[LeetCode] 29. Divide Two Integers 两数相除

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

If it is overflow, return MAX_INT.

求两数相除，不能用乘法，除法和取余操作。

解法：位操作Bit Operation, Time: O(logn)

num=a_0*2^0+a_1*2^1+a_2*2^2+...+a_n*2^n

Java:

public int divide(int dividend, int divisor) {
    //handle special cases
    if(divisor==0) return Integer.MAX_VALUE;
    if(divisor==-1 && dividend == Integer.MIN_VALUE)
        return Integer.MAX_VALUE;
 
    //get positive values
    long pDividend = Math.abs((long)dividend);
    long pDivisor = Math.abs((long)divisor);
 
    int result = 0;
    while(pDividend>=pDivisor){
        //calculate number of left shifts
        int numShift = 0;    
        while(pDividend>=(pDivisor<<numShift)){
            numShift++;
        }
 
        //dividend minus the largest shifted divisor
        result += 1<<(numShift-1);
        pDividend -= (pDivisor<<(numShift-1));
    }
 
    if((dividend>0 && divisor>0) || (dividend<0 && divisor<0)){
        return result;
    }else{
        return -result;
    }
}

　　

Python:

class Solution:
    def divide(self, dividend, divisor):
        """
        :type dividend: int
        :type divisor: int
        :rtype: int
        """
        result, dvd, dvs = 0, abs(dividend), abs(divisor)
        while dvd >= dvs:
            inc = dvs
            i = 0
            while dvd >= inc:
                dvd -= inc
                result += 1 << i
                inc <<= 1
                i += 1
        if dividend > 0 and divisor < 0 or dividend < 0 and divisor > 0:
            return -result
        else:
            return result


if __name__ == "__main__":
    print(Solution().divide(123, 12))
    print(Solution().divide(123, -12))
    print(Solution().divide(-123, 12))
    print(Solution().divide(-123, -12))

Python:

class Solution:
    def divide(self, dividend, divisor):
        """
        :type dividend: int
        :type divisor: int
        :rtype: int
        """
        positive = (dividend < 0) is (divisor < 0)
        dividend, divisor = abs(dividend), abs(divisor)
        res = 0
        while dividend >= divisor:
            temp, i = divisor, 1
            while dividend >= temp:
                dividend -= temp
                res += i
                i <<= 1
                temp <<= 1
        if not positive:
            res = -res
        return min(max(-2147483648, res), 2147483647)

C++:

class Solution {
public:
    int divide(int dividend, int divisor) {
        long long m = abs((long long)dividend), n = abs((long long)divisor), res = 0;
        if (m < n) return 0;    
        while (m >= n) {
            long long t = n, p = 1;
            while (m > (t << 1)) {
                t <<= 1;
                p <<= 1;
            }
            res += p;
            m -= t;
        }
        if ((dividend < 0) ^ (divisor < 0)) res = -res;
        return res > INT_MAX ? INT_MAX : res;
    }
};

C++:

class Solution {
public:
    int divide(int dividend, int divisor) {
        long long res = 0;
        long long m = abs((long long)dividend), n = abs((long long)divisor);
        if (m < n) return 0;
        long long t = n, p = 1;
        while (m > (t << 1)) {
            t <<= 1;
            p <<= 1;
        }
        res += p + divide(m - t, n);
        if ((dividend < 0) ^ (divisor < 0)) res = -res;
        return res > INT_MAX ? INT_MAX : res;
    }
};

　　

　　

　　

　　

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