feat: added Gray Code algorithm

Bit-Manipulation/GrayCodes.js

@@ -0,0 +1,23 @@
+/**
+ * Generates a Gray code sequence for the given number of bits.
+ * @param {number} n - The number of bits in the Gray code sequence.
+ * @returns {string[]} - An array of Gray codes in binary format.
+ */
+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 }

Bit-Manipulation/test/GrayCodes.test.js

@@ -0,0 +1,43 @@
+import { generateGrayCodes } from '../GrayCodes.js' 
+
+/**
+ * Test cases for the generateGrayCodes function.
+ */
+
+test('Generate Gray codes for n=3', () => {
+  const n = 3
+  const expectedGrayCodes = [0, 1, 3, 2, 6, 7, 5, 4]
+  const grayCodes = generateGrayCodes(n)
+  expect(grayCodes).toEqual(expectedGrayCodes)
+})
+test('Generate Gray codes for n=0', () => {
+    const n = 0;
+    const expectedGrayCodes = [0];
+    const grayCodes = generateGrayCodes(n);
+    expect(grayCodes).toEqual(expectedGrayCodes);
+  });
+
+  test('Generate Gray codes for n=1', () => {
+    const n = 1;
+    const expectedGrayCodes = [0, 1];
+    const grayCodes = generateGrayCodes(n);
+    expect(grayCodes).toEqual(expectedGrayCodes);
+  });
+
+  test('Generate Gray codes for n=4', () => {
+    const n = 4;
+    const expectedGrayCodes = [
+      0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8
+    ];
+    const grayCodes = generateGrayCodes(n);
+    expect(grayCodes).toEqual(expectedGrayCodes);
+  });
+
+  test('Generate Gray codes for n=5', () => {
+    const n = 5;
+    const expectedGrayCodes = [
+      0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16
+    ];
+    const grayCodes = generateGrayCodes(n);
+    expect(grayCodes).toEqual(expectedGrayCodes);
+  });