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){
  while(u != NIL && k != (*u).key)
    {
      if(k < (*u).key)
	u = (*u).left;
      else 
	u = (*u).right;
    }
  return u; 
}

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;
      z = y;
    }
}

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;
  
}