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：
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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。
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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：
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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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原文链接：https://www.cnblogs.com/jn-shao/archive/2021/02/03/14369451.html
