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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ALDS1_8_C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            Node root = null;

            for (int i = 0; i < n; i++)
            {
                string[] tmpLine = Console.ReadLine()
                                          .Split()
                                          .ToArray();

                if (tmpLine[0] == "insert")
                {
                    Node tmpNode = new Node(int.Parse(tmpLine[1]));

                    if (root == null)
                    {
                        root = tmpNode;
                    }
                    else
                    {
                        root.Insert(tmpNode);
                    }
                }
                else if (tmpLine[0] == "print")
                {
                    if (root != null)
                    {
                        root.InorderPrint();
                        Console.WriteLine();
                        root.PreorderPrint();
                        Console.WriteLine();
                    }
                }
                else if (tmpLine[0] == "find")
                {
                    if (root == null)
                    {
                        Console.WriteLine("no");
                    }
                    else
                    {
                        Console.WriteLine(root.Find(int.Parse(tmpLine[1])) ? "yes" : "no");
                    }
                }
                else if (tmpLine[0] == "delete")
                {
                    if (root != null)
                    {
                        root.Delete(int.Parse(tmpLine[1]));
                    }
                }
            }
        }
    }

    class Node
    {
        public int val;
        public Node parent;
        public Node left;
        public Node right;

        public Node(int val)
        {
            this.val = val;
        }

        public void Insert(Node target)
        {
            if (target.val < this.val)
            {
                if (this.left == null)
                {
                    this.left = target;
                    target.parent = this;
                }
                else
                {
                    this.left.Insert(target);
                }
            }
            else
            {
                if (this.right == null)
                {
                    this.right = target;
                    target.parent = this;
                }
                else
                {
                    this.right.Insert(target);
                }
            }
        }

        public void PreorderPrint()
        {
            Console.Write(string.Format(" {0}", this.val));

            if (this.left != null)
            {
                this.left.PreorderPrint();
            }

            if (this.right != null)
            {
                this.right.PreorderPrint();
            }
        }

        public void InorderPrint()
        {
            if (this.left != null)
            {
                this.left.InorderPrint();
            }

            Console.Write(string.Format(" {0}", this.val));

            if (this.right != null)
            {
                this.right.InorderPrint();
            }
        }

        public bool Find(int target)
        {
            if (target == this.val)
            {
                return true;
            }
            else if (target < this.val && this.left != null)
            {
                return this.left.Find(target);
            }
            else if (target >= this.val && this.right != null)
            {
                return this.right.Find(target);
            }
            else
            {
                return false;
            }
        }

        public Node GetNode(int target)
        {
            if (target == this.val)
            {
                return this;
            }
            else if (target < this.val && this.left != null)
            {
                return this.left.GetNode(target);
            }
            else if (target >= this.val && this.right != null)
            {
                return this.right.GetNode(target);
            }
            else
            {
                return null;
            }
        }

        public Node GetMinNode()
        {
            return this.left == null ? this : this.left.GetMinNode();
        }

        public void Delete(int target)
        {
            Node targetNode = this.GetNode(target);

            if (targetNode == null)
            {
                return;
            }

            if (targetNode.left == null && targetNode.right == null)
            {
                if (target < targetNode.parent.val)
                {
                    targetNode.parent.left = null;
                }
                else
                {
                    targetNode.parent.right = null;
                }
            }
            else if (targetNode.left == null)
            {
                if (target < targetNode.parent.val)
                {
                    targetNode.parent.left = targetNode.right;

                }
                else
                {
                    targetNode.parent.right = targetNode.right;
                }
                targetNode.right.parent = targetNode.parent;
            }
            else if (targetNode.right == null)
            {
                if (target < targetNode.parent.val)
                {
                    targetNode.parent.left = targetNode.left;

                }
                else
                {
                    targetNode.parent.right = targetNode.left;
                }
                targetNode.left.parent = targetNode.parent;
            }
            else
            {
                Node alterNode = targetNode.right.GetMinNode();

                //targetNodeの右子ノードが削除される可能性があることに注意する
                alterNode.Delete(alterNode.val);

                if (target < targetNode.parent.val)
                {
                    targetNode.parent.left = alterNode;

                }
                else
                {
                    targetNode.parent.right = alterNode;
                }
                alterNode.parent = targetNode.parent;
                alterNode.left = targetNode.left;
                alterNode.right = targetNode.right;
                alterNode.left.parent = alterNode;

                if (alterNode.right != null)
                {
                    alterNode.right.parent = alterNode;
                }
            }

        }
    }
}