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所属分类：.NET技术
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：
1 public class Heap<T> 2 { 3 private T[] _array;//数组，存放堆数据 4 private int _count;//堆数据数量 5 private HeapType _typeName;//堆类型 6 private const int _DefaultCapacity = 4;//默认数组容量/最小容量 7 private const int _ShrinkThreshold = 50;//收缩阈值（百分比） 8 private const int _MinimumGrow = 4;//最小扩容量 9 private const int _GrowFactor = 200; // 数组扩容百分比,默认2倍 10 private IComparer<T> _comparer;//比较器 11 private Func<T, T, bool> _comparerFunc;//比较函数 12 13 14 //堆数据数量 15 public int Count => _count; 16 //堆类型 17 public HeapType TypeName => _typeName; 18 19 20 public Heap() : this(_DefaultCapacity, HeapType.MinHeap, null) { } 21 public Heap(int capacity) : this(capacity, HeapType.MinHeap, null) { } 22 public Heap(HeapType heapType) : this(_DefaultCapacity, heapType, null) { } 23 public Heap(int capacity, HeapType heapType, IComparer<T> comparer) 24 { 25 Init(capacity, heapType, comparer); 26 } 27 public Heap(IEnumerable<T> collection, HeapType heapType, IComparer<T> comparer) 28 { 29 if (collection == null) 30 throw new IndexOutOfRangeException(); 31 Init(collection.Count(), heapType, comparer); 32 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 33 { 34 while (en.MoveNext()) 35 Enqueue(en.Current); 36 } 37 } 38 private void Init(int capacity, HeapType heapType, IComparer<T> comparer) 39 { 40 if (capacity < 0) 41 throw new IndexOutOfRangeException(); 42 _count = 0; 43 _array = new T[capacity]; 44 _comparer = comparer ?? Comparer<T>.Default; 45 _typeName = heapType; 46 switch (heapType) 47 { 48 default: 49 case HeapType.MinHeap: 50 _comparerFunc = (T t1, T t2) => _comparer.Compare(t1, t2) > 0;//目标对象t2小 51 break; 52 case HeapType.MaxHeap: 53 _comparerFunc = (T t1, T t2) => _comparer.Compare(t1, t2) < 0;//目标对象t2大 54 break; 55 } 56 } 57 58 59 public T Dequeue() 60 { 61 if (_count == 0) 62 throw new InvalidOperationException(); 63 T result = _array[0]; 64 _array[0] = _array[--_count]; 65 _array[_count] = default(T); 66 67 if (_array.Length > _DefaultCapacity && _count * 100 <= _array.Length * _ShrinkThreshold)//缩容 68 { 69 int newCapacity = Math.Max(_DefaultCapacity, (int)((long)_array.Length * (long)_ShrinkThreshold / 100)); 70 SetCapacity(newCapacity); 71 } 72 AdjustHeap(_array, 0, _count); 73 return result; 74 } 75 public void Enqueue(T item) 76 { 77 if (_count >= _array.Length)//扩容 78 { 79 int newCapacity = Math.Max(_array.Length+_MinimumGrow, (int)((long)_array.Length * (long)_GrowFactor / 100)); 80 SetCapacity(newCapacity); 81 } 82 83 _array[_count++] = item; 84 int parentIndex; 85 int targetIndex; 86 int targetCount = _count; 87 while (targetCount > 1) 88 { 89 parentIndex = targetCount / 2 - 1; 90 targetIndex = targetCount - 1; 91 if (!_comparerFunc.Invoke(_array[parentIndex], _array[targetIndex])) 92 break; 93 Swap(_array, parentIndex, targetIndex); 94 targetCount = parentIndex + 1; 95 } 96 } 97 private void AdjustHeap(T[] array, int parentIndex, int count) 98 { 99 if (_count < 2) 100 return; 101 int childLeftIndex = parentIndex * 2 + 1; 102 int childRightIndex = (parentIndex + 1) * 2; 103 104 int targetIndex = parentIndex; 105 if (childLeftIndex < count && _comparerFunc.Invoke(array[parentIndex], array[childLeftIndex])) 106 targetIndex = childLeftIndex; 107 if (childRightIndex < count && _comparerFunc.Invoke(array[targetIndex], array[childRightIndex])) 108 targetIndex = childRightIndex; 109 if (targetIndex != parentIndex) 110 { 111 Swap(_array, parentIndex, targetIndex); 112 AdjustHeap(_array, targetIndex, _count); 113 } 114 } 115 116 private void SetCapacity(int capacity) 117 { 118 T[] newArray = new T[capacity]; 119 Array.Copy(_array, newArray, _count); 120 _array = newArray; 121 } 122 123 private void Swap(T[] array, int index1, int index2) 124 { 125 T temp = array[index1]; 126 array[index1] = array[index2]; 127 array[index2] = temp; 128 } 129 130 public void Clear() 131 { 132 Array.Clear(_array, 0, _count); 133 Init(_DefaultCapacity, HeapType.MinHeap, null); 134 } 135 } 136 137 public enum HeapType { MinHeap, MaxHeap }
