Divide Two Integers 解答

Question

Divide two integers without using multiplication, division and mod operator.

If it is overflow, return MAX_INT.

Solution

dividend = divisor * quotient + remainder

而我们知道对于任何一个数可以表示为Σi * 2^x  其中i为0或1。所以我们可以用加法实现乘法。

a = a + a 等同于 a = a * 2

因此我们可以通过对divisor乘以2，求出最大的x，然后继续求出第二大，第三大的x', x''..

注意到可能有溢出问题，解决方法是将要计算的所有数先转为long。

public class Solution {
    public int divide(int dividend, int divisor) {
        boolean negative = (dividend > 0 && divisor < 0) || (dividend < 0 && divisor > 0);
        long a = Math.abs((long)dividend);
        long b = Math.abs((long)divisor);
        if (a < b) {
            return 0;
        }
        long step, sum, result = 0;
        while (a >= b) {
            step = b;
            sum = 1;
            while (step + step <= a) {
                step += step;
                sum += sum;
            }
            a = a - step;
            result += sum;
        }
        result = negative == true ? -result : result;
        if (result > Integer.MAX_VALUE || result < Integer.MIN_VALUE) {
            return Integer.MAX_VALUE;
        }
        return (int)result;
    }
}