#!/usr/bin/env python3
# -*- coding: utf-8 -*-

# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# IMPORTS
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

from src.thirdparty.types import *;
from src.thirdparty.maths import *;

from models.generated.config import *;
from src.core.utils import *;
from src.models.euklid import *;
from src.algorithms.euklid.display import *;

# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# EXPORTS
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

__all__ = [
    'euklidean_algorithm',
];

# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD euklidean algorithm
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

def euklidean_algorithm(
    a: int,
    b: int,
    verbose: bool = False,
) -> Tuple[int, int, int]:
    '''
    Führt den Euklideschen Algorithmus aus, um den größten gemeinsamen Teiler (ggT, en: gcd)
    von zwei positiven Zahlen zu berechnen.
    '''
    ################
    # NOTE:
    # Lemma: gcd(a,b) = gcd(mod(a, b), b)
    # Darum immer weiter (a, b) durch (b, gcd(a,b)) ersetzen, bis b == 0.
    ################
    steps = [];
    d = 0;
    while True:
        if b == 0:
            d = a;
            steps.append(Step(a=a, b=b, gcd=d, div=0, rem=a, coeff_a=1, coeff_b=0));
            break;
        else:
            # Berechne k, r so dass a = k·b + r mit k ≥ 0, 0 ≤ r < b:
            r = a % b;
            k = math.floor(a / b);
            # Speichere Berechnungen:
            steps.append(Step(a=a, b=b, gcd=0, div=k, rem=r, coeff_a=0, coeff_b=0));
            # ersetze a, b durch b, r:
            a = b;
            b = r;

    ################
    # NOTE:
    # In jedem step gilt
    #    a = k·b + r
    # und im folgenden gilt:
    #    d = coeff_a'·a' + coeff_b'·b'
    # wobei
    #    a' = b
    #    b' = r
    # Darum:
    #    d = coeff_a'·b + coeff_b'·(a - k·b)
    #      = coeff_b'·a + (coeff_a' - k·coeff_b)·b
    # Darum:
    #    coeff_a = coeff_b'
    #    coeff_b = coeff_a' - k·coeff_b
    ################
    coeff_a = 1;
    coeff_b = 0;
    for step in steps[::-1][1:]:
        (coeff_a, coeff_b) = (coeff_b, coeff_a - step.div * coeff_b);
        step.coeff_a = coeff_a;
        step.coeff_b = coeff_b;
        step.gcd = d;

    if verbose:
        step = steps[0];
        repr = display_table(steps=steps, reverse=True);
        expr = display_sum(step=step);
        print('');
        print('\x1b[1mEuklidescher Algorithmus\x1b[0m');
        print('');
        print(repr);
        print('');
        print('\x1b[1mLösung\x1b[0m');
        print('');
        print(f'a=\x1b[1m{step.a}\x1b[0m; b=\x1b[1m{step.b}\x1b[0m; d = \x1b[1m{step.gcd}\x1b[0m = {expr}.');
        print('');

    return d, coeff_a, coeff_b;