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>

typedef struct node *t;

struct node{
	int key;
	t left,right;
};

t insert(t head,t z){
	t y=NULL;
	t x=head;
	
	while(x!=NULL)
    {
		y=x;
		if(z->key < x->key)x=x->left;
		else x=x->right;
	}
	
	if(y==NULL)head=z;
	else if(z->key < y->key)y->left=z;
	else y->right=z;
	return head;
}

void preorder(t u){
	if(u==NULL)return;
	printf(" %d",u->key);
	preorder(u->left);
	preorder(u->right);
}

void inorder(t u){
	if(u==NULL)return;
	inorder(u->left);
	printf(" %d",u->key);
	inorder(u->right);
}

int find(t u,int key){
	if(u==NULL)return 0;
	if(u->key==key)return 1;
	if(u->key>key)return find(u->left,key);
	return find(u->right,key);
}

int search(t u){
	if(u->left==NULL)return u->key;
	return search(u->left);
}

t delete(t u,int key){
	if(u==NULL)return NULL;
	
    if(u->key==key){
		if(u->left==NULL && u->right==NULL)return NULL;
		else if(u->right==NULL)
        {
			return u->left;
		}
        else if(u->left==NULL){
			return u->right;
		}
        else{
			u->key=search(u->right);
			u->right=delete(u->right,u->key);
		}
	}
   
    else if(u->key >key){
		u->left=delete(u->left,key);
	}
   
    else{
		u->right=delete(u->right,key);
	}
	return u;
}

int main(void){
	int m,i,key,n,r;
	char cmd[10];
	t head=NULL,z;

	scanf("%d",&m);
	
    for(i=0;i<m;i++){
		
        scanf("%s",cmd);
		
        if(!strcmp(cmd,"insert")){
			scanf("%d",&key);
			z = malloc(sizeof(*z));
			z->key=key;z->left=NULL;z->right=NULL;
			head=insert(head,z);
		}
       
        else if(!strcmp(cmd,"print")){
			inorder(head);
			printf("\n");
			preorder(head);
			printf("\n");
		}
       
        else if(!strcmp(cmd,"find")){
			scanf("%d",&key);
			if(find(head,key)!=0)printf("yes\n");
			else  printf("no\n");
		}
        
        else if(!strcmp(cmd,"delete")){
			scanf("%d",&key);
			head=delete(head,key);
		}
	}
	return 0;
}