我正在寻找优先级队列或堆数据结构的 .NET 实现
优先队列是比简单排序提供更多灵活性的数据结构，因为它们允许新元素以任意间隔进入系统。将新作业插入优先级队列比在每次到达时重新排序所有内容更具成本效益。
基本优先级队列支持三个主要操作：
- 插入（Q，x）。给定一个带有键 k 的项目 x，将其插入优先级队列 Q。
- 查找最小值 (Q)。返回指向其键值小于优先级队列 Q 中任何其他键的项的指针。
- 删除-最小值（Q）。从优先级队列 Q 中移除 key 最小的 item
除非我找错了地方，否则框架中没有一个。有人知道一个好的，还是我应该自己推出？
您可能会喜欢C5 通用集合库中的 IntervalHeap 。引用用户指南
类使用存储为对数组的间隔堆
IntervalHeap<T>实现接口。and 操作和索引器IPriorityQueue<T>的get-accessor 需要时间 O(1)。, , Add 和 Update 操作以及索引器的 set-accessor 需要时间 O(log n)。与普通优先级队列相比，间隔堆以相同的效率提供最小和最大操作。FindMinFindMaxDeleteMinDeleteMax
API 足够简单
> var heap = new C5.IntervalHeap<int>();
> heap.Add(10);
> heap.Add(5);
> heap.FindMin();
5
从 Nuget https://www.nuget.org/packages/C5或 GitHub https://github.com/sestoft/C5/安装
这是我对 .NET 堆的尝试
public abstract class Heap<T> : IEnumerable<T>
{
private const int InitialCapacity = 0;
private const int GrowFactor = 2;
private const int MinGrow = 1;
private int _capacity = InitialCapacity;
private T[] _heap = new T[InitialCapacity];
private int _tail = 0;
public int Count { get { return _tail; } }
public int Capacity { get { return _capacity; } }
protected Comparer<T> Comparer { get; private set; }
protected abstract bool Dominates(T x, T y);
protected Heap() : this(Comparer<T>.Default)
{
}
protected Heap(Comparer<T> comparer) : this(Enumerable.Empty<T>(), comparer)
{
}
protected Heap(IEnumerable<T> collection)
: this(collection, Comparer<T>.Default)
{
}
protected Heap(IEnumerable<T> collection, Comparer<T> comparer)
{
if (collection == null) throw new ArgumentNullException("collection");
if (comparer == null) throw new ArgumentNullException("comparer");
Comparer = comparer;
foreach (var item in collection)
{
if (Count == Capacity)
Grow();
_heap[_tail++] = item;
}
for (int i = Parent(_tail - 1); i >= 0; i--)
BubbleDown(i);
}
public void Add(T item)
{
if (Count == Capacity)
Grow();
_heap[_tail++] = item;
BubbleUp(_tail - 1);
}
private void BubbleUp(int i)
{
if (i == 0 || Dominates(_heap[Parent(i)], _heap[i]))
return; //correct domination (or root)
Swap(i, Parent(i));
BubbleUp(Parent(i));
}
public T GetMin()
{
if (Count == 0) throw new InvalidOperationException("Heap is empty");
return _heap[0];
}
public T ExtractDominating()
{
if (Count == 0) throw new InvalidOperationException("Heap is empty");
T ret = _heap[0];
_tail--;
Swap(_tail, 0);
BubbleDown(0);
return ret;
}
private void BubbleDown(int i)
{
int dominatingNode = Dominating(i);
if (dominatingNode == i) return;
Swap(i, dominatingNode);
BubbleDown(dominatingNode);
}
private int Dominating(int i)
{
int dominatingNode = i;
dominatingNode = GetDominating(YoungChild(i), dominatingNode);
dominatingNode = GetDominating(OldChild(i), dominatingNode);
return dominatingNode;
}
private int GetDominating(int newNode, int dominatingNode)
{
if (newNode < _tail && !Dominates(_heap[dominatingNode], _heap[newNode]))
return newNode;
else
return dominatingNode;
}
private void Swap(int i, int j)
{
T tmp = _heap[i];
_heap[i] = _heap[j];
_heap[j] = tmp;
}
private static int Parent(int i)
{
return (i + 1)/2 - 1;
}
private static int YoungChild(int i)
{
return (i + 1)*2 - 1;
}
private static int OldChild(int i)
{
return YoungChild(i) + 1;
}
private void Grow()
{
