Ad hoc versions of MinHeap, MaxHeap, and DisjointSet (#1117)

* Add DisjointSetMinimalistic

* Add MinHeapMinimalistic and MaxHeapMinimalistic

* Rename minimalistic to adhoc

* Update README

src/data-structures/disjoint-set/DisjointSetAdhoc.js

@@ -0,0 +1,78 @@
+/**
+ * The minimalistic (ad hoc) version of a DisjointSet (or a UnionFind) data structure
+ * that doesn't have external dependencies and that is easy to copy-paste and
+ * use during the coding interview if allowed by the interviewer (since many
+ * data structures in JS are missing).
+ *
+ * Time Complexity:
+ *
+ * - Constructor: O(N)
+ * - Find: O(α(N))
+ * - Union: O(α(N))
+ * - Connected: O(α(N))
+ *
+ * Where N is the number of vertices in the graph.
+ * α refers to the Inverse Ackermann function.
+ * In practice, we assume it's a constant.
+ * In other words, O(α(N)) is regarded as O(1) on average.
+ */
+class DisjointSetAdhoc {
+  /**
+   * Initializes the set of specified size.
+   * @param {number} size
+   */
+  constructor(size) {
+    // The index of a cell is an id of the node in a set.
+    // The value of a cell is an id (index) of the root node.
+    // By default, the node is a parent of itself.
+    this.roots = new Array(size).fill(0).map((_, i) => i);
+
+    // Using the heights array to record the height of each node.
+    // By default each node has a height of 1 because it has no children.
+    this.heights = new Array(size).fill(1);
+  }
+
+  /**
+   * Finds the root of node `a`
+   * @param {number} a
+   * @returns {number}
+   */
+  find(a) {
+    if (a === this.roots[a]) return a;
+    this.roots[a] = this.find(this.roots[a]);
+    return this.roots[a];
+  }
+
+  /**
+   * Joins the `a` and `b` nodes into same set.
+   * @param {number} a
+   * @param {number} b
+   * @returns {number}
+   */
+  union(a, b) {
+    const aRoot = this.find(a);
+    const bRoot = this.find(b);
+
+    if (aRoot === bRoot) return;
+
+    if (this.heights[aRoot] > this.heights[bRoot]) {
+      this.roots[bRoot] = aRoot;
+    } else if (this.heights[aRoot] < this.heights[bRoot]) {
+      this.roots[aRoot] = bRoot;
+    } else {
+      this.roots[bRoot] = aRoot;
+      this.heights[aRoot] += 1;
+    }
+  }
+
+  /**
+   * Checks if `a` and `b` belong to the same set.
+   * @param {number} a
+   * @param {number} b
+   */
+  connected(a, b) {
+    return this.find(a) === this.find(b);
+  }
+}
+
+export default DisjointSetAdhoc;

src/data-structures/disjoint-set/README.md

@@ -19,6 +19,11 @@ _MakeSet_ creates 8 singletons.
 
 After some operations of _Union_, some sets are grouped together.
 
+## Implementation
+
+- [DisjointSet.js](./DisjointSet.js)
+- [DisjointSetAdhoc.js](./DisjointSetAdhoc.js) - The minimalistic (ad hoc) version of a DisjointSet (or a UnionFind) data structure that doesn't have external dependencies and that is easy to copy-paste and use during the coding interview if allowed by the interviewer (since many data structures in JS are missing).
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)