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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。
1 public class Person : IComparable<Person> 2 { 3 public string name { get; set; } 4 public int Age { get; set; } 5 6 public int Height { get; set; } 7 public override string ToString() 8 { 9 return $"我叫{name}，年龄{Age}，身高{Height}"; 10 } 11 12 //小根堆：先排年龄小，年龄相同，按身高大的先排；大根堆相反 13 public int CompareTo(Person other) 14 { 15 if (this.Age.CompareTo(other.Age) != 0) 16 return this.Age.CompareTo(other.Age); 17 else if (this.Height.CompareTo(other.Height) != 0) 18 return ~this.Height.CompareTo(other.Height); 19 else 20 return 0; 21 } 22 } 23 24 public class personComparer : IComparer<Person> 25 { 26 //大根堆：先排年龄大，年龄相同，按身高大的先排；小根堆相反 27 public int Compare(Person x, Person y) 28 { 29 if (x.Age.CompareTo(y.Age) != 0) 30 return x.Age.CompareTo(y.Age); 31 else if (x.Height.CompareTo(y.Height) != 0) 32 return x.Height.CompareTo(y.Height); 33 else 34 return 0; 35 } 36 }
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主函数调用：
1 static void Main(string[] args) 2 { 3 int[] array = { 3, 5, 8, 3, 7, 1 }; 4 Heap<int> heap0 = new Heap<int>(array, HeapType.MaxHeap, null); 5 Console.WriteLine(heap0.TypeName); 6 Console.WriteLine(heap0.Dequeue()); 7 Console.WriteLine(heap0.Dequeue()); 8 Console.WriteLine(heap0.Dequeue()); 9 Console.WriteLine(heap0.Dequeue()); 10 int length = heap0.Count; 11 for (int count = 0; count < length; count++) 12 { 13 Console.WriteLine(heap0.Dequeue()); 14 } 15 16 17 18 Person person1 = new Person() { Age = 12, Height = 158, name = "张三" }; 19 Person person2 = new Person() { Age = 13, Height = 160, name = "李四" }; 20 Person person3 = new Person() { Age = 10, Height = 150, name = "王二" }; 21 Person person4 = new Person() { Age = 10, Height = 152, name = "麻子" }; 22 Person person5 = new Person() { Age = 12, Height = 150, name = "刘五" }; 23 List<Person> people = new List<Person>(); 24 people.Add(person1); 25 people.Add(person2); 26 people.Add(person3); 27 people.Add(person4); 28 people.Add(person5); 29 Heap<Person> heap2 = new Heap<Person>(people, HeapType.MinHeap, null); 30 Person person6 = new Person() { Age = 9, Height = 145, name = "赵六" }; 31 heap2.Enqueue(person6); 32 Console.WriteLine(heap2.TypeName); 33 Console.WriteLine(heap2.Dequeue()); 34 Console.WriteLine(heap2.Dequeue()); 35 Console.WriteLine(heap2.Dequeue()); 36 Console.WriteLine(heap2.Dequeue()); 37 38 39 PersonComparer personComparer = new PersonComparer(); 40 Heap<Person> heap3 = new Heap<Person>(1,HeapType.MaxHeap,personComparer); 41 heap3.Enqueue(person1); 42 heap3.Enqueue(person2); 43 heap3.Enqueue(person3); 44 heap3.Enqueue(person4); 45 heap3.Enqueue(person5); 46 heap3.Enqueue(person6); 47 Console.WriteLine(heap3.TypeName); 48 Console.WriteLine(heap3.Dequeue()); 49 Console.WriteLine(heap3.Dequeue()); 50 Console.WriteLine(heap3.Dequeue()); 51 Console.WriteLine(heap3.Dequeue()); 52 53 54 55 Console.ReadKey(); 56 } 57
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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
