使用C#实现数据结构堆

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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：

   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：

　　

出处：https://www.cnblogs.com/jn-shao/p/14369451.html

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