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>

struct node{
	struct node *right;
	struct node *left;
	struct node *parent;
	int key;
};
typedef struct node * Node;
#define NIL NULL

Node root;

Node treeMinimum(Node x){

	while(x->left != NIL)
		x = x->left;
	return x;
}

Node treeSearch(Node u, int k){
	if(u == NIL || u->key == k)
		return u;
	else if(u->key > k)
		return treeSearch(u->left, k);
	else if(u->key < k)
		return treeSearch(u->right, k);
}

Node treeSuccessor(Node x){
	Node y;

	if(x->right != NIL)
		return treeMinimum(x->right);
	y = x->parent;
	while(y != NIL && x == y->right){
		x = y;
		y = y->parent;
	}
	return y;
}

void treeDelete(Node z){
	Node y; // node to be deleted
	Node x; // child of y

	if(z->left == NIL || z->right == NIL)
		y = z;
	else
		y = treeSuccessor(z);
	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 != z)
		z->key = y->key;



}

void insert(int k){
	Node y = NIL;
	Node x = root;
	Node z;

	z = (Node)malloc(sizeof(struct node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;

	while(x != NIL){
		y = x;
		if(z->key < x->key)
			x = x->left;
		else
			x = x->right;
	}
	z->parent = y;
	if(y == NIL)
		root = z;
	else if(z->key < y->key)
		y->left = z;
	else
		y->right = z;


}

void inorder(Node u){
	if(u->left != NIL)
		inorder(u->left);
	printf(" %d",u->key);
	if(u->right != NIL)
		inorder(u->right);
}
void preorder(Node u){
	printf(" %d",u->key);
	if(u->left != NIL)
		preorder(u->left);
	if(u->right != NIL)
		preorder(u->right);
}


int main(){
	int n, i, x;
	char com[20];
	Node t;
	scanf("%d", &n);

	for ( i = 0; i < n; i++ ){
		scanf("%s", com);
		if ( com[0] == 'f' ){
			scanf("%d", &x);
			t = treeSearch(root, x);
			if ( t != NIL ) printf("yes\n");
			else printf("no\n");
		} else if ( com[0] == 'i' ){
			scanf("%d", &x);
			insert(x);
		} else if ( com[0] == 'p' ){
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		} else if ( com[0] == 'd' ){
			scanf("%d", &x);
			treeDelete(treeSearch(root, x));
		}
	}

	return 0;
}