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>
struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;

 
Node root;
int count =0;
int count2 = 0;
Node treeMinimum(Node x){
   while (x->left != NULL){
    x = x->left;
}
return x;
}
 
 
 
Node IterativetreeSearch(Node u, int k){
  while(u !=NULL && 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 != NULL){
    return treeMinimum(x->right);
      }
  y = x->parent;
 
  while(y != NULL && x == y->right){
    x = y;
    y = y->parent;
  }
  return y;
}
 
void treeDelete(Node z){
  Node y; 
  Node x;   
  if(z->left == NULL || z->right == NULL){
    y = z;
  }
  else 
    y = treeSuccessor(z);
  
 
  if(y->left != NULL)
    x = y->left;
  
  else 
    x = y->right;
  
 
  if(x != NULL)
    x->parent = y->parent;
  
  if(y->parent == NULL)
    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 = NULL;
  Node x = root;
  Node z;
 
  z = malloc(sizeof(struct node));
  z->key = k;
  z->left = NULL;
  z->right = NULL;
 
  while(x != NULL){
    y = x;
    if(z->key < x->key)
      x = x->left;
    
    else x = x->right; 
  }
  z->parent = y;
 
  if(y == NULL)
    root = z;
  
  else if (z->key < y->key)
    y->left = z;
  
   
  else y->right = z;
}
 
void inorder(Node u){
  if(u != NULL){
    inorder(u->left);
    printf(" ");
    printf("%d",u->key);
    inorder(u->right);
  }
  
}
 
 
 
 
void preorder(Node u){
   
   
    if (u != NULL) {
      printf(" ");
      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 = IterativetreeSearch(root, x);
      if ( t != NULL)
    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");
    count = 0;
     
      }
    else if ( com[0] == 'd' ){
      scanf("%d", &x);
      treeDelete(IterativetreeSearch(root, x));
    }
  }
 
  return 0;
  }