feat: add Gray Code generation (#1425)

---------

Co-authored-by: Lars Müller <[email protected]>

Author: Harshdev098

Diff for: Bit-Manipulation/GrayCodes.js

@@ -0,0 +1,42 @@
+/**
+ * Generates a Gray code sequence for the given number of bits.
+ * @param {number} n - The number of bits in the Gray code sequence.
+ * @returns {number[]} - An array of Gray codes in binary format.
+ * @description
+ * Gray codes are binary sequences in which two successive values differ in only one bit.
+ * This function generates a Gray code sequence of length 2^n for the given number of bits.
+ *
+ * The algorithm follows these steps:
+ *
+ * 1. Initialize an array `grayCodes` to store the Gray codes. Start with [0, 1] for n = 1.
+ * 2. Iterate from 1 to n:
+ *    a. Calculate `highestBit` as 2^i, where `i` is the current iteration index.
+ *    b. Iterate in reverse order through the existing Gray codes:
+ *       - For each Gray code `code`, add `highestBit | code` to `grayCodes`.
+ *       - This operation flips a single bit in each existing code, creating new codes.
+ * 3. Return the `grayCodes` array containing the Gray codes in decimal representation.
+ *
+ *resources: [GFG](https://www.geeksforgeeks.org/generate-n-bit-gray-codes/)
+ * @example
+ * const n = 3;
+ * const grayCodes = generateGrayCodes(n);
+ * // grayCodes will be [0, 1, 3, 2, 6, 7, 5, 4] for n=3.
+ */
+function generateGrayCodes(n) {
+  if (n <= 0) {
+    return [0]
+  }
+
+  const grayCodes = [0, 1]
+
+  for (let i = 1; i < n; i++) {
+    const highestBit = 1 << i
+    for (let j = grayCodes.length - 1; j >= 0; j--) {
+      grayCodes.push(highestBit | grayCodes[j])
+    }
+  }
+
+  return grayCodes
+}
+
+export { generateGrayCodes }

Diff for: Bit-Manipulation/test/GrayCodes.test.js

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+import { generateGrayCodes } from '../GrayCodes.js'
+
+describe('Gray codes', () => {
+  test.each([
+    [0, [0b0]],
+    [1, [0b0, 0b1]],
+    [2, [0b00, 0b01, 0b11, 0b10]],
+    [3, [0b000, 0b001, 0b011, 0b010, 0b110, 0b111, 0b101, 0b100]],
+    [
+      4,
+      [
+        0b0000, 0b0001, 0b0011, 0b0010, 0b0110, 0b0111, 0b0101, 0b0100, 0b1100,
+        0b1101, 0b1111, 0b1110, 0b1010, 0b1011, 0b1001, 0b1000
+      ]
+    ]
+  ])('n = %i -> %j', (n, expected) => {
+    expect(generateGrayCodes(n)).toEqual(expected)
+  })
+})