Add binary heap data structure

src/utils/Heap.ts

@@ -0,0 +1,142 @@
+/** Binary heap. */
+abstract class BinHeap<T> {
+  /**
+   * Heap data array consisting of [weight, payload] pairs, arranged by weight
+   * to satisfy heap condition.
+   *
+   * Encodes the binary tree by storing tree root at index 0 and
+   * left child of element i at `i * 2 + 1` and
+   * right child of element i at `i * 2 + 2`.
+   */
+  protected data: [number, T][];
+
+  constructor() {
+    this.data = [];
+  }
+
+  /** Get number of elements in the heap. */
+  public get size() {
+    return this.data.length;
+  }
+
+  /**
+   * Should element with weight `weightA` be closer to root than element with
+   * weight `weightB`?
+   */
+  protected abstract heapOrderABeforeB(weightA: number, weightB: number): boolean;
+
+  /** Restore heap condition, starting at index i and traveling towards root. */
+  protected heapifyUp(i: number): void {
+    // Swap the new element up towards root until it reaches root position or
+    // settles under under a suitable parent
+    while(i > 0) {
+      const p = Math.floor((i - 1) / 2);
+
+      // Reached heap-ordered state already?
+      if(this.heapOrderABeforeB(this.data[p][0], this.data[i][0]))
+         break;
+
+      // Swap
+      const tmp = this.data[p];
+      this.data[p] = this.data[i];
+      this.data[i] = tmp;
+
+      // And repeat at parent index
+      i = p;
+    }
+  }
+
+  /** Restore heap condition, starting at index i and traveling away from root. */
+  protected heapifyDown(i: number): void {
+    // Swap the shifted element down in the heap until it either reaches the
+    // bottom layer or is in correct order relative to it's children
+    while(i < this.data.length) {
+      const l = i * 2 + 1;
+      const r = i * 2 + 2;
+      let toSwap = i;
+
+      // Find which one of element i and it's children should be closest to root
+      if(l < this.data.length && this.heapOrderABeforeB(this.data[l][0], this.data[toSwap][0]))
+        toSwap = l;
+      if(r < this.data.length && this.heapOrderABeforeB(this.data[r][0], this.data[toSwap][0]))
+        toSwap = r;
+
+      // Already in order?
+      if(i == toSwap)
+        break;
+
+      // Not in order. Swap child that should be closest to root up to 'i' and repeat
+      const tmp = this.data[toSwap];
+      this.data[toSwap] = this.data[i];
+      this.data[i] = tmp;
+
+      i = toSwap;
+    }
+  }
+
+  /** Add a new element to the heap. */
+  public push(value: T, weight: number): void {
+    const i = this.data.length;
+    this.data[i] = [weight, value];
+    this.heapifyUp(i);
+  }
+
+  /** Get the value of the root-most element of the heap, without changing the heap. */
+  public peek(): T | undefined {
+    if(this.data.length == 0)
+      return undefined;
+
+    return this.data[0][1];
+  }
+
+  /** Remove the root-most element of the heap and return the removed element's value. */
+  public pop(): T | undefined {
+    if(this.data.length == 0)
+      return undefined;
+
+    const value = this.data[0][1];
+
+    this.data[0] = this.data[this.data.length - 1];
+    this.data.length = this.data.length - 1;
+
+    this.heapifyDown(0);
+
+    return value;
+  }
+
+  /** Change the weight of an element in the heap. */
+  public changeWeight(predicate: (value: T) => boolean, weight: number): void {
+    // Find first element with matching value, if any
+    const i = this.data.findIndex(([_, v]) => predicate(v));
+    if(i == -1)
+      return;
+
+    // Update that element's weight
+    this.data[i][0] = weight;
+
+    // And re-heapify if needed
+    const p = Math.floor((i - 1) / 2);
+    const l = i * 2 + 1;
+    const r = i * 2 + 2;
+
+    if(!this.heapOrderABeforeB(this.data[p][0], this.data[i][0])) // Needs to shift root-wards?
+      this.heapifyUp(i);
+    else // Try shifting deeper
+      this.heapifyDown(i);
+  }
+}
+
+
+/** Binary max-heap. */
+export class MaxHeap<T> extends BinHeap<T> {
+  heapOrderABeforeB(weightA: number, weightB: number): boolean {
+    return weightA > weightB;
+  }
+}
+
+/** Binary min-heap. */
+export class MinHeap<T> extends BinHeap<T> {
+  heapOrderABeforeB(weightA: number, weightB: number): boolean {
+    return weightA < weightB;
+  }
+}