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;

class Program{
    class Node{
        public int key;
        public Node parent;
        public Node left;
        public Node right;
    }

    static void Insert(Node root, Node z){
        var y=root;
        var x=root.left;
        while (x!=null) {
            y=x;
            if (z.key<x.key) {
                x=x.left;
            } else {
                x=x.right;
            }
        }
        z.parent=y;
        if (z.key<y.key) {
            y.left=z;
        } else {
            y.right=z;
        }
    }

    static Node Find(Node node, int key){
        if (node.key==key) {
            return node;
        } else {
            if (node.key>key) {
                return node.left!=null ? Find(node.left, key) : null;
            } else {
                return node.right!=null ? Find(node.right, key) : null;
            }
        }
    }

    static void Delete(Node z){
        if(z.left==null && z.right==null){
            if(z.parent.left==z){
                z.parent.left=null;
            } else{
                z.parent.right=null;
            }
        } else if(z.left!=null && z.right!=null){
            var next=z.right;
            while(next.left!=null){
                next=next.left;
            }
            z.key=next.key;
            Delete(next);
        } else{
            if(z.left!=null){
                if(z.parent.left==z){
                    z.parent.left=z.left;
                } else{
                    z.parent.right=z.left;
                }
                z.left.parent=z.parent;
            } else{
                if(z.parent.left==z){
                    z.parent.left=z.right;
                } else{
                    z.parent.right=z.right;
                }
                z.right.parent=z.parent;
            }
        }
    }

    static void WalkPreorder(Node node){
        Console.Write(" "+node.key);
        if(node.left!=null){
            WalkPreorder(node.left);
        }
        if(node.right!=null){
            WalkPreorder(node.right);
        }
    }

    static void WalkInorder(Node node){
        if(node.left!=null){
            WalkInorder(node.left);
        }
        Console.Write(" "+node.key);
        if(node.right!=null){
            WalkInorder(node.right);
        }
    }

    public static void Main(){
        var m=int.Parse(Console.ReadLine());
        var root=new Node();
        root.key=2*1000*1000*1000+1;
        for (var i=0; i<m; i++) {
            var s=Console.ReadLine().Split(' ');
            if (s[0][0]=='i') {
                var node=new Node();
                node.left=null;
                node.right=null;
                node.key=int.Parse(s[1]);
                Insert(root, node);
            } else if (s[0][0]=='f') {
                Console.WriteLine(Find(root.left, int.Parse(s[1]))!=null ?
                        "yes" : "no");
            } else if (s[0][0]=='d') {
                Delete(Find(root.left, int.Parse(s[1])));
            } else {
                WalkInorder(root.left);
                Console.WriteLine();
                WalkPreorder(root.left);
                Console.WriteLine();
            }
        }
    }
}