使用C#實現數據結構堆的代碼

一、 堆的介紹:

  堆是用來排序的,通常是一個可以被看做一棵樹的數組對象。堆滿足已下特性:

  1. 堆中某個節點的值總是不大於或不小於其父節點的值

  任意節點的值小於(或大於)它的所有後裔,所以最小元(或最大元)在堆的根節點上(堆序性)。堆有大根堆和小根堆,將根節點最大的堆叫做最大堆或大根堆,根節點最小的堆叫做最小堆或小根堆。

  2. 堆總是一棵完全二叉樹

  除瞭最底層,其他層的節點都被元素填滿,且最底層盡可能地從左到右填入。 

  堆示意圖:

  

  將堆元素從上往下從左到右放進數組對象中,子父節點索引滿足關系:

  parentIndex = (index+1)/ 2 – 1;

  childLeftIndex = parentIndex * 2 + 1;

  childRightIndex = (parentIndex + 1) * 2;

  其中:index為任一節點索引;parentIndex該節點父索引;childLeftIndex該父節點下的子左節點;childRightIndex該父節點下的子右節點。

  創建堆的大概思路: 

  1. 向堆中添加元素:

  加到數組尾處,循環比對其父節點值(大根堆和小根堆比對策略不一樣),比對結果的目標索引不是父節點索引則交換子父節點元素,繼續向上比對其父父節點…;直至比對過程中目標索引為父節點索引或達到根節點結束,新堆創建完成。

  2. 向堆中取出元素:

  取出根節點元素,並將堆末尾元素插入根節點(為瞭保證堆的完全二叉樹特性),從根部再循環向下比對父節點、子左節點、子右節點值,比對結果目標索引不為父節點交換目標索引和父節點的值,向下繼續比對;直至比對過程中目標索引為父節點索引或達到堆尾部結束,新堆創建完成。

二、 代碼實現:

  因為大根堆和小根堆隻是比較策略不同,所以整合瞭兩者,用的時候可以直接設置堆的類別;默認小根堆,默認比較器。實現代碼如下:

public class Heap<T>
 {
  private T[] _array;//數組,存放堆數據
  private int _count;//堆數據數量
  private HeapType _typeName;//堆類型
  private const int _DefaultCapacity = 4;//默認數組容量/最小容量
  private const int _ShrinkThreshold = 50;//收縮閾值(百分比)
  private const int _MinimumGrow = 4;//最小擴容量
  private const int _GrowFactor = 200; // 數組擴容百分比,默認2倍
  private IComparer<T> _comparer;//比較器
  private Func<T, T, bool> _comparerFunc;//比較函數

  //堆數據數量
  public int Count => _count;
  //堆類型
  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堆中有非托管資源,GC不能釋放,需手動
   {
    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;//目標對象t2小
     break;
    case HeapType.MaxHeap:
     _comparerFunc = (T t1, T t2) => _comparer.Compare(t1, t2) < 0;//目標對象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)//縮容
   {
    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)//擴容
   {
    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、 使用測試: 

  建一個Person類用來測試,例子中Person比較規則是:先按年齡比較,年齡相同再按身高比較。具體比較大小是由選擇堆的類別進行不同的排序規則:如Person類中小根堆先按年齡小者排序,年齡相同者按身高大者排序;而使用大根堆則相反。兩種比較器寫法,前者直接使用默認比較器;後者需要將比較器註入到堆中。

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},年齡{Age},身高{Height}";
  }

  //小根堆:先排年齡小,年齡相同,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:先排年齡大,年齡相同,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;
  }
 }

  主函數調用:

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 = "張三" };
   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 = "劉五" };
   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 = "趙六" };
   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();
  }

  輸出結果:

  

  參考:

  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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