使用C#实现数据结构堆的代码

一、 堆的介绍：

　　堆是用来排序的，通常是一个可以被看做一棵树的数组对象。堆满足已下特性：

　　1. 堆中某个节点的值总是不大于或不小于其父节点的值

　　任意节点的值小于（或大于）它的所有后裔，所以最小元（或最大元）在堆的根节点上（堆序性）。堆有大根堆和小根堆，将根节点最大的堆叫做最大堆或大根堆，根节点最小的堆叫做最小堆或小根堆。

　　2. 堆总是一棵完全二叉树

　　除了最底层，其他层的节点都被元素填满，且最底层尽可能地从左到右填入。　

　　堆示意图：

　　

　　将堆元素从上往下从左到右放进数组对象中，子父节点索引满足关系：

　　parentIndex = （index+1）/ 2 - 1;

　　childLeftIndex = parentIndex * 2 + 1;

　　childRightIndex = (parentIndex + 1) * 2;

　　其中：index为任一节点索引；parentIndex该节点父索引；childLeftIndex该父节点下的子左节点；childRightIndex该父节点下的子右节点。

　　创建堆的大概思路：　

　　1. 向堆中添加元素：

　　加到数组尾处，循环比对其父节点值（大根堆和小根堆比对策略不一样），比对结果的目标索引不是父节点索引则交换子父节点元素，继续向上比对其父父节点…；直至比对过程中目标索引为父节点索引或达到根节点结束，新堆创建完成。

　　2. 向堆中取出元素：

　　取出根节点元素，并将堆末尾元素插入根节点（为了保证堆的完全二叉树特性），从根部再循环向下比对父节点、子左节点、子右节点值，比对结果目标索引不为父节点交换目标索引和父节点的值，向下继续比对；直至比对过程中目标索引为父节点索引或达到堆尾部结束，新堆创建完成。

二、 代码实现：

　　因为大根堆和小根堆只是比较策略不同，所以整合了两者，用的时候可以直接设置堆的类别；默认小根堆，默认比较器。实现代码如下：

public class Heap<T>
 {
  private T[] _array;//数组，存放堆数据
  private int _count;//堆数据数量
  private HeapType _typeName;//堆类型
  private const int _DefaultCapacity = 4;//默认数组容量/最小容量
  private const int _ShrinkThreshold = 50;//收缩阈值（百分比）
  private const int _MinimumGrow = 4;//最小扩容量
  private const int _GrowFactor = 200; // 数组扩容百分比,默认2倍
  private IComparer<T> _comparer;//比较器
  private Func<T, T, bool> _comparerFunc;//比较函数

  //堆数据数量
  public int Count => _count;
  //堆类型
  public HeapType TypeName => _typeName;


  public Heap() : this(_DefaultCapacity, HeapType.MinHeap, null) { }
  public Heap(int capacity) : this(capacity, HeapType.MinHeap, null) { }
  public Heap(HeapType heapType) : this(_DefaultCapacity, heapType, null) { }
  public Heap(int capacity, HeapType heapType, IComparer<T> comparer)
  {
   Init(capacity, heapType, comparer);
  }
  public Heap(IEnumerable<T> collection, HeapType heapType, IComparer<T> comparer)
  {
   if (collection == null)
    throw new IndexOutOfRangeException();
   Init(collection.Count(), heapType, comparer);
   using (IEnumerator<T> en = collection.GetEnumerator())//避免T在GC堆中有非托管资源，GC不能释放，需手动
   {
    while (en.MoveNext())
     Enqueue(en.Current);
   }
  }
  private void Init(int capacity, HeapType heapType, IComparer<T> comparer)
  {
   if (capacity < 0)
    throw new IndexOutOfRangeException();
   _count = 0;
   _array = new T[capacity];
   _comparer = comparer ?? Comparer<T>.Default;
   _typeName = heapType;
   switch (heapType)
   {
    default:
    case HeapType.MinHeap:
     _comparerFunc = (T t1, T t2) => _comparer.Compare(t1, t2) > 0;//目标对象t2小
     break;
    case HeapType.MaxHeap:
     _comparerFunc = (T t1, T t2) => _comparer.Compare(t1, t2) < 0;//目标对象t2大
     break;
   }
  }

  public T Dequeue()
  {
   if (_count == 0)
    throw new InvalidOperationException();
   T result = _array[0];
   _array[0] = _array[--_count];
   _array[_count] = default(T);

   if (_array.Length > _DefaultCapacity && _count * 100 <= _array.Length * _ShrinkThreshold)//缩容
   {
    int newCapacity = Math.Max(_DefaultCapacity, (int)((long)_array.Length * (long)_ShrinkThreshold / 100));
    SetCapacity(newCapacity);
   }
   AdjustHeap(_array, 0, _count);
   return result;
  }
  public void Enqueue(T item)
  {
   if (_count >= _array.Length)//扩容
   {
    int newCapacity = Math.Max(_array.Length+_MinimumGrow, (int)((long)_array.Length * (long)_GrowFactor / 100));
    SetCapacity(newCapacity);
   }

