#!/usr/bin/python3
# -*- coding: utf-8 -*-
"""Balanced ternary.

To test:

    fades -d pytest -x pytest bt.py

This module has a command-line interface if run as a script; run
./bt.py -h for details.

"""
import argparse


power_digits = u"⁰¹²³⁴⁵⁶⁷⁸⁹"


def test_succ():
    ns = []
    s = ''
    for i in range(12):
        s = succ(s)
        ns.append(s)
    assert ns == ['+', '+-', '+0', '++', '+--', '+-0',
                  '+-+', '+0-', '+00', '+0+', '++-', '++0']


def succ(s="0"):
    "Return the successor of balanced ternary s."
    if not s:
        return "+"

    i = len(s) - 1
    while i > 0 and s[i] == '+':
        i -= 1
    # If i is 0 then we had a whole string of +, so we need to add a new digit
    if i == 0:
        return '+' + '-' * len(s)

    # Otherwise s[i] is the digit we need to increment
    inc = '0' if s[i] == '-' else '+'
    return s[:i] + inc + '-' * (len(s) - i - 1)


def test_to_bt():
    assert to_bt(7) == '+-+'
    assert to_bt(-7) == '-+-'
    assert to_bt(-9) == '-00'
    for i in range(-100, 100):
        assert from_bt(to_bt(i)) == i


def from_bt(s):
    "Convert balanced ternary using -0+ to an integer."
    return 0 if s == '' else 3 * from_bt(s[:-1]) + '0+'.find(s[-1])


def to_bt(n):
    "Convert an integer to balanced ternary using -0+."
    a = natural_to_bt(abs(n))
    return a if n >= 0 else negate(a)


def negate(s):
    "Negates balanced ternary s using -0+."
    return ''.join('-' if d == '+' else '+' if d == '-' else d for d in s)


def test_natural_to_bt():
    for i in range(100):
        assert natural_to_bt(i) == natural_to_bt_dumb(i)


def natural_to_bt_dumb(n):
    "Convert a positive integer to balanced ternary using -0+."
    s = ''
    for i in range(abs(n)):
        s = succ(s)
    return s


def natural_to_bt(n):
    "Convert a positive integer to balanced ternary using -0+."
    if n == 0:
        return ''
    return natural_to_bt((n+1)//3) + '0+-'[n % 3]


def dec(n, digits):
    "Convert a nonnegative integer to base 10 using the supplied digits."
    return ('' if n < 10 else dec(n // 10, digits)) + digits[n % 10]


def test_dec():
    assert dec(319, power_digits) == '³¹⁹'
    assert dec(0, power_digits) == '⁰'


def bt_to_alg(bt):
    "Convert a balanced ternary number ('+0-') to an expression ('3² - 1')."
    terms = reversed([(digit, ('3%s' % dec(i, power_digits) if i > 1
                               else '3' if i == 1
                               else '1'))
                      for i, digit in enumerate(reversed(bt))
                      if digit in '+-'])
    return ' '.join(('-' if sign == '-' and i == 0
                     else '- ' if sign == '-'
                     else '+ ' if i != 0
                     else '')
                    + term
                    for i, (sign, term) in enumerate(terms))


def test_bt_to_alg():
    assert bt_to_alg('+0--') == '3³ - 3 - 1'
    assert bt_to_alg('-0000+00000') == '-3¹⁰ + 3⁵'


def to_alg(n):
    "Convert an integer like 8 to an expression string like '3² - 1'."
    return bt_to_alg(to_bt(n))


if __name__ == '__main__':
    parser = argparse.ArgumentParser(
        description=
        "Convert integers to and from balanced ternary, using"
        + " Unicode algebraic notation (e.g. 3² - 1) by default."
    )
    parser.add_argument('-s', action='store_true',
                        help='Display ternary in -0+ notation.')
    parser.add_argument('-i', action='store_true',
                        help='Convert FROM -0+ notation, not to ternary.'
                        + ' (Add a leading 0 to negative numbers or precede'
                        + ' the numbers with a -- to keep them from being'
                        + ' parsed as options.)')
    parser.add_argument('integer', nargs='+', help='Numbers to convert.')
    args = parser.parse_args()
    if args.i:
        for i in args.integer:
            print(from_bt(i))
    else:
        for i in args.integer:
            print((to_bt if args.s else to_alg)(int(i)))