Add sum of two integers using bit manipulation (#577)

Author: guizo792

src/bit_manipulation/mod.rs

@@ -1,5 +1,7 @@
 mod counting_bits;
 mod highest_set_bit;
+mod sum_of_two_integers;
 
 pub use counting_bits::count_set_bits;
 pub use highest_set_bit::find_highest_set_bit;
+pub use sum_of_two_integers::add_two_integers;

src/bit_manipulation/sum_of_two_integers.rs

@@ -0,0 +1,48 @@
+/**
+ * This algorithm demonstrates how to add two integers without using the + operator
+ * but instead relying on bitwise operations, like bitwise XOR and AND, to simulate
+ * the addition. It leverages bit manipulation to compute the sum efficiently.
+ */
+
+pub fn add_two_integers(a: i32, b: i32) -> i32 {
+    let mut a = a;
+    let mut b = b;
+    let mut carry;
+    let mut sum;
+
+    // Iterate until there is no carry left
+    while b != 0 {
+        sum = a ^ b; // XOR operation to find the sum without carry
+        carry = (a & b) << 1; // AND operation to find the carry, shifted left by 1
+        a = sum;
+        b = carry;
+    }
+
+    a
+}
+
+#[cfg(test)]
+mod tests {
+    use super::add_two_integers;
+
+    #[test]
+    fn test_add_two_integers_positive() {
+        assert_eq!(add_two_integers(3, 5), 8);
+        assert_eq!(add_two_integers(100, 200), 300);
+        assert_eq!(add_two_integers(65535, 1), 65536);
+    }
+
+    #[test]
+    fn test_add_two_integers_negative() {
+        assert_eq!(add_two_integers(-10, 6), -4);
+        assert_eq!(add_two_integers(-50, -30), -80);
+        assert_eq!(add_two_integers(-1, -1), -2);
+    }
+
+    #[test]
+    fn test_add_two_integers_zero() {
+        assert_eq!(add_two_integers(0, 0), 0);
+        assert_eq!(add_two_integers(0, 42), 42);
+        assert_eq!(add_two_integers(0, -42), -42);
+    }
+}