C# 最大二叉堆算法

C#练习二叉堆算法。

namespace 算法
{
    /// <summary>
    /// 最大堆
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class IndexMaxHeap<T> where T:IComparable<T>
    {
        /// <summary>
        /// 堆空间大小
        /// </summary>
        private int capacity;
        /// <summary>
        /// 数据项
        /// </summary>
        private T[] items;
        /// <summary>
        /// 堆实际大小
        /// </summary>
        private int count;

        /// <summary>
        /// 构造方法，由用户指定开辟空间大小，注意元素从1开始
        /// </summary>
        /// <param name="n"></param>
        public IndexMaxHeap(int n)
        {
            capacity = n+1;
            items = new T[capacity];
            count = 0;
        }
        /// <summary>
        /// 堆实际大小
        /// </summary>
        /// <returns>返回堆实际大小int类型</returns>
        public int size()
        {
            return count;
        }
        /// <summary>
        /// 堆中是否有数据
        /// </summary>
        /// <returns></returns>
        public bool isEmpty()
        {
            return count == 0;
        }

        /// <summary>
        /// 堆中插入一个元素
        /// </summary>
        /// <param name="item"></param>
        public void insert(T item)
        {
            if (count+1 > capacity)
            {
                throw new IndexOutOfRangeException("堆空间溢出");
            }
            items[++count] = item;
            shiftUp(count);
        }

        /// <summary>
        /// 出堆
        /// </summary>
        public T extractMax()
        {
            if (count <= 0)
            {
                throw new IndexOutOfRangeException("空数据");
            }
            T maxItem = items[1];
            //先交换位置
            swap(ref items[1], ref items[count]);
            count--;
            //做一次shiftdown操作
            shiftDown(1);

            return maxItem;

        }

        private void shiftDown(int n)
        {
            while (n*2<=count)
            {
                int des = 2*n;
                if (2 * n + 1<=count && items[n * 2].CompareTo(items[2 * n + 1]) < 0)
                {
                    des = 2 * n + 1;
                }
                if (items[n].CompareTo(items[des]) < 0)
                {
                    swap(ref items[n], ref items[des]);
                    n = des;
                }
                else
                {
                    break;
                }

            }

        }

        public void print()
        {
            for(int i = 1; i <= count; i++)
            {
                Console.WriteLine(items[i]);
            }
        }

        /// <summary>
        /// 将堆底元素向上提
        /// </summary>
        /// <param name="n"></param>
        private void shiftUp(int n)
        {
            //只要父级元素大于它，就一直循环并交换
            while (n>1 && items[n].CompareTo(items[n/2])>0)
            {
                int j = n / 2;
                swap(ref items[n], ref items[j]);
                n = j;
            }

        }

        private void swap(ref T a,ref T b)
        {
            T c = a;
            a = b;
            b = c;

        }

    }

    public class Test
    {
        public static void Main()
        {
            IndexMaxHeap<int> heap = new IndexMaxHeap<int>(15);

            for (int i = 0; i < 10; i++)
            {
                Random rd = new Random();
                int a = rd.Next(10, 100);
                heap.insert(a);
               // Console.WriteLine(a);
            }
            Console.WriteLine("---");
            Console.WriteLine($"最大值：{heap.extractMax()}");
            heap.print();
            Console.WriteLine("+++++++++++++++");
            HeapSort<int>(new int[5] { 3, 2, 4, 6, 7 });
            Console.ReadKey();
        }

        /// <summary>
        /// 堆排序
        /// </summary>
        public static T[] HeapSort<T>(T[] arr ) where T:IComparable<T>
        {
            IndexMaxHeap<T> a = new IndexMaxHeap<T>(100);
            for(int i = 0; i < arr.Length; i++)
            {
                a.insert(arr[i]);
            }
            //从小到大
            for(int i = arr.Length-1; i >=0; i--)
            {
                T t = a.extractMax();
                arr[i] = t;
            }
            return arr;

        }

    }

    public class a : IComparable<a>
    {
        public int CompareTo(a other)
        {
            throw new NotImplementedException();
        }
    }
}