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)

#include<stdio.h>
#include<stdlib.h>

struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
#define NIL NULL
Node root;

Node treeMinimum(Node x){
while(x->left!=NIL){
x=x->left;
}
return x;
}

Node treeSearch(Node u, int k){  
if(u==NIL || k==u->key){
return u;
}
if(k<u->key){
return treeSearch(u->left,k);
}
 else{
return treeSearch(u->right,k);
}

}

Node treeSuccessor(Node x){
Node y;  
if(x->right!=NIL){
return treeMinimum(x->right);
}
y=x->parent;
while(y!=NIL && x==y->right){
x=y;
y=y->parent;
return y;
 }
}

void treeDelete(Node z){
Node y; // node to be deleted
Node x; // child of y
if(z->left==NIL || z->right==NIL){
y=z;
}
 else{
y=treeSuccessor(z);
}
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;
}
if(y!=z){
z->key=y->key;
}


}

void insert(int k){
Node y = NIL;
Node x = root;
Node z;

z = malloc(sizeof(struct node));
z->key = k;
z->left = NIL;
z->right = NIL;
while(x!=NIL){
y=x;
if(z->key < x->key){
x=x->left;
}
 else{
x=x->right;
}
z->parent=y;
}
if(y==NIL){
root=z;
}
 else if(z->key < y->key){
y->left=z;
}
 else{
y->right=z;
}
}

void inorder(Node u){
if(u!=NIL){
inorder(u->left);
printf(" %d",u->key);
inorder(u->right);
}
}
void preorder(Node u){
if(u!=NIL){
printf(" %d",u->key);
preorder(u->left);
preorder(u->right);
}
}


int main(){
int n, i, x;
char com[20];
scanf("%d", &n);

for ( i = 0; i < n; i++ ){
scanf("%s", com);
if ( com[0] == 'f' ){
scanf("%d", &x);
Node t = treeSearch(root, x);
if ( t != NIL ) printf("yes\n");
 else printf("no\n");
} else if ( com[0] == 'i' ){
scanf("%d", &x);
insert(x);
} else if ( com[0] == 'p' ){
inorder(root);
printf("\n");
preorder(root);
printf("\n");
} else if ( com[0] == 'd' ){
scanf("%d", &x);
treeDelete(treeSearch(root, x));
}
}

return 0;
}