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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
typedef struct node{
int key;
struct node *parent;
struct node *left;
struct node *right;
}node;
typedef node * NodePointer;
NodePointer root, nil;
NodePointer make(int key, NodePointer p){
NodePointer n;
n = malloc(sizeof(struct node));
n->key = key;
n->parent = p;
n->left = p;
n->right = p;
return n;
}

void insert(int key){
NodePointer n, x, z;
z = make(key, nil);
n = root;
x = nil;
while(n != nil){
x = n;
if(n->key < key) n = n->right;
else n = n->left;
}
z->parent = x;
if(x == nil) root = z;
if(x->key < z->key) x->right = z;
if(x->key > z->key) x->left = z;
}
void find(NodePointer T, int key){
if(T == nil){
printf("no\n");
return;
}
else if(T->key == key){
printf("yes\n");
return ;
}
else if(T->key < key) find(T->right, key);
else if(T->key > key) find(T->left, key);
return ;
}
NodePointer min(NodePointer x){
while(x->left != nil)
x = x->left;
return x;
}
NodePointer suc(NodePointer x){
NodePointer y;
if(x->right != nil)
return min(x->right);
y = x->parent;
while(y != nil && x == y->right){
x = y;
y = y->parent;
}
return y;
}
void delete(NodePointer T, int key){
NodePointer x, y;
while(T->key != key){
if(T->key < key) T = T->right;
else if (T->key > key) T = T->left;
}
if(T->left == nil || T->right == nil){
y = T;
}
else
y = suc(T);
if(y->left != nil) x = y->left;
else x = y->right;
if(x != nil) x->parent = y->parent;
if(y->parent == nil) root = x;
else if(y == y->parent->left) y->parent->left = x;
else y->parent->right = x;
free(T);
}
void inorder(NodePointer T){
if(T->left->key != 0) inorder(T->left);
printf(" %d",T->key);
if(T->right->key != 0) inorder(T->right);
}
void preorder(NodePointer T){
printf(" %d",T->key);
if(T->left != nil) preorder(T->left);
if(T->right != nil) preorder(T->right);
}
void fre(NodePointer T){
free(T);
if(T->left != nil) fre(T->left);
if(T->right != nil) fre(T->right);
}
int main(){
int i ,n, key;
char s[20];
nil = make(0, nil);
root = make(0, nil);
root = nil;
scanf("%d",&n);
for(i = 0; i < n; i++){
scanf("%s", s);
if(s[0] == 'i'){
scanf("%d",&key);
insert(key);
}
else if(s[0] == 'd'){
scanf("%d",&key);
delete(root, key);
}
else if(s[0] == 'f'){
scanf("%d",&key);
find(root, key);
}
else if(s[0] == 'p'){
inorder(root);
printf("\n");
preorder(root);
printf("\n"); 
}
}
fre(root);
free(nil);
return 0;
}