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;

class Node
{
  internal int key;
  internal Node left, right, parent;

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

class C8
{
    static StringBuilder sb = new StringBuilder();
    static Node root;

    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());

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

            switch (input[0][0])
            {
                case 'i':
                    Insert(int.Parse(input[1]));
                    break;
                case 'f':
                    sb.AppendLine(find(root, int.Parse(input[1])) != null ? "yes" : "no");
                    break;
                case 'd':
                    Delete(find(root, int.Parse(input[1])));
                    break;
                default:
                    Inorder(root);
                    sb.AppendLine();
                    Preorder(root);
                    sb.AppendLine();
                    break;
            }
        }
        Console.Write(sb);
    }

    static void Delete(Node z)
    {
        Node x, y;

        if (z.left == null || z.right == null) y = z;
        else y = GetSuccessor(z);

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

        if (x != null) x.parent = y.parent;

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

    static Node GetSuccessor(Node x)
    {
        Node y;

        if (x.right != null)
        {
            y = x.right;

            while (y.left != null)
            {
                y = y.left;
            }
            return y;
        }
        else
        {
            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);
    }
}