feat: add quick select algorithm and test #6

sorts/quick_select.ts

@@ -0,0 +1,54 @@
+/**
+ * @function partition
+ * @description is a helper function used in the QuickSelect algorithm to partition the array around a pivot element
+ * @param {number[]} arr - The array to partition
+ * @param {number} left - The left boundary of the partition range
+ * @param {number} right - The right boundary of the partition range
+ * @param {number} pivotIndex - The index of the pivot element
+ * @returns {number} - The new index of the pivot element after partitioning
+ */
+
+function partition(arr: number[], left: number, right: number, pivotIndex: number): number {
+    const pivotValue = arr[pivotIndex];
+    [arr[pivotIndex], arr[right]] = [arr[right], arr[pivotIndex]];
+    let storeIndex = left;
+
+    for (let i = left; i < right; i++) {
+        if (arr[i] < pivotValue) {
+            [arr[i], arr[storeIndex]] = [arr[storeIndex], arr[i]];
+            storeIndex++;
+        }
+    }
+
+    [arr[storeIndex], arr[right]] = [arr[right], arr[storeIndex]];
+    return storeIndex;
+}
+
+/**
+ * @function quickSelect
+ * @description is an algorithm based on the QuickSort approach that selects the kth smallest element from an array
+ * @param {number[]} arr - The array from which to select the element
+ * @param {number} left - The left boundary of the array or subarray to consider
+ * @param {number} right - The right boundary of the array or subarray to consider
+ * @param {number} k - The index representing the kth smallest element to find
+ * @returns {number} - The kth smallest element from the array
+ */
+
+export function quickSelect(arr: number[], left: number, right: number, k: number): number {
+    if (left === right) {
+        return arr[left];
+    }
+
+    const pivotIndex = Math.floor(Math.random() * (right - left + 1)) + left;
+    const pivotNewIndex = partition(arr, left, right, pivotIndex);
+
+    if (k === pivotNewIndex) {
+        return arr[k];
+    } else if (k < pivotNewIndex) {
+        return quickSelect(arr, left, pivotNewIndex - 1, k);
+    } else {
+        return quickSelect(arr, pivotNewIndex + 1, right, k);
+    }
+}
+
+

sorts/test/quick_select.test.ts

@@ -0,0 +1,18 @@
+import { quickSelect } from "../quick_select";
+
+describe("Quick Select", () => {
+
+    it("should return the correct value for worst case", () => {
+        const arr = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1];
+        const k = 2; // kth smallest element
+
+        expect(quickSelect(arr, 0, arr.length - 1, k)).toBe(3);
+    });
+
+    it("should return the correct value for best case", () => {
+        const arr = [1, 4, 2, 9, 5, 7, 3, 8, 10, 6];
+        const k = 5; // kth smallest element
+
+        expect(quickSelect(arr, 0, arr.length - 1, k)).toBe(6);
+    });
+});