Merge pull request #183 from BrianLusina/feat/bit-manipulation

feat(bit-manipulation): sum two integers

Author: BrianLusina

DIRECTORY.md

@@ -451,6 +451,8 @@
     * [Test Number Of One Bits](https://github.com/BrianLusina/PythonSnips/blob/master/bit_manipulation/number_of_1_bits/test_number_of_one_bits.py)
   * Single Number
     * [Test Single Number](https://github.com/BrianLusina/PythonSnips/blob/master/bit_manipulation/single_number/test_single_number.py)
+  * Sum Two Integers
+    * [Test Sum Of Two Integers](https://github.com/BrianLusina/PythonSnips/blob/master/bit_manipulation/sum_two_integers/test_sum_of_two_integers.py)
 
 ## Cryptography
   * Atbash Cipher

bit_manipulation/sum_two_integers/README.md

@@ -0,0 +1,76 @@
+# Sum of Two Integers
+
+Given two integers a and b, return the sum of the two integers without using the operators + and -.
+
+ 
+## Examples
+
+Example 1:
+```text
+Input: a = 1, b = 2
+Output: 3
+```
+
+Example 2:
+```text
+Input: a = 2, b = 3
+Output: 5
+```
+
+## Constraints
+
+- -1000 <= a, b <= 1000
+
+## Topics
+
+- Math
+- Bit Manipulation
+
+## Solution
+
+We will use the bitwise manipulation pattern to calculate the sum of two integers without using the arithmetic operators.
+To calculate the desired sum, we'll use the bitwise operations.
+
+Let's dive into the logic to get a better idea of how to use bitwise operations for this task:
+
+- Bitwise XOR (`^`) operation: This operation allows us to calculate the sum of corresponding bits in a and b without
+  considering the carry (if any).
+
+- Bitwise AND (`&`) operation: The AND operation will help us determine where carry propagation is necessary. By applying
+  this operation to a and b, we can identify which bit positions require carry consideration.
+
+- Iterative Process: The algorithm functions iteratively, much like how binary addition is carried out. We will start
+  with the least significant bits and advance toward the most significant bits of a and b. At each bit position, we
+  calculate the sum while considering the carry from the previous bit's addition. This ensures that any carry is
+  appropriately propagated throughout the process.
+
+The algorithm to obtain the sum of the given integers is as follows:
+
+1. To limit the result to 32-bits, we set a mask variable to `0xFFFFFFFF`.
+2. Start a loop that continues while b is not equal to 0. We calculate the sum of the two integers without carrying, by
+   taking XOR and then AND the result with the mask.
+3. For calculating the carry which needs to be added to the next pair of integers, we take the AND of a and b,
+   leftshifting the result by 1-bit, and then AND this result with the mask.
+4. We update a and b with the new values for the next iteration, which are the result and carry calculated in steps 2
+   and 3, respectively.
+5. At the end, to handle overflow when performing the addition of two integers, we have a condition that checks if the
+   result exceeds the maximum value of a signed 32-bit integer. If it does, we return the two’s complement of the result
+   to ensure that the returned value remains within the valid range.
+
+![Solution 1](./images/solutions/sum_two_integers_solution_1.png)
+![Solution 2](./images/solutions/sum_two_integers_solution_2.png)
+![Solution 3](./images/solutions/sum_two_integers_solution_3.png)
+![Solution 4](./images/solutions/sum_two_integers_solution_4.png)
+![Solution 5](./images/solutions/sum_two_integers_solution_5.png)
+![Solution 6](./images/solutions/sum_two_integers_solution_6.png)
+![Solution 7](./images/solutions/sum_two_integers_solution_7.png)
+
+### Time Complexity
+
+The time complexity of this solution is O(1), because the while loop runs for a maximum of 32 times, since the integers
+are represented by 32−bits. Each iteration does bitwise operations, which takes constant O(1), time hence making the
+total time complexity as O(1)*O(32) = O(32), which is equivalent to O(1).
+
+### Space Complexity
+
+The solution uses fixed numbers of variables to compute the result. Hence the space complexity is constant. O(1).

bit_manipulation/sum_two_integers/__init__.py

@@ -0,0 +1,36 @@
+def integer_addition(a: int, b: int):
+    # Mask to limit the result to 32-bits (the size of an integer in Python)
+    mask = 0xFFFFFFFF
+    # Setting maximum integer value
+    max_int = 0x7FFFFFFF
+
+    while b != 0:
+        # Sum of the integers without carrying
+        result = (a ^ b) & mask
+
+        # Calculate the carry that needs to be added to the next pair of integers
+        carry = ((a & b) << 1) & mask
+
+        # Update a and b to the new values for the next iteration
+        a = result
+        b = carry
+
+    # We check if the result is greater than the maximum integer value
+    # Return the result as is if result is not greater than max_int
+    if a <= max_int:
+        return a
+
+    # If it is, then return the two's complement of the result
+    else:
+        return ~(a ^ mask)
+
+
+def integer_addition_2(a: int, b: int) -> int:
+    mask = 0xFFFFFFFF
+    max_int = 2 ** 31 - 1
+    while b != 0:
+        sum_ = (a ^ b) & mask
+        carry = (a & b) & mask
+        a = sum_
+        b = carry << 1
+    return a if a <= max_int else ~(a ^ mask)