使用C#實現資料結構堆

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陣列物件。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

　　除了最底層，其他層的節點都被元素填滿，且最底層儘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陣列物件中，子父節點索引滿足關係：

       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。

　　建立堆的大概思路：　

　　1. 向堆中新增元素：

　　加到陣列尾處，迴圈比對其父節點值（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，新堆建立完成。

　　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（為了保證堆的完全二叉樹特性），從根部再迴圈向下比對父節點、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，新堆建立完成。

二、 程式碼實現：

　　因為大根堆和小根堆只是比較策略不同，所以整合了兩者，用的時候可以直接設定堆的類別；預設小根堆，預設比較器。實現程式碼如下：

    public class Heap<T>
    {
        private T[] _array;//陣列，存放堆資料
        private int _count;//堆資料數量
        private HeapType _typeName;//堆型別
        private const int _DefaultCapacity = 4;//預設陣列容量/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;  // 陣列擴容百分比,預設2倍
        private IComparer<T> _comparer;//比較器
        private Func<T, T, bool> _comparerFunc;//比較函式


        //堆資料數量
        public int Count => _count;
        //堆型別
        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堆中有非託管資源，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;//目標物件t2小
                    break;
                case HeapType.MaxHeap:
                    _comparerFunc = (T t1, T t2) => _comparer.Compare(t1, t2) < 0;//目標物件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，前者直接使用預設比較器；後者需要將比較器注入到堆中。

    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;
        }
    }

　　主函式呼叫：

        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