src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js

@@ -0,0 +1,50 @@
+import DisjointSetAdhoc from '../DisjointSetAdhoc';
+
+describe('DisjointSetAdhoc', () => {
+  it('should create unions and find connected elements', () => {
+    const set = new DisjointSetAdhoc(10);
+
+    // 1-2-5-6-7 3-8-9 4
+    set.union(1, 2);
+    set.union(2, 5);
+    set.union(5, 6);
+    set.union(6, 7);
+
+    set.union(3, 8);
+    set.union(8, 9);
+
+    expect(set.connected(1, 5)).toBe(true);
+    expect(set.connected(5, 7)).toBe(true);
+    expect(set.connected(3, 8)).toBe(true);
+
+    expect(set.connected(4, 9)).toBe(false);
+    expect(set.connected(4, 7)).toBe(false);
+
+    // 1-2-5-6-7 3-8-9-4
+    set.union(9, 4);
+
+    expect(set.connected(4, 9)).toBe(true);
+    expect(set.connected(4, 3)).toBe(true);
+    expect(set.connected(8, 4)).toBe(true);
+
+    expect(set.connected(8, 7)).toBe(false);
+    expect(set.connected(2, 3)).toBe(false);
+  });
+
+  it('should keep the height of the tree small', () => {
+    const set = new DisjointSetAdhoc(10);
+
+    // 1-2-6-7-9 1 3 4 5
+    set.union(7, 6);
+    set.union(1, 2);
+    set.union(2, 6);
+    set.union(1, 7);
+    set.union(9, 1);
+
+    expect(set.connected(1, 7)).toBe(true);
+    expect(set.connected(6, 9)).toBe(true);
+    expect(set.connected(4, 9)).toBe(false);
+
+    expect(Math.max(...set.heights)).toBe(3);
+  });
+});

src/data-structures/heap/MaxHeapAdhoc.js

@@ -0,0 +1,115 @@
+/**
+ * The minimalistic (ad hoc) version of a MaxHeap data structure that doesn't have
+ * external dependencies and that is easy to copy-paste and use during the
+ * coding interview if allowed by the interviewer (since many data
+ * structures in JS are missing).
+ */
+class MaxHeapAdhoc {
+  constructor(heap = []) {
+    this.heap = [];
+    heap.forEach(this.add);
+  }
+
+  add(num) {
+    this.heap.push(num);
+    this.heapifyUp();
+  }
+
+  peek() {
+    return this.heap[0];
+  }
+
+  poll() {
+    if (this.heap.length === 0) return undefined;
+    const top = this.heap[0];
+    this.heap[0] = this.heap[this.heap.length - 1];
+    this.heap.pop();
+    this.heapifyDown();
+    return top;
+  }
+
+  isEmpty() {
+    return this.heap.length === 0;
+  }
+
+  toString() {
+    return this.heap.join(',');
+  }
+
+  heapifyUp() {
+    let nodeIndex = this.heap.length - 1;
+    while (nodeIndex > 0) {
+      const parentIndex = this.getParentIndex(nodeIndex);
+      if (this.heap[parentIndex] >= this.heap[nodeIndex]) break;
+      this.swap(parentIndex, nodeIndex);
+      nodeIndex = parentIndex;
+    }
+  }
+
+  heapifyDown() {
+    let nodeIndex = 0;
+
+    while (
+      (
+        this.hasLeftChild(nodeIndex) && this.heap[nodeIndex] < this.leftChild(nodeIndex)
+      )
+      || (
+        this.hasRightChild(nodeIndex) && this.heap[nodeIndex] < this.rightChild(nodeIndex)
+      )
+    ) {
+      const leftIndex = this.getLeftChildIndex(nodeIndex);
+      const rightIndex = this.getRightChildIndex(nodeIndex);
+      const left = this.leftChild(nodeIndex);
+      const right = this.rightChild(nodeIndex);
+
+      if (this.hasLeftChild(nodeIndex) && this.hasRightChild(nodeIndex)) {
+        if (left >= right) {
+          this.swap(leftIndex, nodeIndex);
+          nodeIndex = leftIndex;
+        } else {
+          this.swap(rightIndex, nodeIndex);
+          nodeIndex = rightIndex;
+        }
+      } else if (this.hasLeftChild(nodeIndex)) {
+        this.swap(leftIndex, nodeIndex);
+        nodeIndex = leftIndex;
+      }
+    }
+  }
+
+  getLeftChildIndex(parentIndex) {
+    return (2 * parentIndex) + 1;
+  }
+
+  getRightChildIndex(parentIndex) {
+    return (2 * parentIndex) + 2;
+  }
+
+  getParentIndex(childIndex) {
+    return Math.floor((childIndex - 1) / 2);
+  }
+
+  hasLeftChild(parentIndex) {
+    return this.getLeftChildIndex(parentIndex) < this.heap.length;
+  }
+
+  hasRightChild(parentIndex) {
+    return this.getRightChildIndex(parentIndex) < this.heap.length;
+  }
+
+  leftChild(parentIndex) {
+    return this.heap[this.getLeftChildIndex(parentIndex)];
+  }
+
+  rightChild(parentIndex) {
+    return this.heap[this.getRightChildIndex(parentIndex)];
+  }
+
+  swap(indexOne, indexTwo) {
+    const tmp = this.heap[indexTwo];
+    this.heap[indexTwo] = this.heap[indexOne];
+    this.heap[indexOne] = tmp;
+  }
+}
+
+export default MaxHeapAdhoc;

