在Javascript中实现优先级队列的有效方法？

Question

优先级队列具有每个条目的优先级值和数据.

因此,在向队列添加新元素时,如果它具有比集合中已有的元素更高的优先级值,则它会向表面冒泡.

当一个人调用pop时,我们获得具有最高优先级的元素的数据.

在Javascript中有效实现这样的优先级队列是什么？

有一个名为PriorityQueue的新对象,创建两个带有两个参数(数据,优先级)的方法(推送和弹出)是否有意义？作为一个编码器,这对我来说是有意义的,但我不确定在下腹部使用哪种数据结构将允许操纵元素的排序.或者我们可以将它们全部存储在一个数组中并每次遍历数组以获取具有最高优先级的元素？

这样做的好方法是什么？

Answer 1

下面是我认为是一个真正有效的版本,PriorityQueue它使用基于阵列的二元堆(其中的根源是在索引0和节点的索引的孩子i正处于指数2i + 1和2i + 2,分别).

该实施方式包括经典的优先级队列的方法,如push,peek,pop,和size,以及方便的方法isEmpty和replace(对于后者是一种更有效的替代pop由紧接着push).值不是作为[value, priority]对存储,而是简单地存储为values; 这允许对可以使用>操作员进行本地比较的类型的自动优先化.传递给PriorityQueue构造函数的自定义比较器函数可用于模拟成对语义的行为,但是,如下面的示例所示.

基于堆的实施:

const top = 0;
const parent = i => ((i + 1) >>> 1) - 1;
const left = i => (i << 1) + 1;
const right = i => (i + 1) << 1;

class PriorityQueue {
  constructor(comparator = (a, b) => a > b) {
    this._heap = [];
    this._comparator = comparator;
  }
  size() {
    return this._heap.length;
  }
  isEmpty() {
    return this.size() == 0;
  }
  peek() {
    return this._heap[top];
  }
  push(...values) {
    values.forEach(value => {
      this._heap.push(value);
      this._siftUp();
    });
    return this.size();
  }
  pop() {
    const poppedValue = this.peek();
    const bottom = this.size() - 1;
    if (bottom > top) {
      this._swap(top, bottom);
    }
    this._heap.pop();
    this._siftDown();
    return poppedValue;
  }
  replace(value) {
    const replacedValue = this.peek();
    this._heap[top] = value;
    this._siftDown();
    return replacedValue;
  }
  _greater(i, j) {
    return this._comparator(this._heap[i], this._heap[j]);
  }
  _swap(i, j) {
    [this._heap[i], this._heap[j]] = [this._heap[j], this._heap[i]];
  }
  _siftUp() {
    let node = this.size() - 1;
    while (node > top && this._greater(node, parent(node))) {
      this._swap(node, parent(node));
      node = parent(node);
    }
  }
  _siftDown() {
    let node = top;
    while (
      (left(node) < this.size() && this._greater(left(node), node)) ||
      (right(node) < this.size() && this._greater(right(node), node))
    ) {
      let maxChild = (right(node) < this.size() && this._greater(right(node), left(node))) ? right(node) : left(node);
      this._swap(node, maxChild);
      node = maxChild;
    }
  }
}

例:

{const top=0,parent=c=>(c+1>>>1)-1,left=c=>(c<<1)+1,right=c=>c+1<<1;class PriorityQueue{constructor(c=(d,e)=>d>e){this._heap=[],this._comparator=c}size(){return this._heap.length}isEmpty(){return 0==this.size()}peek(){return this._heap[top]}push(...c){return c.forEach(d=>{this._heap.push(d),this._siftUp()}),this.size()}pop(){const c=this.peek(),d=this.size()-1;return d>top&&this._swap(top,d),this._heap.pop(),this._siftDown(),c}replace(c){const d=this.peek();return this._heap[top]=c,this._siftDown(),d}_greater(c,d){return this._comparator(this._heap[c],this._heap[d])}_swap(c,d){[this._heap[c],this._heap[d]]=[this._heap[d],this._heap[c]]}_siftUp(){for(let c=this.size()-1;c>top&&this._greater(c,parent(c));)this._swap(c,parent(c)),c=parent(c)}_siftDown(){for(let d,c=top;left(c)<this.size()&&this._greater(left(c),c)||right(c)<this.size()&&this._greater(right(c),c);)d=right(c)<this.size()&&this._greater(right(c),left(c))?right(c):left(c),this._swap(c,d),c=d}}window.PriorityQueue=PriorityQueue}

