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++14 (judge verdict: Accepted)

#include <bits/stdc++.h> 

using namespace std;

typedef long long ll;

struct Node {
    int key;
    Node *p, *l, *r;
};

Node *root, *NIL;

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

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

Node* treeSuccessor(Node* x) {
    if (x->r != NIL)
        return treeMinimum(x->r);
    Node *y = x->p;
    while (y != NIL && x == y->r) {
        x = y;
        y = y->p;
    }
    return y;
}

void treeDelete(Node *z) {
    Node *y; // delete node
    Node *x; // y's child

    if (z->l == NIL || z->r == NIL) y = z;
    else y = treeSuccessor(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;

    free(y);
}


void insert(int k) {
    Node *y = NIL, *x = root, *z;
    z = (Node *)malloc(sizeof(Node));
    z->key = k;
    z->l = NIL;
    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;
        }
    }
}

void inorder(Node* u) {
    if (u == NIL) return;
    inorder(u->l);
    cout << " " << u->key;
    inorder(u->r);
}

void preorder(Node* u) {
    if (u == NIL) return;
    cout << " " << u->key;
    preorder(u->l);
    preorder(u->r);
}

int main() {
    int n; cin >> n;
    
    for (int i = 0; i < n; i++) {
        string com; cin >> com;

        if (com[0] == 'f') {
            int x; cin >> x;
            Node* t = find(root, x);
            if (t != NIL) cout << "yes" << endl;
            else cout << "no" << endl;
        } else if (com == "insert") {
            int x; cin >> x;
            insert(x);
        } else if (com == "print") {
            inorder(root);
            cout << endl;
            preorder(root);
            cout << endl;
        } else if (com == "delete") {
            int x; cin >> x;
            treeDelete(find(root, x));
        }
    }
}