如何在C#项目中实现一个数据结构堆？相信很多没有经验的人对此束手无策，为此本文总结了问题出现的原因和解决方法，通过这篇文章希望你能解决这个问题。
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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（或较大元）在堆的根节点上（堆序性）。堆有大根堆和小根堆，将根节点较大的堆叫做较大堆或大根堆，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
{
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 _comparer;//比较器
private Func _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 comparer)
{
Init(capacity, heapType, comparer);
}
public Heap(IEnumerable collection, HeapType heapType, IComparer comparer)
{
if (collection == null)
throw new IndexOutOfRangeException();
Init(collection.Count(), heapType, comparer);
using (IEnumerator 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 comparer)
{
if (capacity < 0)
throw new IndexOutOfRangeException();
_count = 0;
_array = new T[capacity];
_comparer = comparer ?? Comparer.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
{
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
{
//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 heap0 = new Heap(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 people = new List();
people.Add(person1);
people.Add(person2);
people.Add(person3);
people.Add(person4);
people.Add(person5);
Heap heap2 = new Heap(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 heap3 = new Heap(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：
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