Added a bit manipulation program to determine even or odd numbers (#2959)

* Create check_even_odd.cpp

Implementation to Check if a number is Even or Odd using Bitwise Operator

* Update check_even_odd.cpp

* Create factorial_top_down_dp.cpp

* Delete dynamic_programming/factorial_top_down_dp.cpp

Deleted the one file as there was 2 files in the commit

* Create factorial_top_down_dp.cpp

* Delete dynamic_programming/factorial_top_down_dp.cpp

* Update bit_manipulation/check_even_odd.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update bit_manipulation/check_even_odd.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update bit_manipulation/check_even_odd.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update bit_manipulation/check_even_odd.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Update check_even_odd.cpp

modified

* Update check_even_odd.cpp

reverted to boolean to check if number is even or not

---------

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

bit_manipulation/check_even_odd.cpp

@@ -0,0 +1,93 @@
+/**
+ * @file
+ * @brief Implementation to [Check if a number is Even or Odd using Bitwise Operator]
+ * (https://www.log2base2.com/c-examples/bitwise/odd-or-even-program-in-c-using-bitwise-operator.html)
+ *
+ * @details
+ * Given an integer N, determine whether it is even or odd using bitwise manipulation.
+ * The least significant bit (LSB) of a binary number determines its parity:
+ * - If the LSB is 0, the number is even.
+ * - If the LSB is 1, the number is odd.
+ *
+ * This can be checked efficiently using the bitwise AND operator (&) with 1.
+ * - If (N & 1) == 0, N is even.
+ * - If (N & 1) == 1, N is odd.
+ *
+ * Example:
+ * Consider 8-bit binary representations of two numbers:
+ *     Number: 10 (decimal) -> 00001010 (binary)
+ *       LSB = 0 -> Even number
+ * 
+ *     Number: 13 (decimal) -> 00001101 (binary)
+ *       LSB = 1 -> Odd number
+ *
+ * In both cases, evaluating (N & 1) isolates the LSB:
+ * - For 10: 00001010 & 00000001 = 0  (Even)
+ * - For 13: 00001101 & 00000001 = 1  (Odd)
+ *
+ * Worst Case Time Complexity: O(1)
+ * Space Complexity: O(1)
+ *
+ * @author [Vedant Mukhedkar](https://github.com/git5v)
+ */
+
+#include <cassert>   /// for assert
+#include <cstdint>   /// for uint32_t
+#include <iostream>  /// for IO operations
+#include <string>    /// for std::string
+
+/**
+ * @namespace bit_manipulation
+ * @brief Bit manipulation algorithms
+ */
+namespace bit_manipulation {
+/**
+ * @namespace even_odd
+ * @brief Functions for checking if a number is even or odd using bitwise operations
+ */
+namespace even_odd {
+
+/**
+ * @brief Checks if a number is even or odd using bitwise AND.
+ * @param N The number to check.
+ * @returns "Even" if N is even, "Odd" if N is odd.
+     */
+        bool is_even(std::int64_t N) {
+            return (N & 1) == 0 ? true : false;
+        }
+
+    }  // namespace even_odd
+}  // namespace bit_manipulation
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    using bit_manipulation::even_odd::is_even;
+
+    // Test Even numbers
+    assert(is_even(0) == true);
+    assert(is_even(2) == true);
+    assert(is_even(100) == true);
+    assert(is_even(-4) == true);
+    assert(is_even(-1000) == true);
+
+    // Test Odd numbers
+    assert(is_even(1) == false);
+    assert(is_even(3) == false);
+    assert(is_even(101) == false);
+    assert(is_even(-5) == false);
+    assert(is_even(-999) == false);
+
+    std::cout << "All test cases successfully passed!" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}