int newCapacity = _capacity*GrowFactor + MinGrow;
var newHeap = new T[newCapacity];
Array.Copy(_heap, newHeap, _capacity);
_heap = newHeap;
_capacity = newCapacity;
}
public IEnumerator<T> GetEnumerator()
{
return _heap.Take(Count).GetEnumerator();
}
IEnumerator IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
}
public class MaxHeap<T> : Heap<T>
{
public MaxHeap()
: this(Comparer<T>.Default)
{
}
public MaxHeap(Comparer<T> comparer)
: base(comparer)
{
}
public MaxHeap(IEnumerable<T> collection, Comparer<T> comparer)
: base(collection, comparer)
{
}
public MaxHeap(IEnumerable<T> collection) : base(collection)
{
}
protected override bool Dominates(T x, T y)
{
return Comparer.Compare(x, y) >= 0;
}
}
public class MinHeap<T> : Heap<T>
{
public MinHeap()
: this(Comparer<T>.Default)
{
}
public MinHeap(Comparer<T> comparer)
: base(comparer)
{
}
public MinHeap(IEnumerable<T> collection) : base(collection)
{
}
public MinHeap(IEnumerable<T> collection, Comparer<T> comparer)
: base(collection, comparer)
{
}
protected override bool Dominates(T x, T y)
{
return Comparer.Compare(x, y) <= 0;
}
}
一些测试：
[TestClass]
public class HeapTests
{
[TestMethod]
public void TestHeapBySorting()
{
var minHeap = new MinHeap<int>(new[] {9, 8, 4, 1, 6, 2, 7, 4, 1, 2});
AssertHeapSort(minHeap, minHeap.OrderBy(i => i).ToArray());
minHeap = new MinHeap<int> { 7, 5, 1, 6, 3, 2, 4, 1, 2, 1, 3, 4, 7 };
AssertHeapSort(minHeap, minHeap.OrderBy(i => i).ToArray());
var maxHeap = new MaxHeap<int>(new[] {1, 5, 3, 2, 7, 56, 3, 1, 23, 5, 2, 1});
AssertHeapSort(maxHeap, maxHeap.OrderBy(d => -d).ToArray());
maxHeap = new MaxHeap<int> {2, 6, 1, 3, 56, 1, 4, 7, 8, 23, 4, 5, 7, 34, 1, 4};
AssertHeapSort(maxHeap, maxHeap.OrderBy(d => -d).ToArray());
}
private static void AssertHeapSort(Heap<int> heap, IEnumerable<int> expected)
{
var sorted = new List<int>();
while (heap.Count > 0)
sorted.Add(heap.ExtractDominating());
Assert.IsTrue(sorted.SequenceEqual(expected));
}
}
我喜欢使用PowerCollectionsOrderedBag中的和OrderedSet类作为优先级队列。
这是我刚刚写的一个，也许它没有优化（仅使用排序字典）但易于理解。您可以插入不同种类的对象，因此没有通用队列。
using System;
using System.Diagnostics;
using System.Collections;
using System.Collections.Generic;
namespace PrioQueue
{
public class PrioQueue
{
int total_size;
SortedDictionary<int, Queue> storage;
public PrioQueue ()
{
this.storage = new SortedDictionary<int, Queue> ();
this.total_size = 0;
}
public bool IsEmpty ()
{
return (total_size == 0);
}
public object Dequeue ()
{
if (IsEmpty ()) {
throw new Exception ("Please check that priorityQueue is not empty before dequeing");
} else
foreach (Queue q in storage.Values) {
// we use a sorted dictionary
if (q.Count > 0) {
total_size--;
return q.Dequeue ();
}
}
Debug.Assert(false,"not supposed to reach here. problem with changing total_size");
return null; // not supposed to reach here.
}
// same as above, except for peek.
public object Peek ()
{
if (IsEmpty ())
throw new Exception ("Please check that priorityQueue is not empty before peeking");
else
foreach (Queue q in storage.Values) {
if (q.Count > 0)
return q.Peek ();
}
Debug.Assert(false,"not supposed to reach here. problem with changing total_size");
return null; // not supposed to reach here.
