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 JAVA (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.NoSuchElementException;

public class Main {
    public static void main(String[] args) {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        try {
            int n = Integer.parseInt(br.readLine());
            Node r = null;
            String line;
            while ((line = br.readLine()) != null) {
                String[] c_k = line.split(" ");
                if (c_k[0].equals("insert")) {
                    Node z = new Node(Integer.parseInt(c_k[1]));
                    r = insert(r, z);
                }
                if (c_k[0].equals("find")) {
                    int k = Integer.parseInt(c_k[1]);
                    if (find(r, k) == null) {
                        System.out.println("no");
                    } else {
                        System.out.println("yes");
                    }
                }
                if (c_k[0].equals("delete")) {
                    int k = Integer.parseInt(c_k[1]);
                    Node x = find(r, k);
                    deleteNode(r, x);
                }
                if (c_k[0].equals("print")) {
                    printInorder(r);
                    System.out.println();
                    printPreorder(r);
                    System.out.println();
                }
            }
        } catch (IOException
                | NoSuchElementException
                | NumberFormatException e) {
            System.out.println(e);
        }
    }

    private static class Node {
        Node() {}
        Node(int key) {
            this.key = key;
        }
        int key = -1;
        Node parent, left, right;
    }

    private static Node insert(Node r, Node z) {
        Node y = null;
        Node x = r;
        while (x != null) {
            y = x;
            if (z.key < x.key) {
                x = x.left;
            } else {
                x = x.right;
            }
        }
        z.parent = y;

        if (y == null) {
            r = z;
        } else if (z.key < y.key) {
            y.left = z;
        } else {
            y.right = z;
        }
        return r;
    }

    private static Node find(Node x, int k) {
        while (x != null && k != x.key) {
            if (k < x.key) {
                x = x.left;
            } else {
                x = x.right;
            }
        }
        return x;
    }

    private static void deleteNode(Node r, Node z) {
        Node x, y;
        if (z.left == null || z.right == null) {
            y = z;
        } else {
            y = getSuccessor(z);
        }
        if (y.left != null) {
            x = y.left;
        } else {
            x = y.right;
        }
        if (x != null) {
            x.parent = y.parent;
        }

        if (y.parent == null) {
            r = x;
        } else if (y == y.parent.left) {
            y.parent.left = x;
        } else {
            y.parent.right = x;
        }
        if (y != z) {
            z.key = y.key;
        }
    }

    private static Node getSuccessor(Node z) {
        if (z.right != null) {
            return getMinimum(z.right);
        }

        Node y = z.parent;
        while (y != null && z == y.right) {
            z = y;
            z = y.parent;
        }
        return y;
    }

    private static Node getMinimum(Node z) {
        while (z.left != null) {
            z = z.left;
        }
        return z;
    }

    private static void printPreorder(Node r) {
        System.out.printf(" %d", r.key);
        if (r.left != null) {
            printPreorder(r.left);
        }
        if (r.right != null) {
            printPreorder(r.right);
        }
    }

    private static void printInorder(Node r) {
        if (r.left != null) {
            printInorder(r.left);
        }
        System.out.printf(" %d", r.key);
        if (r.right != null) {
            printInorder(r.right);
        }
    }
}