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: Accepted)

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

class Program
{

    public void Proc()
    {
        int comandCount = int.Parse(Console.ReadLine());
        for (int i = 0; i < comandCount; i++)
        {
            long target = 0;
            string cmd;
            string[] inpt = Console.ReadLine().Split(' ');
            cmd = inpt[0];
            if (inpt.Length >= 2)
            {
                target = long.Parse(inpt[1]);
            }


            if (cmd.StartsWith("insert"))
            {
                TreeNd.Insert(target);
            }
            else if (cmd.StartsWith("find"))
            {
                TreeNd.Find(target);
            }
            else if (cmd.StartsWith("delete"))
            {
                TreeNd.Delete(target);
            }
            else
            {
                TreeNd.PrintAll();
            }

        }
    }

    public class TreeNd
    {
        private static TreeNd Root = null;
        /// <summary>
        /// ??????
        /// </summary>
        /// <param name="insKey"></param>
        public static void Insert(long insKey)
        {
            if (Root == null)
            {
                Root = new TreeNd(insKey);
            }
            else
            {
                Root.Add(insKey);
            }
        }

        public static void PrintAll()
        {
            if (Root == null)
            {
                return;
            }
            Root.PrintInorder();
            Console.WriteLine("");
            Root.PringPreorder();
            Console.WriteLine("");
        }

        public static void Find(long target)
        {
            bool isFinded = false;
            if (Root == null)
            {
                isFinded = false;
            }
            else
            {
                isFinded = Root.Search(target);
            }
            Console.WriteLine(isFinded ? "yes" : "no");
        }

        public static void Delete(long target)
        {
            if (Root == null)
            {
                return;
            }

            TreeNd nextItem = Root;
            while (nextItem != null)
            {
                if (nextItem.Key == target)
                {
                    nextItem.Remove();
                    break;
                }
                else if (target < nextItem.Key && nextItem.LeftChild != null)
                {
                    nextItem = nextItem.LeftChild;
                }
                else if (target > nextItem.Key && nextItem.RightChild != null)
                {
                    nextItem = nextItem.RightChild;
                }
                else
                {
                    break;
                }
            }
        }


        public void Remove()
        {
            if (LeftChild == null && RightChild == null)
            {
                if (this.Parent.LeftChild == this)
                {
                    this.Parent.LeftChild = null;
                }
                else
                {
                    this.Parent.RightChild = null;
                }
            }
            else if (LeftChild != null && this.RightChild != null)
            {
                TreeNd next = this.RightChild.GetNextInorder();
                this.Key = next.Key;
                next.Remove();
            }
            else
            {
                TreeNd cld;
                if (this.LeftChild != null)
                {
                    cld = this.LeftChild;
                }
                else
                {
                    cld = this.RightChild;
                }
                if (this.Parent.LeftChild == this)
                {
                    this.Parent.LeftChild = cld;
                    cld.Parent = this.Parent;
                }
                else
                {
                    this.Parent.RightChild = cld;
                    cld.Parent = this.Parent;
                }

            }
        }

        public bool Search(long target)
        {
            if (this.Key == target)
            {
                return true;
            }
            if (target < this.Key)
            {
                if (this.LeftChild != null)
                {
                    return this.LeftChild.Search(target);
                }
                else
                {
                    return false;
                }
            }
            else
            {
                if (this.RightChild != null)
                {
                    return this.RightChild.Search(target);
                }
                else
                {
                    return false;
                }
            }
        }

        public void PringPreorder()
        {
            Console.Write(" ");
            Console.Write(this.Key);
            if (this.LeftChild != null)
            {
                this.LeftChild.PringPreorder();
            }
            if (this.RightChild != null)
            {
                this.RightChild.PringPreorder();
            }
        }
        public void PrintInorder()
        {
            if (this.LeftChild != null)
            {
                this.LeftChild.PrintInorder();
            }
            Console.Write(" ");
            Console.Write(this.Key);
            if (this.RightChild != null)
            {
                this.RightChild.PrintInorder();
            }
        }

        /// <summary>
        /// ??????
        /// </summary>
        /// <param name="addKey"></param>
        public void Add(long addKey)
        {
            if (addKey < this.Key)
            {
                if (this.LeftChild == null)
                {
                    this.LeftChild = new TreeNd(addKey);
                    this.LeftChild.Parent = this;
                }
                else
                {
                    this.LeftChild.Add(addKey);
                }
            }
            else
            {
                if (this.RightChild == null)
                {
                    this.RightChild = new TreeNd(addKey);
                    this.RightChild.Parent = this;
                }
                else
                {
                    this.RightChild.Add(addKey);
                }
            }
        }


        public TreeNd GetNextInorder()
        {
            if (this.LeftChild != null)
            {
                return this.LeftChild.GetNextInorder();
            }
            return this;
        }

        public TreeNd(long newKey)
        {
            this.Key = newKey;
        }
        public long Key;
        public TreeNd Parent = null;
        public TreeNd LeftChild = null;
        public TreeNd RightChild = null;
    }




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