Add Heap

src/algorithms/sorting/merge-sort.ts

@@ -61,7 +61,10 @@ function merge(left: Array<number>, right: Array<number>, order: SortingOrder):
 /**
  * Sort the array of numbers in either ascending or descending order, applying the merge sort algorithm.
  *
- * - Time complexity: O(N log(N)) where N is the size of the array.
+ * - Time complexity: O(N log(N))
+ * - Space complexity: O(N)
+ *
+ * where N is the size of the array.
  *
  * @param input the array of numbers to sort.
  * @param order specify the order of sorting: ascending or descending.

src/collections/Heap.ts

@@ -0,0 +1,65 @@
+import Collection from 'src/collections/Collection';
+import Comparable from 'src/util/Comparable';
+
+/**
+ * A heap is a binary tree that satisfies two properties:
+ *   1) Completeness: Every level of the tree (except last) is completely filled.
+ *      All holes in the last level are all the way to the right.
+ *   2) Heap Order Invariant: Every element in the tree is <= (or >=) its parent
+ *      depending if it's a max heap or a min heap.
+ *
+ * The items stored in this data structure must be comparable. For this reason,
+ * it only accepts types that extends the "Comparable" interface.
+ */
+export default interface Heap<T extends Comparable<T>> extends Collection<T> {
+  /**
+   * Adds a new element to the heap.
+   *
+   * @param element the comparable element to add.
+   * @complexity time: O(log n)
+   */
+  add(element: T): void;
+
+  /**
+   * Removes the root element and returns it.
+   * The root element can be the maximum one if it's a max heap,
+   * or the minimum one if it's a min heap.
+   *
+   * @returns the maximum element if a max heap, or the minimum if a min heap.
+   * @complexity time: O(log n)
+   */
+  poll(): T;
+
+  /**
+   * Returns the root element without removing it.
+   * The root element can be the maximum one if it's a max heap,
+   * or the minimum one if it's a min heap.
+   *
+   * @returns the maximum element if a max heap, or the minimum if a min heap.
+   * @complexity time: O(1)
+   */
+  peek(); T;
+
+  /**
+   * Returns the heap in array form.
+   */
+  toArray(): Array<T>;
+}
+
+// class Person implements Comparable<Person>{
+//   private name;
+
+//   constructor(name: string) {
+//     this.name = name;
+//   }
+
+//   getName() {
+//     return this.name;
+//   }
+
+//   compare(person: Person): Comparison {
+//     if (this.getName() === person.getName()) return Comparison.Equal;
+
+//     return Comparison.LessThan;
+//   }
+// }

