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 * 2x  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;
}
}

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