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.
1def get_sum(a, b):
2 while b != 0:
3 carry = a & b
4 a = a ^ b
5 b = carry << 1
6 return a
7
8print(get_sum(2, 3))Python, being a high-level language, allows easy manipulation of integers. The approach and logic are the same: use ^ for interim sum and & followed by a << 1 for updating the carry.
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.
1public class Main {
2 public static int getSum(int a, int b) {
3 if (b == 0) return a;
4 int sum = a ^ b;
5 int carry = (a & b) << 1;
6 return getSum(sum, carry);
7 }
8
9 public static void main(String[] args) {
10 System.out.println(getSum(1, 2));
11 }
12}The Java recursive implementation follows the pattern of calculating sum and carry and uses recursive method calls, returning the result when carry is zero.