merge: Add MinHeap and test (#817)

* Add MinHeap and test

* Add description and reference link

* Adjust formatting

Data-Structures/Heap/MinHeap.js

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+/**
+ *   Min Heap is one of the two Binary Heap types (the other is Max Heap)
+ *   which maintains the smallest value of its input array on top and remaining values in loosely (but not perfectly sorted) order.
+ *
+ *   Min Heaps can be expressed as a 'complete' binary tree structure
+ *   (in which all levels of the binary tree are filled, with the exception of the last level which must be filled left-to-right).
+ *
+ *   However the Min Heap class below expresses this tree structure as an array
+ *   which represent the binary tree node values in an array ordered from root-to-leaf, left-to-right.
+ *
+ *   In the array representation, the parent node-child node relationship is such that the
+ *      * parent index relative to its two children are: (parentIdx * 2) and (parent * 2 + 1)
+ *      * and either child's index position relative to its parent is: Math.floor((childIdx-1)/2)
+ *
+ *   The parent and respective child values define much of heap behavior as we continue to sort or not sort depending on their values.
+ *      * The parent value must be less than or equal to either child's value.
+ *
+ *   This is a condensed overview but for more information and visuals here is a nice read: https://www.geeksforgeeks.org/binary-heap/
+ */
+
+class MinHeap {
+  constructor (array) {
+    this.heap = this.initializeHeap(array)
+  }
+
+  /**
+   *   startingParent represents the parent of the last index (=== array.length-1)
+   *   and iterates towards 0 with all index values below sorted to meet heap conditions
+  */
+  initializeHeap (array) {
+    const startingParent = Math.floor((array.length - 2) / 2)
+
+    for (let currIdx = startingParent; currIdx >= 0; currIdx--) {
+      this.sinkDown(currIdx, array.length - 1, array)
+    }
+    return array
+  }
+
+  /**
+   *   overall functionality: heap-sort value at a starting index (currIdx) towards end of heap
+   *
+   *   currIdx is considered to be a starting 'parent' index of two children indices (childOneIdx, childTwoIdx).
+   *   endIdx represents the last valid index in the heap.
+   *
+   *   first check that childOneIdx and childTwoIdx are both smaller than endIdx
+   *   and check for the smaller heap value between them.
+   *
+   *   the child index with the smaller heap value is set to a variable called swapIdx.
+   *
+   *   swapIdx's value will be compared to currIdx (the 'parent' index)
+   *   and if swapIdx's value is smaller than currIdx's value, swap the values in the heap,
+   *   update currIdx and recalculate the new childOneIdx to check heap conditions again.
+   *
+   *   if there is no swap, it means the children indices and the parent index satisfy heap conditions and can exit the function.
+  */
+  sinkDown (currIdx, endIdx, heap) {
+    let childOneIdx = currIdx * 2 + 1
+
+    while (childOneIdx <= endIdx) {
+      const childTwoIdx = childOneIdx + 1 <= endIdx ? childOneIdx + 1 : -1
+      const swapIdx = childTwoIdx !== -1 && heap[childTwoIdx] < heap[childOneIdx]
+        ? childTwoIdx
+        : childOneIdx
+
+      if (heap[swapIdx] < heap[currIdx]) {
+        this.swap(currIdx, swapIdx, heap)
+        currIdx = swapIdx
+        childOneIdx = currIdx * 2 + 1
+      } else {
+        return
+      }
+    }
+  }
+
+  /**
+   *   overall functionality: heap-sort value at a starting index (currIdx) towards front of heap.
+   *
+   *   while the currIdx's value is smaller than its parent's (parentIdx) value, swap the values in the heap
+   *   update currIdx and recalculate the new parentIdx to check heap condition again.
+   *
+   *   iteration does not end while a valid currIdx has a value smaller than its parentIdx's value
+  */
+  bubbleUp (currIdx) {
+    let parentIdx = Math.floor((currIdx - 1) / 2)
+
+    while (currIdx > 0 && this.heap[currIdx] < this.heap[parentIdx]) {
+      this.swap(currIdx, parentIdx, this.heap)
+      currIdx = parentIdx
+      parentIdx = Math.floor((currIdx - 1) / 2)
+    }
+  }
+
+  peek () {
+    return this.heap[0]
+  }
+
+  /**
+   *   the min heap value should be the first value in the heap (=== this.heap[0])
+   *
+   *   firstIdx value and lastIdx value are swapped
+   *   the resulting min heap value now resides at heap[heap.length-1] which is popped and later returned.
+   *
+   *   the remaining values in the heap are re-sorted
+  */
+  extractMin () {
+    this.swap(0, this.heap.length - 1, this.heap)
+    const min = this.heap.pop()
+    this.sinkDown(0, this.heap.length - 1, this.heap)
+    return min
+  }
+
+  // a new value is pushed to the end of the heap and sorted up
+  insert (value) {
+    this.heap.push(value)
+    this.bubbleUp(this.heap.length - 1)
+  }
+
+  // index-swapping helper method
+  swap (idx1, idx2, heap) {
+    const temp = heap[idx1]
+    heap[idx1] = heap[idx2]
+    heap[idx2] = temp
+  }
+}
+
+export { MinHeap }

Data-Structures/Heap/test/MinHeap.test.js

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+import { MinHeap } from '../MinHeap'
+
+describe('MinHeap', () => {
+  const array = [2, 4, 10, 23, 43, 42, 39, 7, 9, 16, 85, 1, 51]
+  let heap
+
+  beforeEach(() => {
+    heap = new MinHeap(array)
+  })
+
+  it('should initialize a heap from an input array', () => {
+    expect(heap).toEqual({ 'heap': [1, 4, 2, 7, 16, 10, 39, 23, 9, 43, 85, 42, 51] })   // eslint-disable-line
+  })
+
+  it('should show the top value in the heap', () => {
+    const minValue = heap.peek()
+
+    expect(minValue).toEqual(1)
+  })
+
+  it('should remove and return the top value in the heap', () => {
+    const minValue = heap.extractMin()
+
+    expect(minValue).toEqual(1)
+    expect(heap).toEqual({ 'heap': [2, 4, 10, 7, 16, 42, 39, 23, 9, 43, 85, 51] })      // eslint-disable-line
+  })
+
+  it('should insert a new value and sort until it meets heap conditions', () => {
+    heap.insert(15)
+
+    expect(heap).toEqual({ 'heap': [2, 4, 10, 7, 16, 15, 39, 23, 9, 43, 85, 51, 42] })  // eslint-disable-line
+  })
+})