C# 實現高效能泛型優先隊列

.NET Framework 基礎類庫未內建優先隊列，本文提供基於二元堆的泛型實現 PriorityQueue<T>，時間複雜度優於列表實現。

核心特性

• 四個公共建構函數，支援指定初始容量與自定義比較器 IComparer<T>
• 採用陣列實現二元堆，空間效率最優
• Count 與 Top() 為 O(1)；Push() 與 Pop() 為 O(log N)

完整代碼

using System;
using System.Collections.Generic;

namespace Skyiv.Util
{
    class PriorityQueue<T>
    {
        IComparer<T> comparer;
        T[] heap;

        public int Count { get; private set; }

        public PriorityQueue() : this(null) { }
        public PriorityQueue(int capacity) : this(capacity, null) { }
        public PriorityQueue(IComparer<T> comparer) : this(16, comparer) { }

        public PriorityQueue(int capacity, IComparer<T> comparer)
        {
            this.comparer = (comparer == null) ? Comparer<T>.Default : comparer;
            this.heap = new T[capacity];
        }

        public void Push(T v)
        {
            if (Count >= heap.Length) Array.Resize(ref heap, Count * 2);
            heap[Count] = v;
            SiftUp(Count++);
        }

        public T Pop()
        {
            var v = Top();
            heap[0] = heap[--Count];
            if (Count > 0) SiftDown(0);
            return v;
        }

        public T Top()
        {
            if (Count > 0) return heap[0];
            throw new InvalidOperationException("優先隊列為空");
        }

        void SiftUp(int n)
        {
            var v = heap[n];
            for (var n2 = n / 2; n > 0 && comparer.Compare(v, heap[n2]) > 0; n = n2, n2 /= 2) heap[n] = heap[n2];
            heap[n] = v;
        }

        void SiftDown(int n)
        {
            var v = heap[n];
            for (var n2 = n * 2; n2 < Count; n = n2, n2 *= 2)
            {
                if (n2 + 1 < Count && comparer.Compare(heap[n2 + 1], heap[n2]) > 0) n2++;
                if (comparer.Compare(v, heap[n2]) >= 0) break;
                heap[n] = heap[n2];
            }
            heap[n] = v;
        }
    }
}

效能對比

曾嘗試用 List<T> 實現（代碼僅 23 行），但 Push/Pop 為 O(N) 效率較低。堆實現雖代碼較長，但大數據量下效能優勢明顯。