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>
#define nil NULL 
struct node{
  struct node *left;
  struct node *right;
  struct node *pmid;
  int key;
};
 
typedef struct node * Node;
 
Node root;
 
void DefPre(Node t){

  printf(" %d",t->key);
  if(t != nil){
    if(t->left != nil) DefPre(t->left);
    if(t->right != nil) DefPre(t->right);
  }
}
 
void DefIn(Node t){
   
  if(t != nil){
    if(t->left != nil){
      DefIn(t->left);
      }

    printf(" %d",t->key);
     
    if(t->right != nil){
      DefIn(t->right);
      }

  }

}
 
void Defin(int numk){
  Node y = nil;
  Node x = root;
  Node numz;
 
  numz = malloc(sizeof(struct node));
  numz->key = numk;
  numz->left = nil;
  numz->right = nil;
   
  while(x != nil){
    y = x;
 
    if(numz->key<x->key) x = x->left;
    else x = x->right;
  }
  numz->pmid = y;
   
  if(y == nil) root = numz;
  else if(numz->key<y->key) y->left = numz;
  else y->right = numz;
}
 
Node Search(Node numt,int numk){
  if(numt == nil || numk == numt->key) return numt;

  if(numk<numt->key) return Search(numt->left,numk);

  else return Search(numt->right,numk);
}
 
Node Minimum(Node numt){
  while(numt->left != nil){

    numt = numt->left;

  }
  return numt;
}
 
Node Successor(Node numt){
  if(numt->right != nil)return Minimum(numt->right);
  Node y = numt->pmid;
  while(y != nil && numt == y->right){
    numt = y;
    y = y->pmid;
  }
  return y;
}
 
void Delete(Node numz){

  Node numy;

  Node numx;
 
  if(numz->left == nil || numz->right == nil) 
    numy = numz;
  else numy = Successor(numz);
 
  if(numy->left!=nil) 
    numx = numy->left;
  else numx = numy->right;
 
  if(numx != nil)
    numx->pmid = numy->pmid;
 
  if(numy->pmid == nil)
    root = numx;
  else if(numy == numy->pmid->left)
    numy->pmid->left = numx;
  else 
    numy->pmid->right = numx;
 
  if(numy != numz)
    numz->key = numy->key;
}
 
 
int main(){
  int n, j, x;
  char array[20];
   
  scanf("%d",&n);
 
  for (j = 0; j < n; j++ ){
    scanf("%s",array);
 
    if(array[0]=='i'){

      scanf("%d",&x);

      Defin(x);
    } 
    else if(array[0]=='p'){
      DefIn(root);
      printf("\n");
       
      DefPre(root);
      printf("\n");
    }
    else if(array[0]=='f'){

      scanf("%d",&x);

      Node s=Search(root,x);

      if (s!= nil ) printf("yes\n");
      else printf("no\n");
    }
    else if(array[0]=='d'){

      scanf("%d",&x);

      Delete(Search(root, x));
    }
  }
  return 0;
}