Divide two quantity utilizing Binary search with out utilizing any / and % operator

Given two integers one is a dividend and the opposite is the divisor, we have to discover the quotient when the dividend is split by the divisor with out using any ” / “ and ” % “ operators. 

Examples:

Enter: dividend = 10, divisor = 2
Output: 5
Clarification: 10/2 = 5.

Enter: dividend = 10, divisor = 3
Output: 3
Clarification: 10/3 = 3.33333… which is truncated to three.

Enter: dividend = 10, divisor = -2
Output: -5
Clarification: 10/-2 = -5.

Method: To resolve the issue utilizing Binary Search observe the beneath thought:

We already know that Quotient * Divisor ≤ Dividend and the Quotient lie between 0 and Dividend. Due to this fact, we are able to assume the Quotient  as mid, the Dividend as larger certain and 0 because the decrease certain and might simply use binary search to fulfill the phrases of division which is Quotient * Divisor ≤ Dividend.

Comply with the steps to resolve the issue:

• At first, set excessive = dividend and low  = 0 .
• Then, we have to discover the mid ( i.e Quotient ) = low + (excessive – low ) / 2 .
• Then, we carry out Binary Search within the vary of 0 to the dividend.
• If mid * divisor > dividend, then replace excessive = mid – 1 .
• Else  we replace low = mid + 1
• The worth of mid which satisfies the situation (i.e mid * divisor ≤ dividend) is our Quotient.
• Then, we return it by checking the Parity. 

Under is the implementation of the above method:

The Quotient is : 5

Time Complexity: O(log N), as Binary Search algorithm is used.
Auxiliary House: O(1), since no further house has been used.