使用C#实现数据结构堆

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 }

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     }

　　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     

　　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