   _array[_count++] = item;
   int parentIndex;
   int targetIndex;
   int targetCount = _count;
   while (targetCount > 1)
   {
    parentIndex = targetCount / 2 - 1;
    targetIndex = targetCount - 1;
    if (!_comparerFunc.Invoke(_array[parentIndex], _array[targetIndex]))
     break;
    Swap(_array, parentIndex, targetIndex);
    targetCount = parentIndex + 1;
   }
  }
  private void AdjustHeap(T[] array, int parentIndex, int count)
  {
   if (_count < 2)
    return;
   int childLeftIndex = parentIndex * 2 + 1;
   int childRightIndex = (parentIndex + 1) * 2;

   int targetIndex = parentIndex;
   if (childLeftIndex < count && _comparerFunc.Invoke(array[parentIndex], array[childLeftIndex]))
    targetIndex = childLeftIndex;
   if (childRightIndex < count && _comparerFunc.Invoke(array[targetIndex], array[childRightIndex]))
    targetIndex = childRightIndex;
   if (targetIndex != parentIndex)
   {
    Swap(_array, parentIndex, targetIndex);
    AdjustHeap(_array, targetIndex, _count);
   }
  }

  private void SetCapacity(int capacity)
  {
   T[] newArray = new T[capacity];
   Array.Copy(_array, newArray, _count);
   _array = newArray;
  }

  private void Swap(T[] array, int index1, int index2)
  {
   T temp = array[index1];
   array[index1] = array[index2];
   array[index2] = temp;
  }

  public void Clear()
  {
   Array.Clear(_array, 0, _count);
   Init(_DefaultCapacity, HeapType.MinHeap, null);
  }
 }

 public enum HeapType { MinHeap, MaxHeap }

三、 使用测试：　

　　建一个Person类用来测试，例子中Person比较规则是：先按年龄比较，年龄相同再按身高比较。具体比较大小是由选择堆的类别进行不同的排序规则：如Person类中小根堆先按年龄小者排序，年龄相同者按身高大者排序；而使用大根堆则相反。两种比较器写法，前者直接使用默认比较器；后者需要将比较器注入到堆中。

public class Person : IComparable<Person>
 {
  public string name { get; set; }
  public int Age { get; set; }

  public int Height { get; set; }
  public override string ToString()
  {
   return $"我叫{name}，年龄{Age}，身高{Height}";
  }

  //小根堆：先排年龄小，年龄相同，按身高大的先排；大根堆相反
  public int CompareTo(Person other)
  {
   if (this.Age.CompareTo(other.Age) != 0)
    return this.Age.CompareTo(other.Age);
   else if (this.Height.CompareTo(other.Height) != 0)
    return ~this.Height.CompareTo(other.Height);
   else
    return 0;
  }
 }

 public class personComparer : IComparer<Person>
 {
  //大根堆：先排年龄大，年龄相同，按身高大的先排；小根堆相反
  public int Compare(Person x, Person y)
  {
   if (x.Age.CompareTo(y.Age) != 0)
    return x.Age.CompareTo(y.Age);
   else if (x.Height.CompareTo(y.Height) != 0)
    return x.Height.CompareTo(y.Height);
   else
    return 0;
  }
 }

　　主函数调用：

static void Main(string[] args)
  {
   int[] array = { 3, 5, 8, 3, 7, 1 };
   Heap<int> heap0 = new Heap<int>(array, HeapType.MaxHeap, null);
   Console.WriteLine(heap0.TypeName);
   Console.WriteLine(heap0.Dequeue());
   Console.WriteLine(heap0.Dequeue());
   Console.WriteLine(heap0.Dequeue());
   Console.WriteLine(heap0.Dequeue());
   int length = heap0.Count;
   for (int count = 0; count < length; count++)
   {
    Console.WriteLine(heap0.Dequeue());
   }

   Person person1 = new Person() { Age = 12, Height = 158, name = "张三" };
   Person person2 = new Person() { Age = 13, Height = 160, name = "李四" };
   Person person3 = new Person() { Age = 10, Height = 150, name = "王二" };
   Person person4 = new Person() { Age = 10, Height = 152, name = "麻子" };
   Person person5 = new Person() { Age = 12, Height = 150, name = "刘五" };
   List<Person> people = new List<Person>();
   people.Add(person1);
   people.Add(person2);
   people.Add(person3);
   people.Add(person4);
   people.Add(person5);
   Heap<Person> heap2 = new Heap<Person>(people, HeapType.MinHeap, null);
   Person person6 = new Person() { Age = 9, Height = 145, name = "赵六" };
   heap2.Enqueue(person6);
   Console.WriteLine(heap2.TypeName);
   Console.WriteLine(heap2.Dequeue());
   Console.WriteLine(heap2.Dequeue());
   Console.WriteLine(heap2.Dequeue());
   Console.WriteLine(heap2.Dequeue());

   PersonComparer personComparer = new PersonComparer();
   Heap<Person> heap3 = new Heap<Person>(1,HeapType.MaxHeap,personComparer);
   heap3.Enqueue(person1);
   heap3.Enqueue(person2);
   heap3.Enqueue(person3);
   heap3.Enqueue(person4);
   heap3.Enqueue(person5);
   heap3.Enqueue(person6);
   Console.WriteLine(heap3.TypeName);
   Console.WriteLine(heap3.Dequeue());
   Console.WriteLine(heap3.Dequeue());
   Console.WriteLine(heap3.Dequeue());
   Console.WriteLine(heap3.Dequeue());

   Console.ReadKey();
  }

　　输出结果：

　　

　　参考：

　　https://blog.csdn.net/qq826364410/article/details/79770791

　　https://docs.microsoft.com/zh-cn/dotnet/api/system.collections.generic.comparer-1?view=net-5.0

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