src/data-structures/heap/MinHeapAdhoc.js

@@ -0,0 +1,117 @@
+/**
+ * The minimalistic (ad hoc) version of a MinHeap data structure that doesn't have
+ * external dependencies and that is easy to copy-paste and use during the
+ * coding interview if allowed by the interviewer (since many data
+ * structures in JS are missing).
+ */
+class MinHeapAdhoc {
+  constructor(heap = []) {
+    this.heap = [];
+    heap.forEach(this.add);
+  }
+
+  add(num) {
+    this.heap.push(num);
+    this.heapifyUp();
+  }
+
+  peek() {
+    return this.heap[0];
+  }
+
+  poll() {
+    if (this.heap.length === 0) return undefined;
+    const top = this.heap[0];
+    this.heap[0] = this.heap[this.heap.length - 1];
+    this.heap.pop();
+    this.heapifyDown();
+    return top;
+  }
+
+  isEmpty() {
+    return this.heap.length === 0;
+  }
+
+  toString() {
+    return this.heap.join(',');
+  }
+
+  heapifyUp() {
+    let nodeIndex = this.heap.length - 1;
+    while (nodeIndex > 0) {
+      const parentIndex = this.getParentIndex(nodeIndex);
+      if (this.heap[parentIndex] <= this.heap[nodeIndex]) break;
+      this.swap(parentIndex, nodeIndex);
+      nodeIndex = parentIndex;
+    }
+  }
+
+  heapifyDown() {
+    let nodeIndex = 0;
+
+    while (
+      (
+        this.hasLeftChild(nodeIndex)
+        && this.heap[nodeIndex] > this.leftChild(nodeIndex)
+      )
+      || (
+        this.hasRightChild(nodeIndex)
+        && this.heap[nodeIndex] > this.rightChild(nodeIndex)
+      )
+    ) {
+      const leftIndex = this.getLeftChildIndex(nodeIndex);
+      const rightIndex = this.getRightChildIndex(nodeIndex);
+      const left = this.leftChild(nodeIndex);
+      const right = this.rightChild(nodeIndex);
+
+      if (this.hasLeftChild(nodeIndex) && this.hasRightChild(nodeIndex)) {
+        if (left <= right) {
+          this.swap(leftIndex, nodeIndex);
+          nodeIndex = leftIndex;
+        } else {
+          this.swap(rightIndex, nodeIndex);
+          nodeIndex = rightIndex;
+        }
+      } else if (this.hasLeftChild(nodeIndex)) {
+        this.swap(leftIndex, nodeIndex);
+        nodeIndex = leftIndex;
+      }
+    }
+  }
+
+  getLeftChildIndex(parentIndex) {
+    return 2 * parentIndex + 1;
+  }
+
+  getRightChildIndex(parentIndex) {
+    return 2 * parentIndex + 2;
+  }
+
+  getParentIndex(childIndex) {
+    return Math.floor((childIndex - 1) / 2);
+  }
+
+  hasLeftChild(parentIndex) {
+    return this.getLeftChildIndex(parentIndex) < this.heap.length;
+  }
+
+  hasRightChild(parentIndex) {
+    return this.getRightChildIndex(parentIndex) < this.heap.length;
+  }
+
+  leftChild(parentIndex) {
+    return this.heap[this.getLeftChildIndex(parentIndex)];
+  }
+
+  rightChild(parentIndex) {
+    return this.heap[this.getRightChildIndex(parentIndex)];
+  }
+
+  swap(indexOne, indexTwo) {
+    const tmp = this.heap[indexTwo];
+    this.heap[indexTwo] = this.heap[indexOne];
+    this.heap[indexOne] = tmp;
+  }
+}
+
+export default MinHeapAdhoc;

