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>          // printf(), scanf()
#define MAX_N 500000

typedef struct node_tbl
{
	int key;
	int parent;
	int left;
	int right;
} node;

const int nil = -1;
node t[MAX_N + 1];
int root;
int room;
int ix;

int
tree_minimum(int u)
{
	while (t[u].left != nil)
		u = t[u].left;

	return u;
}

int
find(int u, int k)
{
	while (u != nil && k != t[u].key)
	{
		if (k < t[u].key)
			u = t[u].left;
		else
			u = t[u].right;
	}

	return u;
}

int
tree_successor(int u)
{
	if (t[u].right != nil)
		return tree_minimum(t[u].right);

	int y = t[u].parent;
	while (y != nil && u == t[y].right)
	{
		u = y;
		y = t[y].parent;
	}

	return y;
}

void
delete(int z)
{
	int y; /* ????????????????±? */
	int x; /* y?????? */

	/* ??????????????????????±??????? */
	if (t[z].left == nil || t[z].right == nil)
		y = z;
	else
		y = tree_successor(z);

	/* y??????x????±??????? */
	if (t[y].left != nil)
		x = t[y].left;
	else
		x = t[y].right;

	if (x != nil)
		t[x].parent = t[y].parent;

	if (t[y].parent == nil)
		root = x;
	else
	{
		if (y == t[t[y].parent].left)
			t[t[y].parent].left = x;
		else
			t[t[y].parent].right = x;
	}

	if (y != z)
		t[z].key = t[y].key;

	t[y].right = room;
	room = y;
}

void
insert(int k)
{
	int z;

	int y = nil;
	int x = root;
	if (room == nil)
		z = ix++;
	else
	{
		z = room;
		room = t[room].right;
	}

	t[z].key = k;
	t[z].left = nil;
	t[z].right = nil;

	while (x != nil)
	{
		y = x;
		if (t[z].key < t[x].key)
			x = t[x].left;
		else
			x = t[x].right;
	}

	t[z].parent = y;
	if (y == nil)
		root = z;
	else
	{
		if (t[z].key < t[y].key)
			t[y].left = z;
		else
			t[y].right = z;
	}
}

void
inorder(int u)
{
	if (u == nil)
		return;

	inorder(t[u].left);
	printf(" %d", t[u].key);
	inorder(t[u].right);
}

void
preorder(int u)
{
	if (u == nil)
		return;

	printf(" %d", t[u].key);
	preorder(t[u].left);
	preorder(t[u].right);
}

int
main(int argc, char** argv)
{
	char command[8];
	int n;
	int x;
	int i;

	root = nil;
	room = -1;
	ix = 0;
	scanf("%d", &n);
	for (i = 0; i < n; ++i)
	{
		scanf("%s", command);
		switch (command[0])
		{
		case 'd':
			scanf("%d", &x);
			delete(find(root, x));
			break;

		case 'f':
			scanf("%d", &x);
			printf("%s\n", find(root, x) != nil ? "yes" : "no");
			break;

		case 'i':
			scanf("%d", &x);
			insert(x);
			break;

		case 'p':
		default:
			inorder(root);
			printf("\n");

			preorder(root);
			printf("\n");
			break;
		}
	}

	return 0;
}