LeetCode 29 — Divide Two Integers(两数相除)

Question

    Given two integers dividend and divisor, divide two integers without using multiplication, division and mod operator.

    Return the quotient after dividing dividend by divisor.

    The integer division should truncate toward zero.

    E.g 1:
    Input: dividend = 10, divisor = 3
    Output: 3

    E.g 2:
    Input: dividend = 7, divisor = -3
    Output: -2

Solution

class Solution(object):
    def divide(self, dividend, divisor):
        """
        :type dividend: int
        :type divisor: int
        :rtype: int
        """
        if abs(dividend) < abs(divisor):
            return 0

        positive = (dividend < 0) is (divisor < 0)
        # abs value
        dividend_abs = abs(dividend)
        divisor_abs = abs(divisor)
        
        res = 0
        
           
        dividend = abs(dividend)
        divisor = abs(divisor)
        
        cur_dev = 0
        
        """
        If inner loop runs for say x times, then D gets doubled x times so that     
        D*2^x > N => x > log(N/D)  => O(log(N/D))
        And about outer loop
        N = 2^x * D + M   => such that N > M > D
        So next time inner loop will run for log(M/D)
        So its basically
        log(N/D) + log(M/D) + log(L/D) + ..... + log(D/D)   => log(N/D) * Y  
        """

        while dividend_abs >= divisor_abs:
            temp, index = divisor_abs, 1
            while dividend_abs >= temp:
                dividend_abs -= temp
                res += index
                index <<= 1
                temp <<= 1

        if not positive:
            res = -res
        
        if res < -2147483648:
            return -2147483648
        if res > 2147483647:
            return 2147483647        
        return res