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 dbg(fmt,...) fprintf(stderr,fmt,__VA_ARGS__)
#define dpri(x) dbg(#x ": %d\n", x)
#define dprs(x) dbg(#x ": %s\n", x)
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
typedef long long ll;
const int MYINF = 1e9+7;
typedef int bool;
const bool true = 1;
const bool false = 0;

typedef struct node_st {
	int key;
	struct node_st *left, *right;
} node_t;

node_t *root;

node_t *node_new(int x) {
	node_t *new = malloc(sizeof(node_t));
	if (new == NULL) exit(1);
	new->key = x;
	new->left = new->right = NULL;
	return new;
}

node_t *insert(node_t *nd, int x) {
	if (!nd) return node_new(x);
	if (x < nd->key) nd->left = insert(nd->left, x);
	else if (nd->key < x) nd->right = insert(nd->right, x);
	return nd;
}

node_t *find(node_t *nd, int x) {
	if (!nd) return NULL;
	if (x < nd->key) return find(nd->left, x);
	else if (nd->key < x) return find(nd->right, x);
	return nd;
}

node_t *delete(node_t *nd, int x) {
	if (!nd) return NULL;
	if (x < nd->key) {
		nd->left = delete(nd->left, x);
		return nd;
	} else if (nd->key < x) {
		nd->right = delete(nd->right, x);
		return nd;
	}

	node_t *res;
	if (nd->left && nd->right) {
		node_t *n = nd->right;
		if (!n->left) {
			res = n;
			res->left = nd->left;
		} else {
			while (n->left->left) n = n->left;
			res = n->left;
			n->left = res->right;
			res->left = nd->left;
			res->right = nd->right;
		}
	} else if (nd->left) {
		res = nd->left;
	} else if (nd->right) {
		res = nd->right;
	} else {
		res = NULL;
	}
	free(nd);
	return res;
}

enum {
	PREORDER,
	INORDER,
};

void print_tree(node_t *nd, int order) {
	if (!nd) return;
	if (order == PREORDER) printf(" %d", nd->key);
	print_tree(nd->left, order);
	if (order == INORDER) printf(" %d", nd->key);
	print_tree(nd->right, order);
}

int main(int argc, char **argv)
{
	int i, n, x;
	char cmd[128];

	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%s", cmd);
		if (!strcmp("insert", cmd)) {
			scanf("%d", &x);
			root = insert(root, x);
		} else if (!strcmp("find", cmd)) {
			scanf("%d", &x);
			printf("%s\n", find(root, x) ? "yes" : "no");
		} else if (!strcmp("delete", cmd)) {
			scanf("%d", &x);
			root = delete(root, x);
		} else if (!strcmp("print", cmd)) {
			print_tree(root, INORDER);
			puts("");
			print_tree(root, PREORDER);
			puts("");
		}
	}

	return 0;
}