Problem:
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Reconstruction of a Tree

Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.

Input

In the first line, an integer $n$, which is the number of nodes in the binary tree, is given.

In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters.

In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.

Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.

Output

Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.

Constraints

$1 \leq n \leq 40$

Sample Input 1

5
1 2 3 4 5
3 2 4 1 5

Sample Output 1

3 4 2 5 1

Sample Input 2

4
1 2 3 4
1 2 3 4

Sample Output 2

4 3 2 1

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ALDS1_7_D
{
    class Program
    {
        static void Main(string[] args)
        {
            string line;

            //入力
            line = Console.ReadLine().Trim();
            var nodeCount = int.Parse(line);
            line = Console.ReadLine().Trim();
            var preorders = line.Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries).Select(e => int.Parse(e)).ToArray();
            line = Console.ReadLine().Trim();
            var inorders = line.Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries).Select(e => int.Parse(e)).ToArray();

            //再構成
            var nodes = new Nodes<int>();
            ReConstruct(nodes, preorders, inorders);
            Console.WriteLine(String.Join(" ", nodes.Postorder().Select(x => x.Value).ToArray()));
        }

        static void ReConstruct(Nodes<int> nodes, int[] preorders, int[] inorders)
        {
            var root = nodes.GetNode(preorders[0]);

            var inordersIdx = inorders.Select((val, idx) => new { val, idx }).Where(x => x.val == root.Value).Select(x => x.idx).First();

            var inorderLeft = inorders.Take(inordersIdx).ToArray();
            var inorderRight = inorders.Skip(inordersIdx + 1).ToArray();
            var preordersLeft = preorders.Skip(1).Take(inordersIdx).ToArray();
            var preordersRight = preorders.Skip(inordersIdx + 1).ToArray();

            if (preordersLeft.Length > 0)
            {
                nodes.SetLeft(root, preordersLeft[0]);
                ReConstruct(nodes, preordersLeft, inorderLeft);
            }
            if (inorderRight.Length > 0)
            {
                nodes.SetRight(root, preordersRight[0]);
                ReConstruct(nodes, preordersRight, inorderRight);
            }
        }
    }

    public class Nodes<T>
    {
        private readonly Dictionary<T, Node> nodes = new Dictionary<T, Node>();

        public Node GetNode(T val)
        {
            Node node;
            if (!nodes.TryGetValue(val, out node))
            {
                node = new Node() { Value = val };
                nodes.Add(val, node);
            }
            return node;
        }

        public void SetLeft(Node node, T val)
        {
            var left = GetNode(val);
            left.Parent = node;
            node.Left = left;
        }

        public void SetRight(Node node, T val)
        {
            var right = GetNode(val);
            right.Parent = node;
            node.Right = right;
        }

        public Node GetRoot()
        {
            return nodes.Values.FirstOrDefault(x => x.Parent == null);
        }

        public IEnumerable<Node> Preorder(Node node = null)
        {
            if (node == null)
                node = GetRoot();

            yield return node;
            foreach (var child in node.Children())
            {
                foreach (var grandChild in Preorder(child))
                    yield return grandChild;
            }
        }

        public IEnumerable<Node> Inorder(Node node = null)
        {
            if (node == null)
                node = GetRoot();

            if (node.Left != null)
            {
                foreach (var grandChild in Inorder(node.Left))
                    yield return grandChild;
            }
            yield return node;
            if (node.Right != null)
            {
                foreach (var grandChild in Inorder(node.Right))
                    yield return grandChild;
            }
        }

        public IEnumerable<Node> Postorder(Node node = null)
        {
            if (node == null)
                node = GetRoot();

            foreach (var child in node.Children())
            {
                foreach (var grandChild in Postorder(child))
                    yield return grandChild;
            }
            yield return node;
        }

        public IEnumerable<Node> GetList()
        {
            return nodes.OrderBy(x => x.Key).Select(x => x.Value);
        }

        public class Node
        {
            public T Value { get; set; }
            public Node Parent { get; set; }
            public Node Left { get; set; }
            public Node Right { get; set; }

            public string NodeType
            {
                get
                {
                    if (Parent == null)
                    {
                        return "root";
                    }
                    if (Left != null || Right != null)
                    {
                        return "internal node";
                    }
                    return "leaf";
                }
            }

            public int GetDepth()
            {
                if (Parent == null)
                {
                    return 0;
                }
                return Parent.GetDepth() + 1;
            }

            public IEnumerable<Node> Children()
            {
                if (Left != null) yield return Left;
                if (Right != null) yield return Right;
            }

            public override string ToString()
            {
                return $"node {Value}: parent = {(Parent != null ? Parent.Value.ToString() : "-1")}, {NodeType}";
            }
        }
    }
}