src/data-structures/heap/README.md

@@ -58,6 +58,11 @@ Where:
 
 > In this repository, the [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js) are examples of the **Binary** heap.
 
+## Implementation
+
+- [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js)
+- [MaxHeapAdhoc.js](./MaxHeapAdhoc.js) and [MinHeapAdhoc.js](./MinHeapAdhoc.js) - The minimalistic (ad hoc) version of a MinHeap/MaxHeap data structure that doesn't have external dependencies and that is easy to copy-paste and use during the coding interview if allowed by the interviewer (since many data structures in JS are missing).
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))

src/data-structures/heap/__test__/MaxHeapAdhoc.test.js

@@ -0,0 +1,91 @@
+import MaxHeap from '../MaxHeapAdhoc';
+
+describe('MaxHeapAdhoc', () => {
+  it('should create an empty max heap', () => {
+    const maxHeap = new MaxHeap();
+
+    expect(maxHeap).toBeDefined();
+    expect(maxHeap.peek()).toBe(undefined);
+    expect(maxHeap.isEmpty()).toBe(true);
+  });
+
+  it('should add items to the heap and heapify it up', () => {
+    const maxHeap = new MaxHeap();
+
+    maxHeap.add(5);
+    expect(maxHeap.isEmpty()).toBe(false);
+    expect(maxHeap.peek()).toBe(5);
+    expect(maxHeap.toString()).toBe('5');
+
+    maxHeap.add(3);
+    expect(maxHeap.peek()).toBe(5);
+    expect(maxHeap.toString()).toBe('5,3');
+
+    maxHeap.add(10);
+    expect(maxHeap.peek()).toBe(10);
+    expect(maxHeap.toString()).toBe('10,3,5');
+
+    maxHeap.add(1);
+    expect(maxHeap.peek()).toBe(10);
+    expect(maxHeap.toString()).toBe('10,3,5,1');
+
+    maxHeap.add(1);
+    expect(maxHeap.peek()).toBe(10);
+    expect(maxHeap.toString()).toBe('10,3,5,1,1');
+
+    expect(maxHeap.poll()).toBe(10);
+    expect(maxHeap.toString()).toBe('5,3,1,1');
+
+    expect(maxHeap.poll()).toBe(5);
+    expect(maxHeap.toString()).toBe('3,1,1');
+
+    expect(maxHeap.poll()).toBe(3);
+    expect(maxHeap.toString()).toBe('1,1');
+  });
+
+  it('should poll items from the heap and heapify it down', () => {
+    const maxHeap = new MaxHeap();
+
+    maxHeap.add(5);
+    maxHeap.add(3);
+    maxHeap.add(10);
+    maxHeap.add(11);
+    maxHeap.add(1);
+
+    expect(maxHeap.toString()).toBe('11,10,5,3,1');
+
+    expect(maxHeap.poll()).toBe(11);
+    expect(maxHeap.toString()).toBe('10,3,5,1');
+
+    expect(maxHeap.poll()).toBe(10);
+    expect(maxHeap.toString()).toBe('5,3,1');
+
+    expect(maxHeap.poll()).toBe(5);
+    expect(maxHeap.toString()).toBe('3,1');
+
+    expect(maxHeap.poll()).toBe(3);
+    expect(maxHeap.toString()).toBe('1');
+
+    expect(maxHeap.poll()).toBe(1);
+    expect(maxHeap.toString()).toBe('');
+
+    expect(maxHeap.poll()).toBe(undefined);
+    expect(maxHeap.toString()).toBe('');
+  });
+
+  it('should heapify down through the right branch as well', () => {
+    const maxHeap = new MaxHeap();
+
+    maxHeap.add(3);
+    maxHeap.add(12);
+    maxHeap.add(10);
+
+    expect(maxHeap.toString()).toBe('12,3,10');
+
+    maxHeap.add(11);
+    expect(maxHeap.toString()).toBe('12,11,10,3');
+
+    expect(maxHeap.poll()).toBe(12);
+    expect(maxHeap.toString()).toBe('11,3,10');
+  });
+});

