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{
  int key;
  struct node *p;
  struct node *l;
  struct node *r;
};

typedef struct node *Node;

Node ro;

void delete1(Node k){
	Node a=k->p;
  if(k->r==NIL && k->l==NIL){
  	if(a->l==k)a->l = NIL;
  	else a->r = NIL;
	free(k);
  }else if(k->r==NIL){
  	if(a->l==k){
    	a->l = k->l;
    	k->l->p=a;
  	}else{
		a->r = k->l;
    	k->l->p=a;
	}
	k=NIL;
	free(k);
  }else if(k->l==NIL){
   	if(a->l==k){
    	a->l = k->r;
    	k->r->p=a;
  	}else{
		a->r = k->r;
    	k->r->p=a;
	}
	free(k);
  }else{
   if(k->r!=NIL){
     	a=k->r; 
	  	while(a->l!=NIL)a=a->l;
		k->key=a->key;
		delete1(a);
	  }else{
	  	a=k->p; 
	  	while(a!=NIL && k==a->r){
			k=a;
			a=a->p;
		}
		k->key=a->key;
		delete1(a);
	  }
  }
}

void delete(int k){
  Node x = ro;

  while(x != NIL && x->key!=k){
    if(k < x->key){
      x = x->l;
    }else{
      x = x->r;
    }
  }
  
  if(x== NIL){
  }else{
    delete1(x);
  }
}
Node find(int k,Node node){
  if(node == NIL){
    return node;
  }

  if(node->key == k){
    return node;
  }
  if(node->key > k){
    return find(k , node->l);
  }else{
    return find(k , node->r);
  }
}
void insert(int k){
  Node y = NIL;
  Node x = ro;
  Node z;
  
  z = malloc(sizeof(struct node));
  z->key = k;
  z->l = NIL;
  z->r = NIL;

  while(x != NIL){
    y = x;
    if(z->key < x->key){
      x = x->l;
    }else{
      x = x->r;
    }
  }
  
  z->p = y;
  if(y == NIL){
    ro = z;
  }else{
  	if(z->key < y->key){
    	y->l = z;
  	}else{
    	y->r = z;
  	}
  }
}

void inorder(Node u){
  if(u == NIL)return;
  inorder(u->l);
  printf(" %d",u->key);
  inorder(u->r);
}

void preorder(Node u){
  if(u == NIL)return;
  printf(" %d",u->key);
  preorder(u->l);
  preorder(u->r);
}

int main(){
  int n,i,j,z,k;
  char s[10];
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%s",s);
    if(s[0] == 'i'){
      scanf("%d",&z);
      insert(z);
    }else if(s[0]=='f'){
      scanf("%d",&k);
      if(find(k,ro)!=NIL){
		printf("yes\n");
      }else{
		printf("no\n");
      }
    }else if(s[0]=='d'){
      scanf("%d",&k);
      delete(k);
    }else if(s[0]=='p'){
      inorder(ro);
  	  printf("\n");
      preorder(ro);
      printf("\n");
    }
  }
  free(ro);
  return 0;
}