04-树6 Complete Binary Search Tree （30 分）

04-树6 Complete Binary Search Tree （30 分）

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than the node‘s key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node‘s key.
• Both the left and right subtrees must also be binary search trees.
  
  A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.

  Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

  Input Specification:

  Each input file contains one test case. For each case, the first line contains a positive integer N (≤1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.

  Output Specification:

  For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

  Sample Input:

  10
  1 2 3 4 5 6 7 8 9 0
  

  Sample Output:

  6 3 8 1 5 7 9 0 2 4

using System;
using System.Collections.Generic;
using System.Threading;
using System.Threading.Tasks;
using System.Diagnostics;
using System.Net;
using System.Text;
using System.Xml;

public class MyNode2
{
    public MyNode2(string s)
    {
        Value = int.Parse(s);
    }
    public MyNode2(int s)
    {
        Value = s;
    }
    public MyNode2 Left;
    public MyNode2 Right;
    public int Value;
}
class T
{

    static void Main(string[] args)
    {
        //读取数量
        int count = int.Parse(Console.ReadLine());
        //读取数字行
        var v = Console.ReadLine();

        //数字切分放入list并排序
        var a = v.Split(‘ ‘);
        List<int> listNum = new List<int>();
        foreach (var item in a)
        {
            listNum.Add(int.Parse(item));
        }
        listNum.Sort();

        //以下内容是创建一个列表,把node放进去,为每个node创建左右子节点的同时,也把新创建的节点放入列表.
        //直到列表中node数量与给定的数字数量一致,结束
        List<MyNode2> list = new List<MyNode2>();
        list.Add(new MyNode2(-1));
        int i = 0;
        while (list.Count < count)
        {
            list[i].Left = new MyNode2(-1);
            list.Add(list[i].Left);
            if (list.Count < count)
            {
                list[i].Right = new MyNode2(-1);
                list.Add(list[i].Right);
            }
            i++;

        }

         //为创建好的树,赋值,赋值从0开始
        int x = 0;
        赋值(list[0], ref x);

        StringBuilder sb = new StringBuilder();
        //把node中的值,作为索引,输出listnum
        foreach (var item in list)
        {
            sb.Append(listNum[item.Value] + " ");
        }
        Console.WriteLine(sb.ToString().Trim());

        return;

    }

    /// <summary>
    /// 以左中右的方式赋值,有子节点,则先遍历子节点
    /// </summary>
    /// <param name="n"></param>
    /// <param name="v">ref,便于值累计</param>
    private static void 赋值(MyNode2 n, ref int v)
    {
        if (n.Left != null && n.Left.Value == -1)
        {
            赋值(n.Left, ref v);
        }
        if (n.Value == -1)
        {
            n.Value = v++;
        }
        if (n.Right != null && n.Right.Value == -1)
        {
            赋值(n.Right, ref v);
        }
    }
}

原文地址：https://www.cnblogs.com/interim/p/9734682.html