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

class Node
{
    internal int key;
    internal Node left, right, parent;
    public Node(int key) {
        this.key = key;
    }
}

class C
{
    static Node root;
    public static void Main() {
        int n = int.Parse(Console.ReadLine());
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < n; i++) {
            String[] input = Console.ReadLine().Split(' ');
            if (input[0] == "insert") {
                Insert(int.Parse(input[1]));
            }else if (input[0] == "find") {
                output.Append(find(root, int.Parse(input[1])) != null? "yes":"no");
                if (i != n - 1) {
                    output.AppendLine();
                }
            }else if(input[0]=="delete"){
                Delete(find(root, int.Parse(input[1])));
            } else {
                Inorder(root, output);
                output.AppendLine();
                Preorder(root, output);
                if (i != n - 1) {
                    output.AppendLine();
                }
            }

        }
        Console.WriteLine(output);


    }
    static void Delete(Node z) {
        Node y,x;
        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 z) {
        Node y;
        if (z.right != null) {
            return getMin(z.right);
        }
        y = z.parent;
        while (y != null && z == y.right) {
            z = y;
            y = y.parent;
        }
        return y;
    }
    static Node getMin(Node z) {
        while (z.left != null) {
            z = z.left;
        }
        return z;
    }
    static Node find(Node z, int key) {
        while (z != null&&z.key!=key) {
            z = key < z.key ? z.left : z.right;
        }
        return z;
    }
    static void Insert(int key) {
        Node z = root;
        Node y = null;
        Node x = new Node(key);
        while (z != null) {
            y = z;
            z = x.key < z.key ? z.left : z.right;
        }
        x.parent = y;
        if (y == null) {
            root = x;
        }else if (x.key < y.key) {
            y.left = x;
        } else {
            y.right = x;
        }
    }
    static void Preorder(Node nodes, StringBuilder output) {
        if (nodes == null) {
            return;
        }
        output.Append(" " + nodes.key);
        Preorder(nodes.left, output);
        Preorder(nodes.right, output);
    }

    static void Inorder(Node nodes, StringBuilder output) {
        if (nodes == null) {
            return;
        }
        Inorder(nodes.left, output);
        output.Append(" " + nodes.key);
        Inorder(nodes.right, output);
    }
}