src/collections/HeapArray.ts

@@ -0,0 +1,115 @@
+import Heap from 'src/collections/Heap';
+import Comparable, { Comparison } from 'src/util/Comparable';
+
+enum HeapType {
+  MaxHeap = 0,
+  MinHeap = 1
+}
+
+enum Operand { Left, Right };
+enum HeapType { Max, Min };
+
+/**
+ * Returns the right operand if:
+ * - It's a Max Heap and the right operand is strictly greater than the left one
+ * - It's a Min Heap and the right operand is strictly less than the left one
+ *
+ * Returns the left operand otherwise.
+ *
+ * @param left the left operand
+ * @param right the right operand
+ * @param heapType the type of heap (Max or Min)
+ */
+function whoWins(left: number, right: number, heapType: HeapType): Operand {
+  if (heapType === HeapType.Max && right > left || heapType === HeapType.Min && right < left) {
+    return Operand.Right;
+  } else {
+    return Operand.Left;
+  }
+}
+export default class HeapArray<T extends Comparable<T>> implements Heap<T> {
+
+  private heap: Array<T>;
+  private type: HeapType;
+
+  constructor(input: Array<T> = [], type: HeapType = HeapType.MaxHeap) {
+    this.heap = input;
+    this.type = type;
+    const current = Math.floor(this.heap.length / 2);
+    this.buildHeap(current);
+  }
+
+  private buildHeap(current: number): void {
+    for (let index = current; index >= 0; index--) {
+      this.bubbleDown(index);
+    }
+  }
+
+  private bubbleDown(current: number): void {
+    // if it is a leaf, exit
+    if (this.isLeaf(current)) return;
+    // if it is greater than or equal to the greatest of its children, exit
+    const leftChild = this.getLeftChild(current);
+    const rightChild = this.getRightChild(current);
+    const maxChild = this.getMax(leftChild, rightChild);
+    if (this.heap[current] >= this.heap[maxChild]) return;
+
+    this.swap(current, maxChild);
+    this.bubbleDown(maxChild);
+  }
+
+  private test() {
+    const left = this.heap[leftChild];
+    const right = this.heap[rightChild];
+    const operand = whoWins(left, right);
+    if (operand === Operand.Left)
+  }
+
+  private getMax(indexOne: number, indexTwo: number): number {
+    let one = this.heap[indexOne];
+    let two = this.heap[indexTwo];
+    if (one === undefined) return indexTwo;
+    if (two === undefined) return indexOne;
+    if (two > one) return indexTwo;
+    return indexOne;
+  }
+
+  private swap(indexOne: number, indexTwo: number): void {
+    const temp = this.heap[indexOne];
+    this.heap[indexOne] = this.heap[indexTwo];
+    this.heap[indexTwo] = temp;
+  }
+
+  private getParent(index: number): number {
+    return Math.floor((index - 1) / 2);
+  }
+
+  private getLeftChild(index: number): number {
+    return index * 2 + 1;
+  }
+
+  private getRightChild(index: number): number {
+    return index * 2 + 2;
+  }
+
+  private isRoot(index: number): boolean {
+    return index === 0;
+  }
+
+  private isLeaf(index: number): boolean {
+    // all elements in the second half of the array are leaves
+    return index >= Math.floor(this.heap.length / 2);
+  }
+
+  public add(element: T): void {
+
+  }
+
+  public poll(): T {
+    throw new Error('');
+  }
+
+  public peek(); T {
+    throw new Error('');
+  }
+}

src/collections/PriorityQueueArray.ts

@@ -1,4 +1,4 @@
-import QueueArray from './QueueArray.js';
+import QueueArray from 'src/collections/QueueArray';
 
 export default class PriorityQueueArray extends QueueArray<number> {
 
@@ -12,8 +12,8 @@ export default class PriorityQueueArray extends QueueArray<number> {
     } else {
       let added = false;
       for (let i = 0; i < super.size(); i++) {
-        if (item <= super.queue[i]) {
-          super.queue.splice(i, 0, item);
+        if (item <= this.queue[i]) {
+          this.queue.splice(i, 0, item);
           added = true;
           break;
         }

src/collections/Queue.ts

@@ -1,4 +1,4 @@
-import Collection from './Collection';
+import Collection from 'src/collections/Collection';
 
 /**
  * The {@code Queue} interface represents a first-in-first-out

src/collections/Stack.ts

@@ -1,4 +1,4 @@
-import Collection from './Collection';
+import Collection from 'src/collections/Collection';
 
 /**
  * The {@code Stack} interface represents a last-in-first-out

src/collections/StackArray.ts

@@ -1,5 +1,8 @@
 import Stack from 'src/collections/Stack';
 
+/**
+ * This class implements the Stack interface using the JavaScript dynamic array.
+ */
 export default class StackArray<T> implements Stack<T> {
 
   private stack: Array<T>;

