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<iostream>
using namespace std;

struct Node {
    int key;
    Node* parent;
    Node* left;
    Node* right;
    Node(int key_in){
        key    = key_in;
        parent = NULL;
        left   = NULL;
        right  = NULL;
    }
};

class Tree {
    Node* root;
    void inorder(Node* n){
        if (n == NULL) return;
        inorder(n->left);
        cout << " " << n->key;
        inorder(n->right);
    }
    void preorder(Node* n){
        if (n == NULL) return;
        cout << " " << n->key;
        preorder(n->left);
        preorder(n->right);
    }
public:
    Tree(){
        root = NULL;
    }
    void insert(int key){
        Node* z = new Node(key);
        if (root == NULL) {
            root = z;
            return;
        }
        Node* x = root;
        while (1) {
            Node** child_p;
            if (key < x->key) {
                child_p = &(x->left);
            } else {
                child_p = &(x->right);
            }
            if (*child_p == NULL) {
                *child_p = z;
                z->parent = x;
                return;
            }
            x = *child_p;
        }
    }
    void print(){
        inorder(root);
        cout << endl;
        preorder(root);
        cout << endl;
    }
    Node* find(int key){
        for (Node* x = root; x != NULL;) {
            if (key == x->key) return x;
            if (key < x->key) {
                x = x->left;
            } else {
                x = x->right;
            }
        }
        return NULL;
    }

    void delete_1_child(Node* x){
        Node* child;
        if (x->left == NULL && x->right == NULL) {
            child = NULL;
        } else if (x->left != NULL) {
            child = x->left;
        } else {
            child = x->right;
        }
        if (x == root) {
            root = child;
            delete x;
            return;
        }
        Node* p = x->parent;
        if (x == p->left) {
            p->left = child;
        } else {
            p->right = child;
        }
        if (child != NULL) {
            child->parent = x->parent;
        }
        delete x;
    }

    Node* next_node(Node* x){
        if (x->left == NULL) return x;
        return next_node(x->left);
    }

    void delete_(int key){
        Node* x = find(key);
        if (x == NULL) return;
        if (x->left == NULL || x->right == NULL) {
            delete_1_child(x);
            return;
        }
        Node* y = next_node(x->right);
        x->key = y->key;
        if (y->left == NULL || y->right == NULL) {
            delete_1_child(y);
            return;
        }

    }
};


int main(){
    int m;
    cin >> m;
    Tree T;
    for (int i = 0; i < m; i++) {
        string str;
        cin >> str;
        if (str == "print") {
            T.print();
            continue;
        }
        int num;
        cin >> num;
        if (str == "insert") {
            T.insert(num);
            continue;
        }
        if (str == "find") {
            if (T.find(num) == NULL) {
                cout << "no" << endl;
            } else {
                cout << "yes" << endl;
            }
            continue;
        }
        if (str == "delete") {
            T.delete_(num);
        }
    }
    return 0;
}