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 MAX 500001

typedef struct Node {
    long key;
    struct Node *p, *l, *r;
} Node;

Node *root, *NIL;


void insert(long k) {
    Node *y = NIL;
    Node *x = root;
    Node *z;
    
    z = (Node *)malloc(sizeof(Node));
    z->key = k;
    z->l = z->r = NIL;
    
    while (x != NIL) {
	y = x;
	if (z->key < x->key) x = x->l;
	else x = x->r;
    }
    z->p = y;
    
    if (y == NIL) root = z;
    else if (z->key < y->key) y->l = z;
    else y->r = z;
}

Node * find(Node *x, long k) {
    while (x != NIL && k != x->key) {
	if (k < x->key) x = x->l;
	else x = x->r;
    }
    return x;
}

void inorder(Node *u) {
    if (u == NIL) return;
    inorder(u->l);
    printf(" %d", u->key);
    inorder(u->r);
}

void preorder(Node *u) {
    if (u == NIL) return;
    printf(" %d", u->key);
    preorder(u->l);
    preorder(u->r);
}

void print() {
    inorder(root);
    printf("\n");
    preorder(root);
    printf("\n");
}

Node* getMinimum(Node *x) {
    while (x->l != NIL) x = x->l;
    return x;
}

Node* getSuccessor(Node *x) {
    if (x->r != NIL) return getMinimum(x->r);
    
    Node *y;
    y = x->p;
    while ( y!=NIL && x == y->r) {
	x = y;
	y = y->p;
    }
    return y;
}
void deleteNode(Node *z) {
    Node *y;
    Node *x;
    if (z->l == NIL || z->r == NIL) y = z;
    else y = getSuccessor(z);

    if (y->l != NIL) x = y->l;
    else x = y->r;
    
    if (x != NIL) x->p = y->p;
    
    if (y->p == NIL) root = x;
    else if (y == y->p->l) y->p->l = x;
    else y->p->r = x;

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


int main() {
    long n, i, x;
    char st[20];
    scanf("%ld", &n);
    for (i = 0; i < n; i++) {
 	scanf("%s", st);
	scanf("%ld", &x);
	Node *u = find(root, x);
	if (st[0] == 'f') {
	    if (u != NIL) printf("yes\n");
	    else printf("no\n");
	}
	else if (st[0] == 'i') insert(x);
	else if(st[0] == 'd') deleteNode(find(root, x));
	else if (st[0] == 'p') print();
    }
    return 0;
}