[leetcode] 29. Divide Two Integers @ python

最新推荐文章于 2019-07-09 11:38:39 发布

原创最新推荐文章于 2019-07-09 11:38:39 发布 · 418 阅读

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本文介绍了一种在不使用乘法、除法和取模运算的情况下，实现两个32位有符号整数相除的方法。通过二分搜索法，将除数和商不断乘以2，以快速逼近被除数，实现高效整数除法。

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.

Example 1:

Input: dividend = 10, divisor = 3
Output: 3
Example 2:

Input: dividend = 7, divisor = -3
Output: -2
Note:

Both dividend and divisor will be 32-bit signed integers.
The divisor will never be 0.
Assume we are dealing with an environment which could only store integers within the 32-bit signed integer range: [−231, 231 − 1]. For the purpose of this problem, assume that your function returns 231 − 1 when the division result overflows.

解法

二分搜索法, 不断将除数和商乘以2, 使得能尽快接近被除数
Time: O(log(n))
Space: O(1)

代码

class Solution:
    def divide(self, dividend, divisor):
        """
        :type dividend: int
        :type divisor: int
        :rtype: int
        """        
        if (dividend > 0 and divisor < 0) or (dividend < 0 and divisor > 0):
            neg = True
        else:
            neg = False
        dividend, divisor = abs(dividend), abs(divisor)
        res = 0
        while dividend >= divisor:
            temp, q = divisor, 1
            while dividend >= temp:
                dividend -= temp
                res += q
                temp <<= 1
                q <<= 1
                
        if neg:
            return max(-res, -2**31)
        else:
            return min(res, 2**31 - 1)