先序中序求解二叉树（使用二叉查找树原理）

　　　 二叉树的先序中序序列确定，二叉树也就确认了，但还原二叉树确实有点麻烦，要不断的遍历中序序列。后来学习了二叉查找树，发现了一个很巧的办法。

　　　 二叉查找树的特性是每个节点都有权值，其规律为左子节点小于父节点，右子节点大于父节点，其中序序列是有序的。如果我们把二叉树变成二叉查找树，就是要给每个子节点赋值，最简单的根据中序序列从0->赋值，现在我们来看看二叉查找树先序序列和二叉查找树的关系。以下树的中序序列为DBEGACF,附上权值为（D:0,B:1,E:2,G:3,A:4,C:5,F:6 ）

　　关于这个2插树先序为ABDEGCF,先序序列是先本身节点->左节点->有节点。细心发现二叉查找树的先序序列可以作为节点进入树的先后顺序（节点进入树的先后顺序可以有多个，不一定是先序序列），根据中序的赋值先序可以为4102356（与ABDEGCF相对应）也就是用这个序列来创建二叉查找树。接下来就不用我多说了。附上C#实现代码（PS:写算法不要用C#，坑）

  1 namespace Test
  2 {
  3     class Program
  4     {
  5         static void Main(string[] args)
  6         {
  7             string first = "ABDEGCF";           //先序
  8             string mid = "DBEGACF";             //中序
  9             DouBleTree doubletree = new DouBleTree(first,mid);
 10             Console.WriteLine(doubletree.FirstOrder());     //先序
 11             Console.WriteLine(doubletree.MidOrder());       //中序
 12             Console.WriteLine(doubletree.AfterOrder());     //后序
 13             Console.ReadLine();
 14         }
 15     }
 16     public class DouBleTree
 17     {
 18         /// <summary>
 19         ///
 20         /// </summary>
 21         /// <param name="first">先序</param>
 22         /// <param name="mid">中序</param>
 23         public DouBleTree(string first, string mid)
 24         {
 25             tlist = new List<T>();
 26             for (int i = 0; i < mid.Length; i++)        //  附加权值
 27             {
 28                 T t = new T
 29                 {
 30                     data = mid[i],
 31                     WeigthValue = i,
 32                 };
 33                 tlist.Add(t);
 34             }
 35             doubleTreeRoot = new DoubleTreePoint        //创建根节点
 36             {
 37                 data = first[0],
 38                 WeightValue = tlist.FirstOrDefault(n => n.data == first[0]).WeigthValue,
 39             };
 40             for (int i = 1; i < first.Length; i++)      //创建二叉树
 41             {
 42                 T t = tlist.FirstOrDefault(n => n.data == first[i]);
 43                 doubleTreeRoot = InsertPoint(doubleTreeRoot, t);
 44             }
 45         }
 46         private DoubleTreePoint doubleTreeRoot;                                     //二叉树根节点
 47         private List<T> tlist;                                                      //给中序队列附权值
 48         private DoubleTreePoint InsertPoint(DoubleTreePoint point  ,T t)            //插入节点
 49         {
 50             if (point == null)
 51             {
 52                 point = new DoubleTreePoint
 53                 {
 54                     data = t.data,
 55                     WeightValue = t.WeigthValue,
 56                 };
 57                 return point;
 58             }
 59             if (point.WeightValue > t.WeigthValue)
 60             {
 61                  point.left = InsertPoint(point.left, t);
 62             }
 63             else
 64             {
 65                  point.right = InsertPoint(point.right, t);
 66             }
 67             return point;
 68
 69         }
 70         public string FirstOrder()                      //返回先序队列
 71         {
 72             string str = "";
 73             First(doubleTreeRoot,ref str);
 74             return str;
 75         }
 76         private void First(DoubleTreePoint doubleTreePoint,ref string str)
 77         {
 78             if (doubleTreePoint == null) return;
 79             str += doubleTreePoint.data;
 80             First(doubleTreePoint.left,ref str);
 81             First(doubleTreePoint.right,ref str);
 82         }
 83         public string MidOrder()
 84         {
 85             string str = "";
 86             Mid(doubleTreeRoot, ref str);
 87             return str;
 88         }
 89         private void Mid(DoubleTreePoint doubleTreePoint,ref string str)
 90         {
 91             if (doubleTreePoint == null) return;
 92             Mid(doubleTreePoint.left,ref str);
 93             str += doubleTreePoint.data;
 94             Mid(doubleTreePoint.right,ref str);
 95         }
 96         public string AfterOrder()
 97         {
 98             string str = "";
 99             After(doubleTreeRoot,ref str);
100             return str;
101         }
102         private void After(DoubleTreePoint doubleTreePoint,ref string str)
103         {
104             if (doubleTreePoint == null) return;
105             After(doubleTreePoint.left,ref str);
106             After(doubleTreePoint.right,ref str);
107             str += doubleTreePoint.data;
108         }
109     }
110     public class DoubleTreePoint
111     {
112         public char data { get; set; }          //数据
113         public DoubleTreePoint left { get; set; }
114         public DoubleTreePoint right { get; set; }
115         public int WeightValue { get; set; }    //权值
116     }
117     public class T
118     {
119         public char data { get; set; }
120         public int WeigthValue { get; set; }
121     }
122 }