}
public object Dequeue (int prio)
{
total_size--;
return storage[prio].Dequeue ();
}
public void Enqueue (object item, int prio)
{
if (!storage.ContainsKey (prio)) {
storage.Add (prio, new Queue ());
}
storage[prio].Enqueue (item);
total_size++;
}
}
}
.NET 6+：正如@rustyx 评论的那样，.NET 6 添加了一个System.Collections.Generic.PriorityQueue<TElement,TPriority>类。FWIW 它是开源的，并在 c# 中实现。
较早的 .NET Core 版本和 .NET Framework： Microsoft 在 .NET Framework 中编写（并在线共享）了2 个内部 PriorityQueue 类。但是，正如@mathusum-mut 评论的那样，其中一个存在错误（当然，SO 社区已经为它提供了修复）：Microsoft 内部 PriorityQueue<T> 中的错误？
我在这里的博客上找到了 Julian Bucknall 的一篇文章 - http://www.boyet.com/Articles/PriorityQueueCSharp3.html
我们稍微修改了它，以便队列中的低优先级项目最终会随着时间的推移“冒泡”到顶部，因此它们不会遭受饥饿。
class PriorityQueue<T>
{
IComparer<T> comparer;
T[] heap;
public int Count { get; private set; }
public PriorityQueue() : this(null) { }
public PriorityQueue(int capacity) : this(capacity, null) { }
public PriorityQueue(IComparer<T> comparer) : this(16, comparer) { }
public PriorityQueue(int capacity, IComparer<T> comparer)
{
this.comparer = (comparer == null) ? Comparer<T>.Default : comparer;
this.heap = new T[capacity];
}
public void push(T v)
{
if (Count >= heap.Length) Array.Resize(ref heap, Count * 2);
heap[Count] = v;
SiftUp(Count++);
}
public T pop()
{
var v = top();
heap[0] = heap[--Count];
if (Count > 0) SiftDown(0);
return v;
}
public T top()
{
if (Count > 0) return heap[0];
throw new InvalidOperationException("优先队列为空");
}
void SiftUp(int n)
{
var v = heap[n];
for (var n2 = n / 2; n > 0 && comparer.Compare(v, heap[n2]) > 0; n = n2, n2 /= 2) heap[n] = heap[n2];
heap[n] = v;
}
void SiftDown(int n)
{
var v = heap[n];
for (var n2 = n * 2; n2 < Count; n = n2, n2 *= 2)
{
if (n2 + 1 < Count && comparer.Compare(heap[n2 + 1], heap[n2]) > 0) n2++;
if (comparer.Compare(v, heap[n2]) >= 0) break;
heap[n] = heap[n2];
}
heap[n] = v;
}
}
简单的。
您可能会发现此实现很有用：http: //www.codeproject.com/Articles/126751/Priority-queue-in-Csharp-with-help-of-heap-data-st.aspx
它是通用的并且基于堆数据结构
我编写了一个名为AlgoKit的开源库，可通过NuGet获得。它包含：
该代码已经过广泛的测试。我绝对建议你试一试。
var comparer = Comparer<int>.Default;
var heap = new PairingHeap<int, string>(comparer);
heap.Add(3, "your");
heap.Add(5, "of");
heap.Add(7, "disturbing.");
heap.Add(2, "find");
heap.Add(1, "I");
heap.Add(6, "faith");
heap.Add(4, "lack");
while (!heap.IsEmpty)
Console.WriteLine(heap.Pop().Value);
实现的最佳选择与输入密切相关——正如 Larkin、Sen 和 Tarjan 在A back-to-basics 优先级队列的实证研究arXiv:1403.0252v1 [cs.DS]中所展示的那样。他们测试了隐式 d-ary 堆、配对堆、Fibonacci 堆、二项式堆、显式 d-ary 堆、等级配对堆、地震堆、违规堆、等级松弛弱堆和严格 Fibonacci 堆。
AlgoKit 具有三种类型的堆，它们似乎在测试的那些堆中效率最高。
对于数量相对较少的元素，您可能会对使用隐式堆感兴趣，尤其是四元堆（隐式 4 进制）。如果在更大的堆大小上运行，二项式堆和配对堆等摊销结构应该表现更好。
一个简单的最大堆实现。
https://github.com/bharathkumarms/AlgorithmsMadeEasy/blob/master/AlgorithmsMadeEasy/MaxHeap.cs
using System;
using System.Collections.Generic;
using System.Linq;
namespace AlgorithmsMadeEasy
{
class MaxHeap
{
private static int capacity = 10;
private int size = 0;
int[] items = new int[capacity];
private int getLeftChildIndex(int parentIndex) { return 2 * parentIndex + 1; }
private int getRightChildIndex(int parentIndex) { return 2 * parentIndex + 2; }
