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>
#include <cstdio>
#include <vector>
#include <list>
#include <algorithm>
#include <cmath>
#include <stack>
#include <map>
using namespace std;

#define REP(i,n) for(int (i)=0; (i)<(n); (i)++)
#define FOR(i,a,b) for(int (i)=(a); (i)<(b); (i)++)
#define PUSH(n,v) for(int i=0; i<(n); i++) {int j; cin >> j; v.push_back(j);}
#define ALL(v) v.begin(), v.end()

struct Node3 {
    int key;
    Node3 *left;
    Node3 *right;
    Node3 *parent;
public:
    Node3(Node3 *l, Node3 *r, Node3 *p, int k) : left(l), right(r), parent(p), key(k) {};
};

class BinarySearchTree3 {
private:
    Node3 *root;
    void preorder(Node3 node);
    void inorder(Node3 node);
    Node3* inorderItr(Node3* node);
    Node3* getNode(int n);
    Node3* inorderNext(Node3 node);
public:
    void insert(int n);
    BinarySearchTree3() {root = 0;}
    void print() {
        inorder(*root);
        cout << endl;
        preorder(*root);
        cout << endl;
    }
    bool find(int n);
    void erase(int n);
};

void BinarySearchTree3::preorder(Node3 node) {
    cout << " " << node.key;
    if (node.left != 0) {
        preorder(*node.left);
    }
    if (node.right != 0) {
        preorder(*node.right);
    }
}

void BinarySearchTree3::inorder(Node3 node) {
    if (node.left != 0) {
        inorder(*node.left);
    }
    cout << " " << node.key;
    if (node.right != 0) {
        inorder(*node.right);
    }
}

Node3* BinarySearchTree3::inorderItr(Node3* node) {
    if (node->left != 0) return inorderItr(node->left);
    return node;
}

Node3* BinarySearchTree3::inorderNext(Node3 node) {
    if (node.right == 0) return node.parent;
    else return inorderItr(node.right);
}

void BinarySearchTree3::insert(int n) {
    Node3 *z = new Node3(0,0,0,n);
    Node3 *y = 0;
    Node3 *x = root;
    while (x != 0) {
        y = x;
        if (z->key < x->key) {
            x = x->left;
        }else {
            x = x->right;
        }
    }
    z -> parent = y;
    if (y == 0) {
        root = z;
    }else if (z->key < y->key) {
        y->left = z;
    }else {
        y->right = z;
    }
}

bool BinarySearchTree3::find(int n) {
    Node3 *p = root;
    while(p != 0) {
        if (p->key < n) {
            p = p->right;
        }else if (p->key == n) {
            return true;
        }else {
            p = p->left;
        }
    }
    return false;
}

Node3* BinarySearchTree3::getNode(int n) {
    Node3 *p = root;
    while(p != 0) {
        if (p->key < n) {
            p = p->right;
        }else if (p->key == n) {
            return p;
        }else {
            p = p->left;
        }
    }
    return 0;
}

void BinarySearchTree3::erase(int n) {
    Node3 *deleted = getNode(n);
    if (deleted->left == 0 && deleted->right == 0) {
        Node3 *parent = deleted->parent;
        if (parent->key < deleted->key) {
            parent->right = 0;
        }else {
            parent->left = 0;
        }
        deleted = 0;
    }else if (deleted->left == 0) { // only has right child
        Node3 *parent = deleted->parent;
        Node3 *child = deleted->right;
        if (parent->key < deleted->key) {
            parent->right = child;
            child->parent = parent;
        }else {
            parent->left = child;
            child->parent = parent;
        }
        deleted = 0;
    }else if (deleted->right == 0) { // only has left child
        Node3 *parent = deleted->parent;
        Node3 *child = deleted->left;
        if (parent->key < deleted->key) {
            parent->right = child;
            child->parent = parent;
        }else {
            parent->left = child;
            child->parent = parent;
        }
        deleted = 0;
    }else { // has both children
        Node3 *next = inorderNext(*deleted);
        int k = next->key;
        erase(k);
        deleted->key = k;
    }
}

int main() {
    int n;
    cin >> n;
    string s;
    BinarySearchTree3 tree;
    REP(i,n) {
        cin >> s;
        if (s[0] == 'i') {
            int j;
            cin >> j;
            tree.insert(j);
        }else if (s[0] == 'p'){
            tree.print();
        }else if (s[0] == 'f'){
            int j;
            cin >> j;
            if (tree.find((j))) cout << "yes" << endl;
            else cout << "no" << endl;
        }else {
            int j;
            cin >> j;
            tree.erase(j);
        }
    }
    return 0;
}