[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:

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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:

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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:

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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++:

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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++:

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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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