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Divide Two Integers

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

分析:

不能用乘、除、取模运算,我们可以用的运算还有加、减、位运算。一个比较简单的想法是在dividend上不断减去divisor,知道余数小于divisor,然后减的次数就是所求结果。这里我们可以用类似binary search的方法用幂级跳跃试探dividend是divisor的多少倍,从而达到加速的目的。幂级跳跃又有两种方式,一种是dividend先减去divisor的1倍,另一种是dividend先减去比dividend小的divisor的最大倍数。由于乘2幂运算我们可以用位左移来实现,所以第二种方式要比第一种方式快,特别是dividend和divisor相差很多的时候。

Leetcode 通过版本:

class Solution {public:    int divide(int dividend, int divisor) {        long long div = (dividend > 0)? dividend:-(long long)dividend;        long long dis = (divisor > 0)? divisor: -(long long)divisor;        int result = 0;        while(div >= dis){            int counter = 0;            while(div >= dis<<counter){                counter++;            }            result += 1<<(counter-1);            div -= dis<<(counter-1);        }        return ((dividend^divisor)>>31)?(-result):result;    }};

超时版本:

class Solution {public:    int divide(int dividend, int divisor) {        long long div = (dividend > 0)? dividend:-(long long)dividend;        long long dis = (divisor > 0)? divisor: -(long long)divisor;        int result = 0;        while(div >= dis){            long long c = dis;            for(int i = 0; div >= c; i++, c<<i){                div -= c;                result += 1<<i;             }        }        return ((dividend^divisor)>>31)?(-result):result;    }};

 

Divide Two Integers