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>

typedef struct node {
	struct node *left;
	struct node *right;
	struct node *parent;
	int key;
} node_t;

struct node *root = NULL;

int n;

void constructTree(int);
struct node* newNode(int);
void insert(struct node*);

struct node* found(int);
struct node* successor(struct node *);
struct node* minimum(struct node *);
void deleteNode(struct node *);
void transplant(struct node *, struct node *);

void printInorder(struct node*);
void printPreorder(struct node*);

int main()
{
	int i, insertCount = 0;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		char cmd[10];
		scanf("%s", cmd);

		if (cmd[0] == 'p') {
			printInorder(root);
			printf("\n");
			printPreorder(root);
			printf("\n");
			continue;
		}

		int key;
		scanf("%d", &key);
		if (cmd[0] == 'i') {
			(insertCount == 0) ? constructTree(key) : insert(newNode(key));
			insertCount++;
		}
		else if (cmd[0] == 'f') {
			(found(key) != NULL) ? printf("yes\n") : printf("no\n");
		}
		else {
			struct node *deleteKey = found(key);
			if (deleteKey != NULL) deleteNode(deleteKey);
		}
	}
	return 0;
}

void constructTree(int insertValue) {
	root = newNode(insertValue);
}

struct node* newNode(int insertValue) {
	struct node *newNode = (struct node*) malloc(sizeof(struct node));
	newNode->left = NULL;
	newNode->right = NULL;
	newNode->parent = NULL;
	newNode->key = insertValue;

	return(newNode);
}

void insert(struct node *newNode) {
	struct node *y = (struct node*) malloc(sizeof(struct node));
	struct node *x = root;

	while (x != NULL) {
		y = x;
		if (newNode->key < x->key) {
			x = x->left;
		}
		else {
			x = x->right;
		}
	}
	newNode->parent = y;

	if (y == NULL) {
		root = newNode;
	}
	else if (newNode->key < y->key) {
		y->left = newNode;
	}
	else {
		y->right = newNode;
	}
}

struct node* found(int targetKey) {
	struct node* current = (struct node *)malloc(sizeof(struct node));
	current = root;
	while (targetKey != current->key) {
		if (targetKey < current->key) {
			current = current->left;
		}
		else {
			current = current->right;
		}

		if (current == NULL) return NULL;
	}
	return current;
}

struct node* minimum(struct node *fromKey) {
	struct node *min = (struct node *)malloc(sizeof(struct node));
	min = fromKey;
	while (min->left != NULL) min = min->left;
	return min;
}

struct node* successor(struct node *targetKey) {
	if (targetKey->right != NULL) return minimum(targetKey);

	struct node *current = (struct node *)malloc(sizeof(struct node));
	struct node *parent = (struct node *)malloc(sizeof(struct node));
	current = targetKey;
	parent = current->parent;

	while (parent != NULL && current == parent->right) {
		current = parent;
		parent = parent->parent;
	}
	return parent;
}

void deleteNode(struct node *deleteKey) {
	struct node *x = (struct node *)malloc(sizeof(struct node));
	struct node *y = (struct node *)malloc(sizeof(struct node));
	if (deleteKey->left == NULL) {
		transplant(deleteKey, deleteKey->right);
	}
	else if (deleteKey->right == NULL) {
		transplant(deleteKey, deleteKey->left);
	}
	else {
		y = minimum(deleteKey->right);
		if (y->parent != deleteKey) {
			transplant(y, y->right);
			y->right = deleteKey->right;
			y->right->parent = y;
		}
		transplant(deleteKey, y);
		y->left = deleteKey->left;
		y->left->parent = y;
	}
}

void transplant(struct node* first, struct node* second) {
	if (first->parent == NULL) root = second;
	else if (first == first->parent->left) first->parent->left = second;
	else first->parent->right = second;

	if (second != NULL) second->parent = first->parent;
}


void printInorder(struct node *x) {
	if (x != NULL) {
		printInorder(x->left);
		printf(" %d", x->key);
		printInorder(x->right);
	}
}

void printPreorder(struct node *x) {
	if (x != NULL) {
		printf(" %d", x->key);
		printPreorder(x->left);
		printPreorder(x->right);
	}
}