// Default comparison semantics
const queue = new PriorityQueue();
queue.push(10, 20, 30, 40, 50);
console.log('Top:', queue.peek()); //=> 50
console.log('Size:', queue.size()); //=> 5
console.log('Contents:');
while (!queue.isEmpty()) {
  console.log(queue.pop()); //=> 40, 30, 20, 10
}

// Pairwise comparison semantics
const pairwiseQueue = new PriorityQueue((a, b) => a[1] > b[1]);
pairwiseQueue.push(['low', 0], ['medium', 5], ['high', 10]);
console.log('\nContents:');
while (!pairwiseQueue.isEmpty()) {
  console.log(pairwiseQueue.pop()[0]); //=> 'high', 'medium', 'low'
}

.as-console-wrapper{min-height:100%}

Answer 2

我对现有优先级队列实现的效率不满意，所以我决定自己制作：

https://github.com/luciopaiva/heapify

npm i heapify

由于使用了类型化数组，这将比任何其他公开已知的实现运行得更快。

适用于客户端和服务器端，代码库具有 100% 测试覆盖率，小型库（~100 LoC）。而且，界面非常简单。这是一些代码：

npm i heapify

Answer 3

我在这里提供我使用的实现。我做出了以下决定：

• 我经常发现我需要将一些有效负载与堆排序的值一起存储。因此，我选择让堆由数组组成，其中数组的第一个元素必须是用于堆顺序的值。这些数组中的任何其他元素都只是未检查的有效负载。确实，没有空间容纳有效负载的纯整数数组将使更快的实现成为可能，但在实践中，我发现自己创建了一个映射来将这些值与附加数据（有效负载）链接起来。这样的 Map 的管理（还处理重复的值！）破坏了您从这样的纯整数数组中获得的好处。
• 使用用户定义的比较器函数会带来性能成本，因此我决定不使用它。相反，这些值是使用比较运算符（<、、>...）进行比较的。这适用于数字、bigint、字符串和 Date 实例。如果这些值是不能很好排序的对象，valueOf则应覆盖它们以保证所需的排序。或者，此类对象应作为有效负载提供，并且真正定义顺序的对象属性应作为值给出（在第一个数组位置）。
• 扩展 Array 类也会在一定程度上降低性能，因此我选择提供将堆（Array 实例）作为第一个参数的实用程序函数。这类似于 Python 中heapq模块的工作方式，并给人一种“轻松”的感觉：您可以直接使用自己的数组。不new，没有继承，只是作用于数组的普通函数。
• 通常的sift-up 和 sift-down 操作不应在父级和子级之间执行重复交换，而应仅沿一个方向复制树值，直到找到最终的插入点，然后才应将给定值存储在该位置。
• 它应该包含一个heapify函数，以便可以将已填充的数组重新排序到堆中。它应该以线性时间运行，这样比从空堆开始然后将每个节点推入其中的效率更高。

