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.Text;

namespace ALDS1_8_C
{
    class Program
    {
        static Node root;
        static StringBuilder sb = new StringBuilder();

        class Node
        {
            public int key;
            public Node left, right, parent;
            public Node(int key) { this.key = key; }
        }
        
        static Node getmimum(Node x)
        {
            while (x.left != null)
            {
                x = x.left;
            }
            return x;
        }

        static void Main(string[] args)
        {
            int m = int.Parse(Console.ReadLine());
      
            for (int i = 0; i < m; i++)
            {
                var a = Console.ReadLine().Split(' ');
                if (a[0] == "insert")
                {
                    insert(int.Parse(a[1]));
                }
                else if (a[0] == "print")
                {
                    inorder(root);
                    sb.AppendLine();
                    preorder(root);
                    sb.AppendLine();
                }
                else if (a[0] == "find")
                {
                    Node n =find(root, int.Parse(a[1]));
                    sb.AppendLine(n!=null ? "yes" : "no");
                }
                else if(a[0] == "delete")
                {
                    delete(find(root, int.Parse(a[1])));
                }
            }
            Console.Write(sb);
        }
        static void delete(Node z)
        {
            //????????????????±??????????y??¨??????
            Node x, y;
            //??????0???1?????¨????????\????????????z
            if (z.left == null || z.right == null) y = z;
            //??????2?????¨???????¬???????y????????????z????????????????????¢
            else y = getsuccessor(z);

            //y??????x????±???????
            if (y.left != null) x = y.left;
            else x = y.right;

            //x??????????¨??????????
            if (x != null) x.parent = y.parent;

            //y???????????????x?????¨????????¨??????
            if (y.parent == null) root = x;
            //??????????????????????????????????????????x
            else if (y == y.parent.left) y.parent.left = x;
            //??????????????????????????????????????????x
            else y.parent.right = x;

            if (y!=z) z.key = y.key;
            
        }
        static Node getsuccessor(Node x)
        {
            if (x.right != null) return getmimum(x.right);

            Node y = x.parent;
            while (y != null && x == y.right)
            {
                x = y;
                y = y.parent;
            }
            return y;

        }
        static Node find(Node u, int k)
        {
            while (u != null && k != u.key)
            {
                u = k < u.key ? u.left : u.right;
            }
            return u;
        }
        static void insert(int k)
        {
            Node x = root;
            Node y = null;
            Node z = new Node(k);

            while (x != null)
            {
                y = x;
                x = z.key < x.key ? x.left : x.right;
            }

            z.parent = y;

            if (y != null)
            {
                if (z.key < y.key) y.left = z;
                else y.right = z;
            }
            else root = z;

        }   
        static void inorder(Node u)
        {
            if (u == null)
            {
                return;
            } 
            inorder(u.left);
            sb.Append(" " + u.key);
            inorder(u.right);
        }
        static void preorder(Node u)
        {
            if (u == null)
            { 
                return;
            }
            sb.Append(" " + u.key);
            preorder(u.left);
            preorder(u.right);
        }
    }
}