Given a two integers say a and b. Find the quotient after diving a by b without using multiplication, division and mod operator.

Input : a = 10, b = 3 Output : 3 Input : a = 43, b = -8 Output : -5

**Approach : **Keep subtracting the divisor from dividend until dividend becomes less than divisor. The dividend becomes the remainder, and the number of times subtraction is done becomes the quotient. Below is the implementation of above approach :

// C++ implementation to Divide two // integers without using multiplication, // division and mod operator #include <bits/stdc++.h> using namespace std; // Function to divide a by b and // return floor value it int divide(int dividend, int divisor) { // Calculate sign of divisor i.e., // sign will be negative only iff // either one of them is negative // otherwise it will be positive int sign = ((dividend < 0) ^ (divisor < 0)) ? -1 : 1; // Update both divisor and // dividend positive dividend = abs(dividend); divisor = abs(divisor); // Initialize the quotient int quotient = 0; while (dividend >= divisor) { dividend -= divisor; ++quotient; } return sign * quotient; } // Driver code int main() { int a = 10, b = 3; cout << divide(a, b) << "n"; a = 43, b = -8; cout << divide(a, b); return 0; }

Output :

3 -5

**Time complexity : **O(a)**Auxiliary space : **O(1)

**Efficient Approach : **Use bit manipulation in order to find the quotient. The divisor and dividend can be written as

dividend = quotient * divisor + remainder

As every number can be represented in base 2(0 or 1), represent the quotient in binary form by using shift operator as given below :

- Determine the most significant bit in the quotient. This can easily be calculated by iterating on the bit position
*i*from 31 to 1. - Find the first bit for which is less than dividend and keep updating the i
^{th}bit position for which it is true. - Add the result in
*temp*variable for checking the next position such that**(temp + (divisor << i) )**is less than**dividend**. - Return the final answer of quotient after updating with corresponding sign.

Below is the implementation of above approach :

// C++ implementation to Divide two // integers without using multiplication, // division and mod operator #include <bits/stdc++.h> using namespace std; // Function to divide a by b and // return floor value it int divide(long long dividend, long long divisor) { // Calculate sign of divisor i.e., // sign will be negative only iff // either one of them is negative // otherwise it will be positive int sign = ((dividend < 0) ^ (divisor < 0)) ? -1 : 1; // remove sign of operands dividend = abs(dividend); divisor = abs(divisor); // Initialize the quotient long long quotient = 0, temp = 0; // test down from the highest bit and // accumulate the tentative value for // valid bit for (int i = 31; i >= 0; --i) { if (temp + (divisor << i) <= dividend) { temp += divisor << i; quotient |= 1LL << i; } } return sign * quotient; } // Driver code int main() { int a = 10, b = 3; cout << divide(a, b) << "n"; a = 43, b = -8; cout << divide(a, b); return 0; }

Output :

3 -5

**Time complexity : **O(log(a))**Auxiliary space : **O(1)

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