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>
#include<string.h>
  
struct Node{
  
  int key;
  struct Node *parent;
  struct Node *left;
  struct Node *right;
  
};
  
struct Node *root,*NIL;
void insert(int );
void preorder(struct Node *);
void inorder(struct Node *);
struct Node *successor(struct Node*);
struct Node *find(struct Node *, int);
void deleteNode( struct Node *);
struct Node * miniNode(struct Node*);
int main(){
  
  int sumnode,inputdata,i,findnumber;
  char string[10];
  int deletenum;
  struct Node *deletenode;
  struct Node *answer;

  scanf("%d",&sumnode);
  
  for(i = 0; i < sumnode; i++){
  
    scanf("%s",string);
  
    if((strcmp(string,"insert")) == 0){
  
      scanf("%d",&inputdata);
      insert(inputdata);
  
    }
  
  
    else if((strcmp(string,"print"))==0){
  
      inorder(root);
  
      printf("\n");
  
      preorder(root);
  
      printf("\n");
     
          
    }
  
    else if((strcmp(string,"delete")) == 0){

      scanf("%d",&deletenum);

      deleteNode(find(root,deletenum));

    }

    else if((strcmp(string,"find")) == 0){
  
  
      struct Node *answer;
      scanf("%d",&findnumber);
  
      answer =  find(root,findnumber);

   
   if(answer !=NIL){
  
     printf("yes\n");
  
   }
  
   else{
  
     printf("no\n");
  
   }
    }

  }
 
 return 0;
}

void insert(int inputdata){
  
  struct Node *correntNode; 
  struct Node *beforeNode; 
  struct Node *newNode;
  
  newNode = (struct Node*)malloc(sizeof(struct Node));
  
  newNode -> key = inputdata;
  
  newNode->parent = NIL;
  
  newNode->left = NIL;
  
  newNode->right = NIL;
  
  correntNode = root;
  beforeNode = NIL;
  
  while(correntNode != NIL){
  
    beforeNode = correntNode;
  
    if(newNode->key < correntNode->key){
  
      correntNode = correntNode->left;
  
    }
  
    else{
  
      correntNode =  correntNode->right;
  
    }
  } 
  
  newNode->parent = beforeNode;
  
  
  if(beforeNode == NIL){ 
  
    root = newNode;;
  
  }
  
  else if(newNode->key > beforeNode->key){
  
    beforeNode->right = newNode;
  
  }
  
  else{
  
    beforeNode->left = newNode;
  
  }
  
}
  
void preorder(struct Node *inputdata){
  
  if(inputdata != NIL){
  
    printf(" %d",inputdata->key);
  
    preorder(inputdata->left);
    preorder(inputdata->right);
  
  }
  
}
  
void inorder(struct Node *inputdata){
  
  if(inputdata != NIL){
  
    inorder(inputdata->left);
  
    printf(" %d",inputdata->key);
  
    inorder(inputdata->right);
  
  }
  
}
  
  
struct Node * find(struct Node *inputdata ,int findnumber){
  
  int flag = 0;
  
  while( inputdata != NIL && inputdata->key != findnumber){
  
    if(inputdata->key < findnumber){
  
      inputdata = inputdata->right;
  
    }
  
    else if(inputdata->key > findnumber){
  
      inputdata = inputdata->left;
  
    }
  }
  
  
  
  return inputdata;
  
}

 struct Node *Successor(struct Node *inputdata){

   struct Node *y;
   if(inputdata->right != NIL){

     return miniNode(inputdata->right);

   }

   y = inputdata->parent;

   while(y != NIL && inputdata == y->right){

     inputdata = y;

     y = y->parent;

   }
    
   
   return y;

 }

 void deleteNode(struct Node *deletenode){

   struct Node *x,*y;

   if(deletenode->left == NIL || deletenode->right == NIL){

     y = deletenode;

   }

   else{

     y = Successor(deletenode);

   }

   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 != deletenode){

     deletenode->key = y->key;

   }

 }

struct Node* miniNode(struct Node *inputdata){

  while(inputdata->left != NIL){

    inputdata = inputdata->left;

  }

  return inputdata;

}