029 Divide Two Integers

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：

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

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

Note：

Both dividend and divisor will be32-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: [−2^31, 2^31 − 1]. For the purpose of this problem, assume that your function returns 2^31 − 1 when the division result overflows.

解释下题目：

实现计算机除法，用int足够了，而且除数不会是0

1. 老实做

实际耗时：超时

public int divide(int dividend, int divisor) {
        int result = 0;
        if (0 == dividend) {
            return 0;
        }
        if (dividend == Integer.MIN_VALUE && divisor == -1) {
            return Integer.MAX_VALUE;
        }
        
        if (dividend > 0 && divisor > 0) {
            //相当于 10/3
            while (dividend >= 0) {
                dividend -= divisor;
                result++;
            }
            result--;
        } else if (dividend < 0 && divisor > 0) {
            //相当于 -10/3
            while (dividend <= 0) {
                dividend += divisor;
                result--;
            }
            result++;
        } else if (dividend > 0 && divisor < 0) {
            //相当于 10/-3
            while (dividend >= 0) {
                dividend += divisor;
                result--;
            }
            result++;
        } else {
            //相当于 -10/-3
            while (dividend <= 0) {
                dividend -= divisor;
                result++;
            }
            result--;
        }
        return result;
    }

  思路很简单，就是把除数化为减法，不停去做就行了。当然这么暴力，显然没过。。。。

时间复杂度O(a) a=答案

空间复杂度O(1)

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2. 类似二分法的思想

实际耗时：xxms

public int divide(int dividend, int divisor) {
        if (dividend == Integer.MIN_VALUE && divisor == -1) {
            return Integer.MAX_VALUE;
        }
        if (dividend > 0 && divisor > 0) {
            return divideHelper(-dividend, -divisor);
        } else if (dividend > 0) {
            return -divideHelper(-dividend, divisor);
        } else if (divisor > 0) {
            return -divideHelper(dividend, -divisor);
        } else {
            return divideHelper(dividend, divisor);
        }
    }

    private int divideHelper(int dividend, int divisor) {
        //首先处理被除数小于除数的问题
        if (divisor < dividend) {
            return 0;
        }
        //得到可以除的最大的
        int cur = 0, res = 0;
        while ((divisor << cur) >= dividend && divisor << cur < 0 && cur < 31) {
            cur++;
        }
        res = dividend - (divisor << cur - 1);
        if (res > divisor) {
            return 1 << cur - 1;
        }
        return (1 << cur - 1) + divide(res, divisor);
    }

  思路就是我先不断扩大除数，然后就把这个最大的除数去除被除数，剩下的余数我在用相同的方法去做，把它们相加即可。

时间复杂度O(logn)

空间复杂度O(1)

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