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>
#define NIL NULL

struct node {
	int key;
	struct node *right, *left, *parent;
};

typedef struct node Node;

Node *root;

void insert(int);
void print_i(Node *);
void print_p(Node *);
Node *find(int);
void delete (Node *);
Node *Minimum(Node *);
Node *getSuccessor(Node *);

int main() {
	int i;
	int n, k;
	char com[32];
	Node *u;

	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%s", com);

		if (com[0] == 'i') {
			scanf("%d", &k);
			insert(k);
		} else if (com[0] == 'p') {
			print_i(root);
			printf("\n");
			print_p(root);
			printf("\n");
		} else if (com[0] == 'd') {
			scanf("%d", &k);
			delete (find(k));
		} else {
			scanf("%d", &k);
			if (find(k) != NIL) {
				printf("yes\n");
			} else {
				printf("no\n");
			}
		}
	}
}

void insert(int k) {
	Node *y = NIL;
	Node *x = root;
	Node *z;

	z = (Node *)malloc(sizeof(Node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;

	//場所決め
	while (x != NIL) {
		y = x;
		if (z->key < x->key) {
			x = x->left;
		} else {
			x = x->right;
		}
	}
	z->parent = y;
	if (y == NIL) {
		root = z;
	} else {
		if (z->key < y->key) {
			y->left = z;
		} else {
			y->right = z;
		}
	}
}

void print_i(Node *s) {
	if (s == NIL) return;
	print_i(s->left);
	printf(" %d", s->key);
	print_i(s->right);
}
void print_p(Node *s) {
	if (s == NIL) return;
	printf(" %d", s->key);
	print_p(s->left);
	print_p(s->right);
}

Node *find(int k) {
	Node *s = root;
	while (s != NIL && k != s->key) {
		if (k < s->key) {
			s = s->left;
		} else {
			s = s->right;
		}
	}
	return s;
}

void delete (Node *z) {
	Node *y;  //削除対象
	Node *x;  // yの子

	//削除する節点を決める
	if (z->left == NIL || z->right == NIL) {
		y = z;
	} else {
		y = getSuccessor(z);
	}

	// yの子を決める
	if (y->left != NIL) {
		x = y->left;
	} else {
		x = y->right;
	}

	if (x != NIL) {
		x->parent = y->parent;
	}

	if (y->parent == NIL) {
		root = x;
	} else {
		if (y == y->parent->left) {
			y->parent->left = x;
		} else {
			y->parent->right = x;
		}
	}

	if (y != z) {
		z->key = y->key;
	}

	free(y);
}

Node *getSuccessor(Node *x) {
	if (x->right != NIL) {
		return Minimum(x->right);
	}
	Node *y = x->parent;
	while (y != NIL && x == y->right) {
		x = y;
		y = y->parent;
	}
	return y;
}

Node *Minimum(Node *s) {
	while (s->left != NIL) {
		s = s->left;
	}
	return s;
}