在Javascript中实现优先级队列的有效方法?

时间:2017-03-21 06:00:04

标签: javascript priority-queue

优先级队列对每个条目都有优先级值和数据。

因此,当向队列添加新元素时,如果它具有比集合中已有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,我们会获得具有最高优先级的元素的数据。

Javascript中这种优先级队列的有效实现是什么?

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?

这是一个很好的方法吗?

4 个答案:

答案 0 :(得分:18)

以下是我认为真正有效的PriorityQueue版本,它使用基于数组的二进制堆(其中根位于索引0,而节点的子节点位于索引处i分别位于索引2i + 12i + 2

此实现包括经典优先级队列方法,如pushpeekpopsize,以及便捷方法isEmpty和{{ 1}}(后者是replace更有效的替代品,紧接着是pop。值不是push对存储,而是[value, priority] s;这允许自动确定可以使用value运算符进行本机比较的类型的优先级。传递给>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,如下例所示。

基于堆的实施

PriorityQueue

示例:



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;
    }
  }
}
&#13;
{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'
}
&#13;
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答案 1 :(得分:7)

您应该使用标准库,例如闭包库(goog.structs.PriorityQueue):

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

点击源代码,您就会知道它实际上是链接到您可以关注的goog.structs.Heap

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

答案 2 :(得分:3)

我对现有优先级队列实现的效率不满意,所以我决定自己做:

https://github.com/luciopaiva/heapify

npm i heapify

由于使用了类型化数组,它的运行速度比任何其他公知实现都要快。

在客户端和服务器端均可使用,代码库具有100%的测试覆盖率,纤巧的库(〜100 LoC)。而且,界面真的很简单。这是一些代码:

import Heapify from "heapify";

const queue = new Heapify();
queue.push(1, 10);  // insert item with key=1, priority=10
queue.push(2, 5);  // insert item with key=2, priority=5
queue.pop();  // 2
queue.peek();  // 1
queue.peekPriority();  // 10

答案 3 :(得分:1)

我在这里提供了我使用的实现。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所依据的值一起存储。所以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将只是未被检查的有效载荷。 确实,一个没有空间容纳有效载荷的纯整数数组可以实现更快的实现,但在实践中,我发现自己创建了一个 Map 以将这些值与附加数据(有效载荷)联系起来。这种 Map 的管理(也处理重复值!)破坏了您从这种只有整数的数组中获得的好处。
  • 使用用户定义的比较器函数会带来性能成本,所以我决定不使用它。而是使用比较运算符(<>、...)比较这些值。这适用于数字、大整数、字符串和日期实例。如果值是这样排序的对象,则应覆盖它们的 valueOf 以保证所需的排序。或者,此类对象应作为有效负载提供,而真正定义顺序的对象属性应作为值(在第一个数组位置)给出。
  • 事实证明,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(一个 Array 实例)作为第一个参数的实用函数。这类似于 Python 中 heapq 模块的工作方式,并给它一种“轻松”的感觉:您可以直接使用自己的数组。没有 new,没有继承,只有作用于数组的普通函数。
  • 通常的sift-up and sift-down operations不应该在父子之间重复交换,而只复制一个方向的树值直到 找到了最后的插入点,然后才应将给定的值存储在该位置。
  • 它应该包含一个 heapify 函数,以便可以将已经填充的数组重新排序到堆中。它应该在 linear time 中运行,以便比从空堆开始然后将每个节点推送到它的效率更高。

下面是函数集合,带有注释,最后是一个简单的演示:

/* 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`);

有关更现实的示例,请参阅 Dijkstra's shortest path algorithm 的实现。

这里是同一个 MinHeap 集合,但是缩小了,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}};