29. 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 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.

Solution

用减法计算除法
优化点:指数扩大,类似快速幂思想

Complexity

Code

    public int divide(int dividend, int divisor) {
        int sign = (dividend >>> 31) ^ (divisor >>> 31);
        long a = Math.abs((long)dividend), b = Math.abs((long)divisor);
        long res = sign > 0 ? -helper(a, b) : helper(a, b);
        if(res - 1 == Integer.MAX_VALUE) return Integer.MAX_VALUE;
        return (int) res;
    }

    public long helper(long a, long b){
        if(a < b)
            return 0;
        long sum = 0, count = 1;
        long oriB = b;
        while(a >= b){
            a -= b;
            sum += count;
            b <<= 1;
            count <<= 1;

        }
        return sum + helper(a, oriB);
    }