src/heapWithNumbers.ts

@@ -0,0 +1,102 @@
+class Heap {
+
+  private heap: Array<number>;
+
+  constructor(input: Array<number> = []) {
+    this.heap = input;
+    const current = Math.floor(this.heap.length / 2);
+    this.buildHeap(current);
+  }
+
+  private buildHeap(current: number): void {
+    for (let index = current; index >= 0; index--) {
+      this.bubbleDown(index);
+    }
+  }
+
+  private bubbleDown(current: number): void {
+    // If the current node is a leaf, exit
+    if (this.isLeaf(current)) return;
+    // Get the max child
+    const maxChild = this.getMax(this.getLeftChild(current), this.getRightChild(current));
+    // If the current node is smaller than the max child
+    if (this.heap[current] < this.heap[maxChild]) {
+      // swap positio between the current node and its child
+      this.swap(current, maxChild);
+      // recursively call this function
+      this.bubbleDown(maxChild);
+    }
+  }
+
+  private bubbleUp(current: number): void {
+    // if it is root, exit
+    if (this.isRoot(current)) return;
+    // if it is not strictly greater than its parent, exit
+    const parent = this.getParent(current);
+    if (this.heap[current] <= this.heap[parent]) return;
+
+    this.swap(current, parent);
+    this.bubbleUp(parent);
+  }
+
+  private getParent(index: number): number {
+    return Math.floor((index - 1) / 2);
+  }
+
+  private getLeftChild(index: number): number {
+    return index * 2 + 1;
+  }
+
+  private getRightChild(index: number): number {
+    return index * 2 + 2;
+  }
+
+  private isRoot(index: number): boolean {
+    return index === 0;
+  }
+
+  private isLeaf(index: number): boolean {
+    const leftChild = this.getLeftChild(index);
+    const rightChild = this.getRightChild(index);
+    const N = this.heap.length;
+    return leftChild >= N && rightChild >= N;
+  }
+
+  private getMax(indexOne: number, indexTwo: number): number {
+    let one = this.heap[indexOne];
+    let two = this.heap[indexTwo];
+
+    if (one === undefined) return indexTwo;
+    if (two === undefined) return indexOne;
+
+    if (two > one) return indexTwo;
+
+    return indexOne;
+  }
+
+  private swap(indexOne: number, indexTwo: number): void {
+    const temp = this.heap[indexOne];
+    this.heap[indexOne] = this.heap[indexTwo];
+    this.heap[indexTwo] = temp;
+  }
+}
+
+
+const h = new Heap([2, 4, 7, 1, 5, 3]);
+// const h = new Heap();
+// h.add(2).add(4).add(7).add(1).add(5).add(3);
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());
+console.log(h.getRoot());
+console.log(h.toArray());

src/util/Comparable.ts

@@ -1,19 +1,43 @@
 /**
- * An enumeration that represents the result
- * of the comparison.
+ * A comparable object.
  */
-export enum Comparison {
-  EqualTo = 1,
-  LessThan = 2,
-  GreaterThan = 4,
-  LessThanOrEqualTo = 3,
-  GreaterThanOrEqualTo = 5
+export default interface Comparable<T> {
+  compare(item: T): ComparisonOperator;
 }
 
 /**
- * A class that implements this interface must define
- * a way to compare its objects.
+ * An enumeration that represents the comparison operator:
+ * - EqualTo: "="
+ * - LessThan: "<" (strictly less than)
+ * - GreaterThan: ">" (strictly greater than)
  */
-export default interface Comparable<T> {
-  compare(element: T): Comparison;
+export enum ComparisonOperator { EqualTo, LessThan, GreaterThan };
+
+/**
+ *
+ */
+export enum ComparisonType { Max, Min };
+
+/**
+ * An enumeration that represents the left and right operands of a comparison.
+ */
+export enum Operand { Left, Right };
+
+/**
+ * Tells which operand wins based on the comparison type (i.e. max or min).
+ * @param leftOperand
+ * @param rightOperand
+ * @param comparisonType
+ */
+export function whoWins<T extends Comparable<T>>(leftOperand: T, rightOperand: T, comparisonType: ComparisonType): Operand {
+  const comparison = rightOperand.compare(leftOperand);
+
+  if (
+    comparisonType === ComparisonType.Max && comparison === ComparisonOperator.GreaterThan ||
+    comparisonType === ComparisonType.Min && comparison === ComparisonOperator.LessThan
+  ) {
+    return Operand.Right;
+  }
+
+  return Operand.Left;
 }