private int getParentIndex(int childIndex) { return (childIndex - 1) / 2; }
private int getLeftChild(int parentIndex) { return this.items[getLeftChildIndex(parentIndex)]; }
private int getRightChild(int parentIndex) { return this.items[getRightChildIndex(parentIndex)]; }
private int getParent(int childIndex) { return this.items[getParentIndex(childIndex)]; }
private bool hasLeftChild(int parentIndex) { return getLeftChildIndex(parentIndex) < size; }
private bool hasRightChild(int parentIndex) { return getRightChildIndex(parentIndex) < size; }
private bool hasParent(int childIndex) { return getLeftChildIndex(childIndex) > 0; }
private void swap(int indexOne, int indexTwo)
{
int temp = this.items[indexOne];
this.items[indexOne] = this.items[indexTwo];
this.items[indexTwo] = temp;
}
private void hasEnoughCapacity()
{
if (this.size == capacity)
{
Array.Resize(ref this.items,capacity*2);
capacity *= 2;
}
}
public void Add(int item)
{
this.hasEnoughCapacity();
this.items[size] = item;
this.size++;
heapifyUp();
}
public int Remove()
{
int item = this.items[0];
this.items[0] = this.items[size-1];
this.items[this.size - 1] = 0;
size--;
heapifyDown();
return item;
}
private void heapifyUp()
{
int index = this.size - 1;
while (hasParent(index) && this.items[index] > getParent(index))
{
swap(index, getParentIndex(index));
index = getParentIndex(index);
}
}
private void heapifyDown()
{
int index = 0;
while (hasLeftChild(index))
{
int bigChildIndex = getLeftChildIndex(index);
if (hasRightChild(index) && getLeftChild(index) < getRightChild(index))
{
bigChildIndex = getRightChildIndex(index);
}
if (this.items[bigChildIndex] < this.items[index])
{
break;
}
else
{
swap(bigChildIndex,index);
index = bigChildIndex;
}
}
}
}
}
/*
Calling Code:
MaxHeap mh = new MaxHeap();
mh.Add(10);
mh.Add(5);
mh.Add(2);
mh.Add(1);
mh.Add(50);
int maxVal = mh.Remove();
int newMaxVal = mh.Remove();
*/
在 Java Collections 框架中的 Java 实现 (java.util.PriorityQueue) 上使用 Java 到 C# 转换器，或者更智能地使用算法和核心代码并将其插入到您自己制作的符合 C# Collections 框架的 C# 类中队列的 API，或者至少是集合的 API。
这是 NGenerics 团队的另一个实现：
我最近遇到了同样的问题，最终为此创建了一个NuGet 包。
这实现了一个标准的基于堆的优先级队列。它还具有 BCL 集合的所有常见细节：ICollection<T>和IReadOnlyCollection<T>实现、自定义IComparer<T>支持、指定初始容量的能力，以及DebuggerTypeProxy使集合更易于在调试器中使用。
还有一个包的内联版本，它只是将单个 .cs 文件安装到您的项目中（如果您想避免采用外部可见的依赖项，这很有用）。
更多信息可在github 页面上找到。
下面的实现PriorityQueue使用SortedSet来自 System 库。
using System;
using System.Collections.Generic;
namespace CDiggins
{
interface IPriorityQueue<T, K> where K : IComparable<K>
{
bool Empty { get; }
void Enqueue(T x, K key);
void Dequeue();
T Top { get; }
}
class PriorityQueue<T, K> : IPriorityQueue<T, K> where K : IComparable<K>
{
SortedSet<Tuple<T, K>> set;
class Comparer : IComparer<Tuple<T, K>> {
public int Compare(Tuple<T, K> x, Tuple<T, K> y) {
return x.Item2.CompareTo(y.Item2);
}
}
PriorityQueue() { set = new SortedSet<Tuple<T, K>>(new Comparer()); }
public bool Empty { get { return set.Count == 0; } }
public void Enqueue(T x, K key) { set.Add(Tuple.Create(x, key)); }
public void Dequeue() { set.Remove(set.Max); }
public T Top { get { return set.Max.Item1; } }
}
}