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++11 (judge verdict: Accepted)

#include <cstdio>
#include <cstdlib>
#include <string>
#include <iostream>
using namespace std;

struct BINNODE {
	int key;
	BINNODE *parent;
	BINNODE *left;
	BINNODE *right;

	BINNODE (int k) {
		key=k;
		parent=nullptr;
		left=nullptr;
		right=nullptr;
	}
};

void preorderwalk(BINNODE* root) {
	if(root==nullptr) return;
	printf(" %d",root->key);
	preorderwalk(root->left);
	preorderwalk(root->right);
	return;
}

void inorderwalk(BINNODE* root) {
	if(root==nullptr) return;
	inorderwalk(root->left);
	printf(" %d",root->key);
	inorderwalk(root->right);
	return;
}

BINNODE* findnode(int v, BINNODE* root) {
	if(root == nullptr) return nullptr;
	if(root->key ==v ) return root;
	return (v< root->key)?findnode(v,root->left) : findnode(v,root->right);
}

int main() {
	int m,v;
	int i;
	string cmd;
	BINNODE* root=nullptr;
	BINNODE* x;
	BINNODE* y;
	BINNODE* z;
	cin >> m;
	for(i=0; i<m; ++i) {
		cin >> cmd;
		if(cmd=="delete") {
			cin >> v;
			z=findnode(v,root);
			while(1) {
				if(z->left==nullptr && z->right==nullptr) {
					if(z->parent==nullptr) {
						root=nullptr;
						delete z;
						break;
					} else if(z->parent->key > z->key) {
						z->parent->left=nullptr;
						delete z;
						break;
					} else if(z->parent->key < z->key) {
						z->parent->right=nullptr;
						delete z;
						break;
					}
				} else if(z->right==nullptr) {
					if(z->parent==nullptr) {
						root=z->left;
						delete z;
						break;
					} else if(z->key < z->parent->key) {
						z->parent->left=z->left;
						delete z;
						break;
					} else {
						z->parent->right=z->left;
						delete z;
						break;
					}
				} else if(z->left==nullptr) {
					if(z->parent==nullptr) {
						root=z->right;
						z->right->parent=nullptr;
						delete z;
						break;
					} else if(z->key < z->parent->key) {
						z->parent->left=z->right;
						z->right->parent=z->parent;
						delete z;
						break;
					} else {
						z->parent->right=z->right;
						z->right->parent=z->parent;
						delete z;
						break;
					}
				} else {
					y=z->right;
					while(y->left!=nullptr || y->right!=nullptr) {
						if(y->left!=nullptr) {
							y=y->left;
						} else {
							y=y->right;
						}
					}
					z->key=y->key;
					if(y->parent->left==y) {
						y->parent->left=nullptr;
					} else {
						y->parent->right=nullptr;
					}
					free(y);
					break;
				}
			}
		} else if(cmd=="find") {
			cin >> v;
			printf(findnode(v,root)!=nullptr ? "yes\n" : "no\n");
		} else if(cmd=="insert") {
			cin >> v;
			z=new BINNODE(v);
			y=nullptr;
			x=root;
			while(x!=nullptr) {
				y=x;
				if (z->key < x->key) {
					x=x->left;
				} else {
					x=x->right;
				}
			}
			z->parent = y;

			if(y==nullptr) {
				root=z;
			} else if(z->key < y->key) {
				y->left = z;
			} else {
				y->right = z;
			}
		} else {
			inorderwalk(root);
			printf("\n");
			preorderwalk(root);
			printf("\n");
		}
	}
	return 0;
}