資料結構C#版筆記–雙向鏈表(DbLinkList)

這是資料結構C#版筆記--線性表(Data Structure)之單鏈表(LinkList)的繼續，對於雙向連結，節點上除了Next屬性外，還要有Prev屬性用來指向前一個節點，DbNode定義如下：

namespace 線性表{    public class DbNode<T>    {        private T data;        private DbNode<T> prev;        private DbNode<T> next;        public DbNode(T data, DbNode<T> next,DbNode<T> prev)        {            this.data = data;            this.next = next;            this.prev = prev;        }        public DbNode(T data, DbNode<T> next)         {            this.data = data;            this.next = next;            this.prev = null;        }        public DbNode(DbNode<T> next)         {            this.data = default(T);            this.next = next;            this.prev = null;        }        public DbNode(T data)         {            this.data = data;            this.next = null;            this.prev = null;        }        public DbNode()         {            data = default(T);            next = null;            prev = null;        }        public T Data         {            set { this.data = value; }            get { return this.data; }        }        public DbNode<T> Prev         {            get { return prev; }            set { prev = value; }        }        public DbNode<T> Next         {            get { return next; }            set { next = value; }        }    }}

雙鏈表的插入操作要稍微複雜一點，如下：

同樣對於刪除操作，也要額外處理prev指向

完整實現DbLinkList<T>：

using System;using System.Text;namespace 線性表{    public class DbLinkList<T> : IListDS<T>    {        private DbNode<T> head;        public DbNode<T> Head        {            get { return head; }            set { head = value; }        }        public DbLinkList()        {            head = null;        }        /// <summary>        /// 類索引器        /// </summary>        /// <param name="index"></param>        /// <returns></returns>        public T this[int index]         {            get             {                return this.GetItemAt(index);            }        }        /// <summary>        /// 返回單鏈表的長度        /// </summary>        /// <returns></returns>        public int Count()        {            DbNode<T> p = head;            int len = 0;            while (p != null)            {                len++;                p = p.Next;            }            return len;        }        /// <summary>        /// 清空        /// </summary>        public void Clear()        {            head = null;        }        /// <summary>        /// 是否為空白        /// </summary>        /// <returns></returns>        public bool IsEmpty()        {            return head == null;        }        /// <summary>        /// 在最後附加元素        /// </summary>        /// <param name="item"></param>        public void Append(T item)        {            DbNode<T> d = new DbNode<T>(item);            DbNode<T> n = new DbNode<T>();            if (head == null)            {                head = d;                return;            }            n = head;            while (n.Next != null)            {                n = n.Next;            }            n.Next = d;            d.Prev = n;        }        //前插        public void InsertBefore(T item, int i)        {            if (IsEmpty() || i < 0)            {                Console.WriteLine("List is empty or Position is error!");                return;            }            //在最開頭插入            if (i == 0)            {                DbNode<T> q = new DbNode<T>(item);                q.Next = head;//把"頭"改成第二個元素                head.Prev = q;                head = q;//把自己設定為"頭"                return;            }            DbNode<T> n = head;            DbNode<T> d = new DbNode<T>();            int j = 0;            //找到位置i的前一個元素d            while (n.Next != null && j < i)            {                d = n;                n = n.Next;                j++;            }            if (n.Next == null) //說明是在最後節點插入(即追加)            {                DbNode<T> q = new DbNode<T>(item);                n.Next = q;                q.Prev = n;                q.Next = null;            }            else            {                if (j == i)                {                    DbNode<T> q = new DbNode<T>(item);                    d.Next = q;                    q.Prev = d;                    q.Next = n;                    n.Prev = q;                }            }        }        /// <summary>        /// 在位置i後插入元素item        /// </summary>        /// <param name="item"></param>        /// <param name="i"></param>        public void InsertAfter(T item, int i)        {            if (IsEmpty() || i < 0)            {                Console.WriteLine("List is empty or Position is error!");                return;            }            if (i == 0)            {                DbNode<T> q = new DbNode<T>(item);                q.Next = head.Next;                head.Next.Prev = q;                head.Next = q;                q.Prev = head;                return;            }            DbNode<T> p = head;            int j = 0;            while (p != null && j < i)            {                p = p.Next;                j++;            }            if (j == i)            {                DbNode<T> q = new DbNode<T>(item);                q.Next = p.Next;                if (p.Next != null)                {                    p.Next.Prev = q;                }                p.Next = q;                q.Prev = p;            }            else                         {                Console.WriteLine("Position is error!");            }        }        /// <summary>        /// 刪除位元置i的元素        /// </summary>        /// <param name="i"></param>        /// <returns></returns>        public T RemoveAt(int i)        {            if (IsEmpty() || i < 0)            {                Console.WriteLine("Link is empty or Position is error!");                return default(T);            }            DbNode<T> q = new DbNode<T>();            if (i == 0)            {                q = head;                head = head.Next;                head.Prev = null;                return q.Data;            }            DbNode<T> p = head;            int j = 0;            while (p.Next != null && j < i)            {                j++;                q = p;                p = p.Next;            }            if (j == i)            {                p.Next.Prev = q;                q.Next = p.Next;                                return p.Data;            }            else            {                Console.WriteLine("The node is not exist!");                return default(T);            }        }        /// <summary>        /// 擷取指定位置的元素        /// </summary>        /// <param name="i"></param>        /// <returns></returns>        public T GetItemAt(int i)        {            if (IsEmpty())            {                Console.WriteLine("List is empty!");                return default(T);            }            DbNode<T> p = new DbNode<T>();            p = head;            if (i == 0)             {                 return p.Data;             }            int j = 0;            while (p.Next != null && j < i)            {                j++;                p = p.Next;            }            if (j == i)            {                return p.Data;            }            else            {                Console.WriteLine("The node is not exist!");                return default(T);            }        }        //按元素值尋找索引        public int IndexOf(T value)        {            if (IsEmpty())            {                Console.WriteLine("List is Empty!");                return -1;            }            DbNode<T> p = new DbNode<T>();            p = head;            int i = 0;            while (!p.Data.Equals(value) && p.Next != null)            {                p = p.Next;                i++;            }            return i;        }        /// <summary>        /// 元素反轉        /// </summary>        public void Reverse()        {            DbLinkList<T> result = new DbLinkList<T>();            DbNode<T> t = this.head;            result.Head = new DbNode<T>(t.Data);            t = t.Next;            //(把當前連結的元素從head開始遍曆，逐個插入到另一個空鏈表中，這樣得到的新鏈表正好元素順序跟原鏈表是相反的)            while (t!=null)            {                                result.InsertBefore(t.Data, 0);                t = t.Next;            }            this.head = result.head;//將原鏈表直接掛到"反轉後的鏈表"上            result = null;//顯式清空原鏈表的引用，以便讓GC能直接回收        }        //得到某個指定的節點(為了下面測試從後向前遍曆)        private DbNode<T> GetNodeAt(int i){            if (IsEmpty())            {                Console.WriteLine("List is empty!");                return null;            }            DbNode<T> p = new DbNode<T>();            p = head;            if (i == 0)            {                return p;            }            int j = 0;            while (p.Next != null && j < i)            {                j++;                p = p.Next;            }            if (j == i)            {                return p;            }            else            {                Console.WriteLine("The node is not exist!");                return null;            }        }        /// <summary>        /// 測試用prev屬性從後面開始遍曆        /// </summary>        /// <returns></returns>        public string TestPrevErgodic()         {            DbNode<T> tail = GetNodeAt(Count() - 1);            StringBuilder sb = new StringBuilder();            sb.Append(tail.Data.ToString() + ",");            while (tail.Prev != null)            {                sb.Append(tail.Prev.Data.ToString() + ",");                tail = tail.Prev;            }            return sb.ToString().TrimEnd(',');                    }        public override string ToString()        {            StringBuilder sb = new StringBuilder();            DbNode<T> n = this.head;            sb.Append(n.Data.ToString() + ",");            while (n.Next != null)            {                sb.Append(n.Next.Data.ToString() + ",");                n = n.Next;            }            return sb.ToString().TrimEnd(',');        }    }}

