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 Rust (judge verdict: Accepted)

use std::io::Read;
use std::rc::Rc;
use std::cell::RefCell;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    print!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let m: usize = iterator.next().unwrap().parse().unwrap();

    let tree = Rc::new(RefCell::new(BST::new()));
    let mut result = String::new();
    for _ in 0..m {
        let command = iterator.next().unwrap();
        if command == "insert" {
            let key: i64 = iterator.next().unwrap().parse().unwrap();
            tree.borrow_mut().insert(key);
        } else if command == "find" {
            let key: i64 = iterator.next().unwrap().parse().unwrap();
            if tree.borrow().find(key) {
                result.push_str("yes\n");
            } else {
                result.push_str("no\n");
            }
        } else if command == "delete" {
            let key: i64 = iterator.next().unwrap().parse().unwrap();
            BST::delete(Rc::clone(&tree), key);
        } else {
            tree.borrow().print_in_order(&mut result);
            result.push('\n');
            tree.borrow().print_pre_order(&mut result);
            result.push('\n');
        }
    }

    return result;
}

#[derive(PartialEq)]
enum BST {
    Node {
        value: i64,
        left: Rc<RefCell<BST>>,
        right: Rc<RefCell<BST>>,
    },
    Nil
}

impl BST {
    fn new() -> Self {
        BST::Nil
    }

    fn print_in_order(&self, buf: &mut String) {
        match *self {
            BST::Nil => {},
            BST::Node {
                ref value,
                ref left,
                ref right
            } => {
                left.borrow().print_in_order(buf);
                buf.push_str(&format!(" {}", value));
                right.borrow().print_in_order(buf);
            }
        }
    }

    fn print_pre_order(&self, buf: &mut String) {
        match *self {
            BST::Nil => {},
            BST::Node {
                ref value,
                ref left,
                ref right
            } => {
                buf.push_str(&format!(" {}", value));
                left.borrow().print_pre_order(buf);
                right.borrow().print_pre_order(buf);
            }
        }
    }

    fn insert(&mut self, new_value: i64) {
        match *self {
            BST::Nil => {
                *self = BST::Node {
                    value: new_value,
                    left: Rc::new(RefCell::new(BST::Nil)),
                    right: Rc::new(RefCell::new(BST::Nil)),
                }
            },
            BST::Node {
                ref mut value,
                ref mut left,
                ref mut right,
            } => {
                if new_value < *value {
                    left.borrow_mut().insert(new_value);
                } else {
                    right.borrow_mut().insert(new_value);
                }
            },
        }
    }

    fn find(&self, target_value: i64) -> bool {
        match *self {
            BST::Nil => {
                false
            },
            BST::Node {
                ref value,
                ref left,
                ref right
            } => {
                if target_value == *value {
                    true
                } else if target_value < *value {
                    left.borrow().find(target_value)
                } else {
                    right.borrow().find(target_value)
                }
            }
        }
    }

    fn delete(node: Rc<RefCell<BST>>, target_value: i64) {
        let mut delete_self = false;
        let mut derive_node = None;

        match *node.borrow_mut() {
            BST::Nil => {},
            BST::Node {
                ref mut value,
                ref mut left,
                ref mut right,
            } => {
                if target_value == *value {
                    if *left.borrow() == BST::Nil && *right.borrow() == BST::Nil {
                        delete_self = true
                    } else if *right.borrow() == BST::Nil {
                        derive_node = Some(Rc::clone(left));
                    } else if *left.borrow() == BST::Nil {
                        derive_node = Some(Rc::clone(right));
                    } else {
                        if let Some(m) = Self::min(right.clone()) {
                            Self::delete(right.clone(), m);
                            *value = m;
                        }
                    }
                } else if target_value < *value {
                    Self::delete(left.clone(), target_value);
                } else {
                    Self::delete(right.clone(), target_value);
                }
            }
        }

        if delete_self {
            *node.borrow_mut() = BST::Nil;
        } else if let Some(n) = derive_node {
            if let BST::Node {
                ref value,
                ref left,
                ref right,
            } = *n.borrow() {
                *node.borrow_mut() = BST::Node {
                    value: *value,
                    left: left.clone(),
                    right: right.clone(),
                };
            }
        }
    }

    fn min(node: Rc<RefCell<BST>>) -> Option<i64> {
        match *node.borrow() {
            BST::Nil => { None },
            BST::Node {
                ref value,
                ref left,
                ref right,
            } => {
                if let BST::Node {..} = *left.borrow() {
                    Self::min(left.clone())
                } else {
                    Some(*value)
                }
            }
        }
    }
}