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 <math.h>
#include <string.h>
#include <stdlib.h>
#define N 200001
#define MAX 1000

struct node_t {
	int key;
	struct node_t *pare;
	struct node_t *left;
	struct node_t *right;
};
typedef struct node_t Node;

Node *tree_insert(Node *top, Node *z) {
	Node *y, *x;
	x = top;
	y = NULL;
	while (x != NULL) {
		y = x;
		if (z->key < x->key) {	x = x->left;}
		else {	x = x->right;}
	}
	z->pare = y;
	if (y == NULL) {	top = z;}
	else if (z->key < y->key) {y->left = z;	}
	else {y->right = z;}
	return top;
}

Node *tree_find(Node *node, int key) {
	if (node == NULL){return NULL;}
	if (node->key == key){return node;}
	if (key < node->key){return tree_find(node->left, key);}
	return tree_find(node->right, key);
}

Node *tree_minimum(Node *x) {
	while (x->left != NULL) {x = x->left;}
	return x;
}

Node *tree_successor(Node *x) {
	Node *y;
	if (x->right != NULL) {return tree_minimum(x->right);}
	y = x->pare;
	while (y != NULL && x == y->right) {
		x = y;
		y = y->pare;
	}
	return y;
}

Node *tree_delete(Node *top, Node *z) {
	Node *y, *x;
	if (z->left == NULL || z->right == NULL) {y = z;}
	else {y = tree_successor(z);}
	if (z->left != NULL) {x = y->left;}
	else {x = y->right;}
	if (x != NULL) {x->pare = y->pare;}
	if (y->pare == NULL) {top = x;}
	else if (y == y->pare->left) {y->pare->left = x;}
	else {y->pare->right = x;}
	if (y != z) {z->key = y->key;}
	return top;
}

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

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

int main(void) {
	char c[20];
	int i,n, key;

	Node *top = NULL, *p;
	scanf("%d ", &n);
	for (i = 0; i < n; i++) {
		scanf("%s %d ", c, &key);
		if (c[0] == 'i') {
			p = malloc(sizeof(Node));
			p->key = key;
			p->pare = p->left = p->right = NULL;
			top = tree_insert(top, p);
		}
		else if (c[0] == 'f') {
			puts(tree_find(top, key) != NULL ? "yes" : "no");
		}
		else if (c[0] == 'd') {
			p = tree_find(top, key);
			if (p != NULL) {top = tree_delete(top, p);}
		}
		else {
			inorder_walk(top);
			putchar('\n');
			preorder_walk(top);
			putchar('\n');
		}
	}
	return 0;
}