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>
#define mymalloc(p,n) {p = malloc((n)*sizeof(*p));if ((p)==NULL) {printf("not enough memory?\n"); exit(1);};}

typedef struct node{
	struct node *parent;
	struct node *right;
	struct node *left;
	long key;
}node;

typedef struct{
	struct node *root;
}tree;

node *createNode(long n){
	node *node;
	mymalloc(node,1);
	node->parent=NULL;
	node->right=NULL;
	node->left=NULL;
	node->key=n;
	return node;
}

void insert(tree *T, node *z){
	node *x,*y;
	y=NULL;
	x=T->root;
	while(x!=NULL){
		y=x;
		if(z->key<x->key){
			x=x->left;
		}else{
			x=x->right;
		}
	}
	z->parent=y;
	if(y==NULL){
		T->root=z;
	}else{
	if(z->key<y->key){
		y->left=z;
	}else{
		y->right=z;
	}}
}

node *find(tree *T,long key){
	node *x;
	x=T->root;
	while(x!=NULL){
		if(key==x->key){
			return x;
		}
		if(key<x->key){
			x=x->left;
		}else{
			x=x->right;
		}
	}
	return NULL;
}

node *findNext(node *x){
	node *y;
	y=x->right;
	while(y->left!=NULL){
		y=y->left;
	}
	return y;
}

void delete(node *x){
	int dim;
	node *y;
	y=NULL;dim=0;
	if(x->left!=NULL){
		y=x->left;
		dim++;
	}
	if(x->right!=NULL){
		y=x->right;
		dim++;
	}
	if(dim==2){
		y=findNext(x);
		x->key=y->key;
		delete(y);
	}else{
		if(x->parent!=NULL){
			if(x==x->parent->left){
				x->parent->left=y;
			}else{
				x->parent->right=y;
			}
		}
		if(dim==1){
			y->parent=x->parent;
		}
		free(x);
	}
}
	
void preorder(node *root){
	printf(" %ld",root->key);
	if(root->left!=NULL){
		preorder(root->left);
	}
	if(root->right!=NULL){
		preorder(root->right);
	}
}

void inorder(node *root){
	if(root->left!=NULL){
		inorder(root->left);
	}
	printf(" %ld",root->key);
	if(root->right!=NULL){
		inorder(root->right);
	}
}


void freeNode(node *root){
	if(root->left!=NULL){
		freeNode(root->left);
	}
	if(root->right!=NULL){
		freeNode(root->right);
	}
	free(root);
}

void printTree(node *root){
	inorder(root);
	printf("\n");
	preorder(root);
	printf("\n");
}

main(){
	long i,n,m;
	tree *T;
	node *obj;
	char s[10];
	mymalloc(T,1);
	T->root=NULL;
	scanf("%ld",&n);
	for(i=0;i<n;i++){
		scanf(" %s",s);
		if(strcmp(s,"print")==0){
			printTree(T->root);
		}else{
			scanf(" %ld",&m);
			if(strcmp(s,"insert")==0){
				obj=createNode(m);
				insert(T,obj);
			}else{
			if(strcmp(s,"find")==0){
				if(find(T,m)!=NULL){puts("yes");}
				else{puts("no");}
			}else{
			if(strcmp(s,"delete")==0){
				delete(find(T,m));
			}}}}
	}
	freeNode(T->root);
	free(T);
	return 0;
}