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)

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<stdlib.h>

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

Node root;

Node treeSearch(Node u, int k){//kに一致するノードを探す
	if (u == NIL){return NIL;}//なかた
	if (u->key == k){ return u; }//あた
	else if (u->key > k){
		return treeSearch(u->left, k);
	}
	else{
		return treeSearch(u->right, k);
	}
}

void treeDelete(Node z){
	Node tmp;

	if (z->left == NIL && z->right == NIL){//子なし
		if (z->parent->left == z){//zが親の左側に属していたら
			z->parent->left = NIL;
		}
		else{
			z->parent->right = NIL;
		}
		free(z);
	}
	else if (z->left != NIL && z->right != NIL){//子2人
		tmp = z->right;//右側から最少を探す
		while (tmp->left != NIL){
			tmp = tmp->left;
		}
		z->key = tmp->key;
		treeDelete(tmp);		
	}
	else{//子1人
		if (z->left!=NIL){//左に子がいたら
			if (z->parent->left == z){//zが親の左側にいたら
				z->parent->left = z->left;
				z->left->parent = z->parent;
			}
			else{//zが親の右側にいたら
				z->parent->right = z->left;
				z->left->parent = z->parent;
			}
		}
		else{//右に子がいたら
			if (z->parent->left == z){//zが親の左側にいたら
				z->parent->left = z->right;
				z->right->parent = z->parent;
				free(z);
			}
			else{//zが親の右側にいたら
				z->parent->right = z->right;
				z->right->parent = z->parent;
			}
		}
	}
}

Node sss(int k, Node x){
	if (x == NIL){ return x; }//root
	if (k < x->key){
		if (x->left != NIL){
			return sss(k, x->left);
		}
		else{
			return x;
		}
	}
	else{
		if (x->right != NIL){
			return sss(k, x->right);
		}
		else{
			return x;
		}
	}
}

void insert(int k){
	Node y = sss(k,root);//入れるべき場所の親探し
	Node z;

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

	if (y == NIL){ root=z; }
	else if (y->key < k){//kが親キーより大きい
		y->right = z;
	}
	else{
		y->left = 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];
	scanf("%d", &n);

	for (i = 0; i < n; i++){
		scanf("%s", com);
		if (com[0] == 'f'){
			scanf("%d", &x);
			Node 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;
}