[Feat] : Added Quick Sort (#35)

Author: Rajat379

Sorts/QuickSort.ts

@@ -0,0 +1,74 @@
+/**
+ * @function quickSort
+ * @description is an algorithm based on divide and conquer approach in which an array is split into sub-arrays and these sub arrays are recursively sorted to get final array
+ * @see [Quick Sort](https://www.javatpoint.com/quick-sort)
+ * @example QuickSort([8, 3, 5, 1, 4, 2]) = [1, 2, 3, 4, 5, 8]
+ */
+
+export const partition = (
+  array: number[],
+  left: number = 0,
+  right: number = array.length - 1
+) => {
+  const pivot = array[Math.floor((right + left) / 2)];
+  let i = left;
+  let j = right;
+
+  while (i <= j) {
+    while (array[i] < pivot) {
+      i++;
+    }
+
+    while (array[j] > pivot) {
+      j--;
+    }
+
+    if (i <= j) {
+      [array[i], array[j]] = [array[j], array[i]];
+      i++;
+      j--;
+    }
+  }
+
+  return i;
+};
+
+/**
+ * Quicksort implementation
+ *
+ * @param {number[]} array
+ * @param {number} [left=0]
+ * @param {number} [right=array.length - 1]
+ * @returns {number[]}
+ * @complexity_analysis
+ * Space complexity - O(nlogn)
+ * Time complexity 
+ *      Best case   -   O(nlogn)
+ *                      When pivot element lies in the middle of the list
+ *      Worst case  -   O(n^2)
+ *                      When pivot element lies on the extreme ends
+ *      Average case -  O(nlogn)
+ *                      When the above two cases are not met
+ */
+
+export const QuickSort = (
+  array: number[],
+  left: number = 0,
+  right: number = array.length - 1
+) => {
+  let index;
+
+  if (array.length > 1) {
+    index = partition(array, left, right);
+
+    if (left < index - 1) {
+      QuickSort(array, left, index - 1);
+    }
+
+    if (index < right) {
+      QuickSort(array, index, right);
+    }
+  }
+
+  return array;
+};

Sorts/test/QuickSort.test.ts

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+import { QuickSort } from "../QuickSort";
+
+describe("Quick Sort", () => {
+    it("should return the correct value for average case", () => {
+        expect(QuickSort([1, 4, 2, 5, 9, 6, 3, 8, 10, 7])).toStrictEqual([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
+    });
+  
+    it("should return the correct value for worst case", () => {
+      expect(QuickSort([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])).toStrictEqual([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
+    });
+  
+    it("should return the correct value for best case", () => {
+      expect(QuickSort([1, 4, 2, 9, 5, 7, 3, 8, 10, 6])).toStrictEqual([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
+    });
+  });