測試程式碼片段：

            Console.WriteLine("-------------------------------------");            Console.WriteLine("雙鏈表測試開始...");            DbLinkList<string> dblink = new DbLinkList<string>();            dblink.Head = new DbNode<string>("x");            dblink.InsertBefore("w", 0);            dblink.InsertBefore("v", 0);            dblink.Append("y");            dblink.InsertBefore("z", dblink.Count());            Console.WriteLine(dblink.Count());//5            Console.WriteLine(dblink.ToString());//v,w,x,y,z            Console.WriteLine(dblink[1]);//w            Console.WriteLine(dblink[0]);//v            Console.WriteLine(dblink[4]);//z            Console.WriteLine(dblink.IndexOf("z"));//4            Console.WriteLine(dblink.RemoveAt(2));//x            Console.WriteLine(dblink.ToString());//v,w,y,z            dblink.InsertBefore("x", 2);            Console.WriteLine(dblink.ToString());//v,w,x,y,z            Console.WriteLine(dblink.GetItemAt(2));//x            dblink.Reverse();            Console.WriteLine(dblink.ToString());//z,y,x,w,v            dblink.InsertAfter("1", 0);            dblink.InsertAfter("2", 1);            dblink.InsertAfter("6", 5);            dblink.InsertAfter("8", 7);            dblink.InsertAfter("A", 10);//Position is error!            Console.WriteLine(dblink.ToString()); //z,1,2,y,x,w,6,v,8              string _tail = dblink.GetItemAt(dblink.Count()-1);            Console.WriteLine(_tail);            Console.WriteLine(dblink.TestPrevErgodic());//8            Console.ReadKey(); //8,v,6,w,x,y,2,1,z

當然從上面的測試代碼中，似乎並不能看出雙鏈表的優點，雙鏈表的好處在於，如果需要在鏈表中，需要通過某個節點得到它的前驅節點時，雙鏈表直接用prev屬性就能找到；而單鏈表要做到這一點，必須再次從Head節點開始一個一個用Next向下找，這樣時間複雜度從O(n)降到O(1)，顯然更有效率。

 

註：如果把雙鏈表再做一下改造，讓頭尾接起來，即Head的Prev屬性指向最後一個節點(就叫做Tail吧)，同時把Tail節點的Next屬性指向Head節點，就形成了所謂的“迴圈雙向鏈表”

當然，這樣的結構可以在鏈表中再增加一個Tail節點屬性，在做元素插入或刪除時，可以迴圈到底以更新尾節點Tail(當然這樣會給插入/刪除元素帶來一些額外的開銷)，但是卻可以給GetItemAt(int i)方法帶來最佳化的空間，比如要尋找的元素在前半段時，可以從Head開始用next向後找；反之，如果要找的元素在後半段，則可以從Tail節點用prev屬性向前找。

 

註：.Net中微軟已經給出了一個內建的雙向鏈表System.Collections.Generic.LinkedList<T>，在瞭解雙鏈表的原理後，建議大家直接系統內建的鏈表。