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.IO;

namespace Binary_search_trees
{
    class Binary_Search_Tree_III
    {
        class BinaryTree
        {
            public class Node
            {
                internal int val;
                internal Node left, right, parent;

                internal Node() : this(0, null) { }

                internal Node(int val, Node parent)
                {
                    this.val = val;
                    this.parent = parent;
                    left = right = null;
                }

                internal Node Min
                {
                    get
                    {
                        Node n = this;
                        for (; n.left != null; n = n.left) ;
                        return n;
                    }
                }
            }

            Node root;

            public BinaryTree()
            {
                root = null;
            }

            public void Insert(int elem)
            {
                if (root == null)
                {
                    root = new Node(elem, null);
                    return;
                }

                Node n = root;
                Node p = null;
                while (n != null)
                {
                    p = n;
                    if (n.val > elem) n = n.left;
                    else n = n.right;
                }

                n = new Node(elem, p);
                if (p.val > elem) p.left = n;
                else p.right = n;
            }

            void Replace(Node n, Node m)
            {
                Node p = n.parent;
                if (m != null) m.parent = p;
                if (n == root) root = m;
                else if (p.left == n) p.left = m;
                else p.right = m;
            }

            public void Erase(Node n)
            {
                if (n == null) return;

                if (n.left == null) Replace(n, n.right);
                else if (n.right == null) Replace(n, n.left);
                else
                {
                    Node m = n.right.Min;
                    n.val = m.val;
                    Replace(m, m.right);
                }
            }

            public void Erase(int elem)
            {
                Erase(Find(elem));
            }

            public Node Find(int elem)
            {
                Node n = root;
                while (n != null)
                {
                    if (n.val > elem) n = n.left;
                    else if (n.val < elem) n = n.right;
                    else break;
                }
                return n;
            }

            public bool Contains(int elem)
            {
                return Find(elem) != null;
            }

            public void PrintPreorder(Node n)
            {
                if (n == null) return;
                Console.Write(" " + n.val);
                PrintPreorder(n.left);
                PrintPreorder(n.right);
            }

            public void PrintPreorder()
            {
                PrintPreorder(root);
                Console.WriteLine();
            }

            public void PrintInorder(Node n)
            {
                if (n == null) return;
                PrintInorder(n.left);
                Console.Write(" " + n.val);
                PrintInorder(n.right);
            }

            public void PrintInorder()
            {
                PrintInorder(root);
                Console.WriteLine();
            }
        }

        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var bt = new BinaryTree();
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            for (int i = 0; i < n; i++)
            {
                var line = Console.ReadLine();
                switch (line[0])
                {
                    case 'i':
                        bt.Insert(int.Parse(line.Substring(7)));
                        break;
                    case 'f':
                        if (bt.Contains(int.Parse(line.Substring(5)))) Console.WriteLine("yes");
                        else Console.WriteLine("no");
                        break;
                    case 'd':
                        bt.Erase(int.Parse(line.Substring(7)));
                        break;
                    case 'p':
                        bt.PrintInorder();
                        bt.PrintPreorder();
                        break;
                }
            }
            Console.Out.Flush();
        }
    }
}