Реализовать операции вычитания, умножения и деления через операцию сложения

task73.py

def reverse(a):
    '''Complexity - O(a).'''
    if a == 0:
        return 0

    result = 0
    change = -1 if a > 0 else +1
    
    while a != 0:
        result += change
        a += change
    return result

assert(reverse(-10) == 10)
assert(reverse(-1) == 1)
assert(reverse(-0) == 0)
assert(reverse(0) == 0)
assert(reverse(1) == -1)
assert(reverse(10) == -10)


def abs(a):
    '''Complexity - O(a) in case a is negative.'''
    if a >= 0:
        return a
    return reverse(a)

assert(abs(-10) == 10)
assert(abs(-1) == 1)
assert(abs(-0) == 0)
assert(abs(0) == 0)
assert(abs(1) == 1)
assert(abs(10) == 10)


def add(a, b):
    '''The only realized operation.'''
    return a + b

assert(add(-10, 10) == 0)
assert(add(-10, -10) == -20)
assert(add(-10, 0) == -10)
assert(add(0, -10) == -10)
assert(add(0, 0) == 0)
assert(add(0, 10) == 10)
assert(add(10, 0) == 10)
assert(add(10, 10) == 20)
assert(add(10, -10) == 0)


def subtract(a, b):
    '''Complexity - O(b).'''
    return a + reverse(b)

assert(subtract(-10, 10) == -20)
assert(subtract(-10, -10) == 0)
assert(subtract(-10, 0) == -10)
assert(subtract(0, -10) == 10)
assert(subtract(0, 0) == 0)
assert(subtract(0, 10) == -10)
assert(subtract(10, 0) == 10)
assert(subtract(10, 10) == 0)
assert(subtract(10, -10) == 20)


def multiply(a, b):
    '''Complexity - 2*(a + b):
        abs(a) -> a
        abs(b) -> b
        reverse(mx) -> max(|a|,|b|)
        range(mnabs) -> min(|a|,|b|)
    '''
    if not a or not b:
        return 0

    # Searhing absolute minimum to take less loop steps below
    mn, mx, result = a, b, 0
    mnabs, mxabs = abs(a), abs(b)
    if mnabs > mxabs:
        mn, mx = mx, mn
        mnabs, mxabs = mxabs, mnabs

    if mn < 0:
        mx = reverse(mx)

    # Main calculation loop
    for i in range(mnabs):
        result += mx
    return result

assert(multiply(-10, 10) == -100)
assert(multiply(-10, -10) == 100)
assert(multiply(-10, 0) == 0)
assert(multiply(0, -10) == 0)
assert(multiply(0, 0) == 0)
assert(multiply(0, 10) == 0)
assert(multiply(10, 0) == 0)
assert(multiply(10, 10) == 100)
assert(multiply(10, -10) == -100)


def divide(a, b):
    '''Division is checked by multiplication.
    We calculate the sign of result and operate with absolute values of a and b.
    Then we count how many times b is in a.
    Complexity - O(a + b + a//b):
        abs(a) -> a
        abs(b) -> b
        main loop -> a//b
    '''
    if b == 0:
        return 0
        raise Exception

    absa, absb = abs(a), abs(b)

    if absa < absb:
        return 0
    if a == b:
        return 1
    if absa == absb:
        return -1

    # Sign of result
    change = +1 if a > 0 and b > 0 or a < 0 and b < 0 else -1

    # Main calculation loop
    accumulator, result = 0, 0
    while accumulator < absa:
        accumulator += absb
        result += change

    # If a mod b == 0, so we return result.
    if accumulator == absa:
        return result

    # Otherwise we have made one unnecessary step and need to decrease result by 1.
    return subtract(result, change)

assert(divide(-1, 0) == 0)
assert(divide(0, 0) == 0)
assert(divide(1, 0) == 0)

assert(divide(0, 1) == 0)
assert(divide(0, -1) == 0)

assert(divide(-2, -2) == 1)
assert(divide(-1, -1) == 1)
assert(divide(1, 1) == 1)
assert(divide(2, 2) == 1)

assert(divide(-2, 2) == -1)
assert(divide(-1, 1) == -1)
assert(divide(1, -1) == -1)
assert(divide(2, -2) == -1)

assert(divide(-1, -2) == 0)
assert(divide(-1, 2) == 0)
assert(divide(1, -2) == 0)
assert(divide(1, 2) == 0)

assert(divide(-2, -1) == 2)
assert(divide(-2, 1) == -2)
assert(divide(2, -1) == -2)
assert(divide(2, 1) == 2)

assert(divide(-5, -2) == 2)
assert(divide(-5, 2) == -2)
assert(divide(5, -2) == -2)
assert(divide(5, 2) == 2)

assert(divide(-5, -3) == 1)
assert(divide(-5, 3) == -1)
assert(divide(5, -3) == -1)
assert(divide(5, 3) == 1)