)
    return tuple(result)