Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

delete $k$: Delete a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C# (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;

class Program
{

    public void Proc()
    {
        int cmdCount = int.Parse(Console.ReadLine());
        TreeNd root = null;

        for (int i = 0; i < cmdCount; i++)
        {
            string[] inpt = Console.ReadLine().Split(' ');
            if (inpt[0].Equals("print"))
            {
                this.GetInorderText(root);
                Console.WriteLine(string.Empty);
                this.GetPreorderText(root);
                Console.WriteLine(string.Empty);
            }
            else if (inpt[0].Equals("find"))
            {
                long target = long.Parse(inpt[1]);
                TreeNd parent = root;
                bool isFinded = false;
                for (int j = 0; j < cmdCount; j++)
                {
                    if (parent == null)
                    {
                        break;
                    }
                    if (parent.NodeId == target)
                    {
                        isFinded = true;
                        break;
                    }
                    else if (parent.NodeId < target)
                    {
                        parent = parent.RightChild;
                    }
                    else
                    {
                        parent = parent.LeftChild;
                    }
                }
                Console.WriteLine(isFinded ? "yes" : "no");
            }
            else if (inpt[0].Equals("delete"))
            {
                long target = long.Parse(inpt[1]);
                TreeNd node = root;
                for (int j = 0; j < cmdCount; j++)
                {
                    if (node == null)
                    {
                        break;
                    }
                    if (node.NodeId == target)
                    {
                        // ????????????

                        if (node.LeftChild == null && node.RightChild == null)
                        {
                            // ????????????????????????
                            if (node.Parent.LeftChild == node)
                            {
                                node.Parent.LeftChild = null;
                            }
                            else
                            {
                                node.Parent.RightChild = null;
                            }
                        }
                        else 
                        {
                            TreeNd chd = null;
                            if (node.LeftChild != null && node.RightChild != null)
                            {
                                // ??????2?????????????????????
                                chd = this.GetNextChild(node.RightChild);
                            }
                            else if (node.LeftChild != null)
                            {
                                // ?????????????±????????????????
                                chd = node.LeftChild;
                            }
                            else
                            {
                                // ????????????????±????????????????
                                chd = node.RightChild;
                            }
                            if (node.Parent.LeftChild == node)
                            {
                                node.Parent.LeftChild = chd;
                            }
                            else
                            {
                                node.Parent.RightChild = chd;
                            }
                            chd.Parent = node.Parent;
                        }
                    }
                    else if (node.NodeId < target)
                    {
                        node = node.RightChild;
                    }
                    else
                    {
                        node = node.LeftChild;
                    }
                }
            }
            else
            {
                long num = long.Parse(inpt[1]);
                if (root == null)
                {
                    root = new TreeNd(num);
                }
                else
                {
                    TreeNd target = root;
                    for (int j = 0; j < cmdCount; j++)
                    {
                        if (target.NodeId > num)
                        {
                            if (target.LeftChild == null)
                            {
                                target.LeftChild = new TreeNd(num);
                                target.LeftChild.Parent = target;
                                break;
                            }
                            else
                            {
                                target = target.LeftChild;
                            }
                        }
                        else
                        {
                            if (target.RightChild == null)
                            {
                                target.RightChild = new TreeNd(num);
                                target.RightChild.Parent = target;
                                break;
                            }
                            else
                            {
                                target = target.RightChild;
                            }
                        }
                    }
                }
            }

        }
        // ????????????

    }

    private TreeNd GetNextChild(TreeNd node)
    {
        if (node.LeftChild != null)
        {
            return GetNextChild(node.LeftChild);
        }
        return node;
    }

    private void GetPreorderText(TreeNd root)
    {
        Console.Write(" " + root.NodeId);
        if (root.LeftChild != null)
        {
            this.GetPreorderText(root.LeftChild);
        }
        if (root.RightChild != null)
        {
            this.GetPreorderText(root.RightChild);
        }
    }

    private void GetInorderText(TreeNd root)
    {
        if (root.LeftChild != null)
        {
            this.GetInorderText(root.LeftChild);
        }
        Console.Write(" " + root.NodeId);
        if (root.RightChild != null)
        {
            this.GetInorderText(root.RightChild);
        }
    }

    public class TreeNd
    {
        public TreeNd Parent;
        public long NodeId;
        public TreeNd LeftChild;
        public TreeNd RightChild;


        public TreeNd(long nodeid)
        {
            this.NodeId = nodeid;
        }


    }


    static void Main(string[] args)
    {
        Program prg = new Program();
        prg.Proc();
    }
}