下面是函数的集合，带有注释，最后还有一个简单的演示：

/* MinHeap:
 * A collection of functions that operate on an array 
 * of [key,...data] elements (nodes).
 */
const MinHeap = { 
    /* siftDown:
     * The node at the given index of the given heap is sifted down in  
     * its subtree until it does not have a child with a lesser value. 
     */
    siftDown(arr, i=0, value=arr[i]) {
        if (i < arr.length) {
            let key = value[0]; // Grab the value to compare with
            while (true) {
                // Choose the child with the least value
                let j = i*2+1;
                if (j+1 < arr.length && arr[j][0] > arr[j+1][0]) j++;
                // If no child has lesser value, then we've found the spot!
                if (j >= arr.length || key <= arr[j][0]) break;
                // Copy the selected child node one level up...
                arr[i] = arr[j];
                // ...and consider the child slot for putting our sifted node
                i = j;
            }
            arr[i] = value; // Place the sifted node at the found spot
        }
    },
    /* heapify:
     * The given array is reordered in-place so that it becomes a valid heap.
     * Elements in the given array must have a [0] property (e.g. arrays). 
     * That [0] value serves as the key to establish the heap order. The rest 
     * of such an element is just payload. It also returns the heap.
     */
    heapify(arr) {
        // Establish heap with an incremental, bottom-up process
        for (let i = arr.length>>1; i--; ) this.siftDown(arr, i);
        return arr;
    },
    /* pop:
     * Extracts the root of the given heap, and returns it (the subarray).
     * Returns undefined if the heap is empty
     */
    pop(arr) {
        // Pop the last leaf from the given heap, and exchange it with its root
        return this.exchange(arr, arr.pop()); // Returns the old root
    },
    /* exchange:
     * Replaces the root node of the given heap with the given node, and 
     * returns the previous root. Returns the given node if the heap is empty.
     * This is similar to a call of pop and push, but is more efficient.
     */
    exchange(arr, value) {
        if (!arr.length) return value;
        // Get the root node, so to return it later
        let oldValue = arr[0];
        // Inject the replacing node using the sift-down process
        this.siftDown(arr, 0, value);
        return oldValue;
    },
    /* push:
     * Inserts the given node into the given heap. It returns the heap.
     */
    push(arr, value) {
        let key = value[0],
            // First assume the insertion spot is at the very end (as a leaf)
            i = arr.length,
            j;
        // Then follow the path to the root, moving values down for as long 
        // as they are greater than the value to be inserted
        while ((j = (i-1)>>1) >= 0 && key < arr[j][0]) {
            arr[i] = arr[j];
            i = j;
        }
        // Found the insertion spot
        arr[i] = value;
        return arr;
    }
};

// Simple Demo:

let heap = [];
MinHeap.push(heap, [26, "Helen"]);
MinHeap.push(heap, [15, "Mike"]);
MinHeap.push(heap, [20, "Samantha"]);
MinHeap.push(heap, [21, "Timothy"]);
MinHeap.push(heap, [19, "Patricia"]);

let [age, name] = MinHeap.pop(heap);
console.log(`${name} is the youngest with ${age} years`);
([age, name] = MinHeap.pop(heap));
console.log(`Next is ${name} with ${age} years`);

有关更实际的示例，请参阅Dijkstra 最短路径算法的实现。

这是相同的MinHeap集合，但缩小了，连同它的MaxHeap镜像：

const MinHeap={siftDown(h,i=0,v=h[i]){if(i<h.length){let k=v[0];while(1){let j=i*2+1;if(j+1<h.length&&h[j][0]>h[j+1][0])j++;if(j>=h.length||k<=h[j][0])break;h[i]=h[j];i=j;}h[i]=v}},heapify(h){for(let i=h.length>>1;i--;)this.siftDown(h,i);return h},pop(h){return this.exchange(h,h.pop())},exchange(h,v){if(!h.length)return v;let w=h[0];this.siftDown(h,0,v);return w},push(h,v){let k=v[0],i=h.length,j;while((j=(i-1)>>1)>=0&&k<h[j][0]){h[i]=h[j];i=j}h[i]=v;return h}};
const MaxHeap={siftDown(h,i=0,v=h[i]){if(i<h.length){let k=v[0];while(1){let j=i*2+1;if(j+1<h.length&&h[j][0]<h[j+1][0])j++;if(j>=h.length||k>=h[j][0])break;h[i]=h[j];i=j;}h[i]=v}},heapify(h){for(let i=h.length>>1;i--;)this.siftDown(h,i);return h},pop(h){return this.exchange(h,h.pop())},exchange(h,v){if(!h.length)return v;let w=h[0];this.siftDown(h,0,v);return w},push(h,v){let k=v[0],i=h.length,j;while((j=(i-1)>>1)>=0&&k>h[j][0]){h[i]=h[j];i=j}h[i]=v;return h}};

Answer 4

您应该使用标准库,例如Closure Library(goog.structs.PriorityQueue):

https://google.github.io/closure-library/api/goog.structs.PriorityQueue.html

通过单击源代码,您将知道它实际上是goog.structs.Heap您可以关注的链接:

https://github.com/google/closure-library/blob/master/closure/goog/structs/heap.js