src/data-structures/heap/__test__/MinHeapAdhoc.test.js

@@ -0,0 +1,91 @@
+import MinHeapAdhoc from '../MinHeapAdhoc';
+
+describe('MinHeapAdhoc', () => {
+  it('should create an empty min heap', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    expect(minHeap).toBeDefined();
+    expect(minHeap.peek()).toBe(undefined);
+    expect(minHeap.isEmpty()).toBe(true);
+  });
+
+  it('should add items to the heap and heapify it up', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    minHeap.add(5);
+    expect(minHeap.isEmpty()).toBe(false);
+    expect(minHeap.peek()).toBe(5);
+    expect(minHeap.toString()).toBe('5');
+
+    minHeap.add(3);
+    expect(minHeap.peek()).toBe(3);
+    expect(minHeap.toString()).toBe('3,5');
+
+    minHeap.add(10);
+    expect(minHeap.peek()).toBe(3);
+    expect(minHeap.toString()).toBe('3,5,10');
+
+    minHeap.add(1);
+    expect(minHeap.peek()).toBe(1);
+    expect(minHeap.toString()).toBe('1,3,10,5');
+
+    minHeap.add(1);
+    expect(minHeap.peek()).toBe(1);
+    expect(minHeap.toString()).toBe('1,1,10,5,3');
+
+    expect(minHeap.poll()).toBe(1);
+    expect(minHeap.toString()).toBe('1,3,10,5');
+
+    expect(minHeap.poll()).toBe(1);
+    expect(minHeap.toString()).toBe('3,5,10');
+
+    expect(minHeap.poll()).toBe(3);
+    expect(minHeap.toString()).toBe('5,10');
+  });
+
+  it('should poll items from the heap and heapify it down', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    minHeap.add(5);
+    minHeap.add(3);
+    minHeap.add(10);
+    minHeap.add(11);
+    minHeap.add(1);
+
+    expect(minHeap.toString()).toBe('1,3,10,11,5');
+
+    expect(minHeap.poll()).toBe(1);
+    expect(minHeap.toString()).toBe('3,5,10,11');
+
+    expect(minHeap.poll()).toBe(3);
+    expect(minHeap.toString()).toBe('5,11,10');
+
+    expect(minHeap.poll()).toBe(5);
+    expect(minHeap.toString()).toBe('10,11');
+
+    expect(minHeap.poll()).toBe(10);
+    expect(minHeap.toString()).toBe('11');
+
+    expect(minHeap.poll()).toBe(11);
+    expect(minHeap.toString()).toBe('');
+
+    expect(minHeap.poll()).toBe(undefined);
+    expect(minHeap.toString()).toBe('');
+  });
+
+  it('should heapify down through the right branch as well', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    minHeap.add(3);
+    minHeap.add(12);
+    minHeap.add(10);
+
+    expect(minHeap.toString()).toBe('3,12,10');
+
+    minHeap.add(11);
+    expect(minHeap.toString()).toBe('3,11,10,12');
+
+    expect(minHeap.poll()).toBe(3);
+    expect(minHeap.toString()).toBe('10,11,12');
+  });
+});