This approach imitates the addition mechanism in digital circuits using bitwise operations. The key operations involved are:
Time Complexity: O(n), where n is the number of bits needed to represent the numbers.
Space Complexity: O(1), constant space usage.
1function getSum(a, b) {
2 while (b !== 0) {
3 let carry = a & b;
4 a = a ^ b;
5 b = carry << 1;
6 }
7 return a;
8}
9
10console.log(getSum(1, 2));JavaScript, with its dynamic typing, handles integers gracefully. The method is consistent: XOR for sum without carry, AND for determining carry, and left shift to add carried value to the next higher place value.
This approach is an extension of the iterative bitwise method but uses recursive calls to achieve the result. Instead of using a loop, it relies on recursive function calls to process the sum and carry until the carry becomes zero.
Time Complexity: O(n), where n is the number of bits.
Space Complexity: O(n), due to the recursive call stack.
1def get_sum(a, b):
2 if b == 0:
3 return a
4 else:
5 return get_sum(a ^ b, (a & b) << 1)
6
7print(get_sum(2, 3))Python's recursive solution handles the addition through a base case check and recursive calls. Each recursive call passes the updated sum and carry until carry is zero.