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 Python (judge verdict: Wrong Answer)

class node:
    def __init__(self,key=None):
        self.left=None
        self.right=None
        self.parent=None
        self.key=key

def insert(T,z):
    x=T
    y=None
    while isinstance(x,node):
        y=x
        if z.key<x.key:
            x=x.left
        else:
            x=x.right
    z.parent=y
    if y is None:
        T=z
    elif z.key<y.key:
        y.left=z
    else:
        y.right=z
    return T

def find(T,z):
    if T is None:
        return False
    else:
        y=None
        x=T
        while 1:
            y=x
            if x is None:
                return False
            elif z.key==x.key:
                return True
            elif z.key<x.key:
                x=x.left
            else:
                x=x.right
                
def delete(T,z,i):
    if i==0:
        x=T
        y=None
        while 1:    
            y=x
            if x is None:
                return 
            elif z.key==x.key:
                break
            elif z.key<x.key:
                x=x.left
            else:
                x=x.right
            z.parent=y
        z=x     
    if z.left is None and z.right is None:
        if z is z.parent.right:
            z.parent.right=None
        else:
            z.parent.left=None
    elif z.left is None:
        if z is z.parent.left:
            z.parent.left=z.right
            z.right.parent=z.parent
        else:
            z.parent.right=z.right
            z.right.parent=z.parent
    elif z.right is None:
        if z is z.parent.left:
            z.parent.left=z.left
            z.left.parent=z.parent
        else:
            z.parent.right=z.left
            z.left.parent=z.parent
    else:
        y=del_inorder(z)
        z.key=y.key
        delete(T,y,1)
           
def preorder(u):
    if u is None:
        return
    pripre.append(str(u.key))
    preorder(u.left)
    preorder(u.right)

def inorder(u):
    if u is None:
        return
    inorder(u.left)
    priin.append(str(u.key))
    inorder(u.right)
    
def del_inorder(u):
    if u is None:
        return
    del_inorder(u.left)
    Min.append(u)
    del_inorder(u.right)
    return Min[0]

m=input()
root=None
for i in xrange(m):
    cmd=map(str,raw_input().split())
    if cmd[0]=="print":
        pripre=[]
        priin=[]
        preorder(root)
        inorder(root)
        print(' '+' '.join(priin))
        print(' '+' '.join(pripre))
    elif cmd[0]=="find":
        key=int(cmd[1])
        z=node(key)
        if find(root,z):
            print('yes')
        else:
            print('no')
    elif cmd[0]=='delete':
        Min=[]
        key=int(cmd[1])
        z=node(key)
        delete(root,z,0)
    else:
        key=int(cmd[1])
        z=node(key)
        root=insert(root,z)