Multiply two integers without using multiplication, division and bitwise operators, and no loops

By making use of recursion, we can multiply two integers with the given constraints. 
To multiply x and y, recursively add x y times. 
 

Approach:

Since we cannot use any of the given symbols, the only way left is to use recursion, with the fact that x is to be added to x y times.

Base case: When the numbers of times  x has to be added becomes 0. 

Recursive call: If the base case is not met, then add x to the current resultant value and pass it to the next iteration.

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Time Complexity: O(y) where y is the second argument to function multiply().

Auxiliary Space: O(y) for the recursion stack

Another approach: The problem can also be solved using basic math property

(a+b)² = a² + b² + 2a*b

⇒  a*b = ((a+b)² - a² - b²) / 2

For computing the square of numbers, we can use the power function in C++ and for dividing by 2 in the above expression we can write a recursive function.

Below is the implementation of the above approach: 

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Time complexity: O(num)

Auxiliary space: O(num) for recursive call stack

Russian Peasant (Multiply two numbers using bitwise operators)
Please write comments if you find any of the above code/algorithm incorrect, or find better ways to solve the same problem.