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 <stdio.h>
#include <limits.h>
#include <stdlib.h>
#include <limits.h>
#include <stdbool.h>
#define NIL NULL
#define TREE_VALUE INT_MAX

typedef struct Node* NodePointer;
typedef NodePointer Tree;

typedef struct Node {
  int key;
  NodePointer p, left, right;
} Node;

NodePointer makeNode(int key) {
  NodePointer node = (NodePointer)malloc(sizeof(Node));
  node->key = key;
  node->p = node->left = node->right = NIL;
  return node;
}

void treeInsert(Tree tree, NodePointer z) {
  NodePointer y = NIL;
  NodePointer x = tree->left;
  while(x != NIL) {
    y = x;
    if(z->key < x->key) {
      x = x->left;
    } else {
      x = x->right;
    }
  }

  z->p = y;
  if(y == NIL) {
    tree->left = z; // if T is empty
  } else if(z->key < y->key) {
    y->left = z;
  } else {
    y->right = z;
  }
}

void printInorder(NodePointer node) {
  if(node->left  != NIL) printInorder(node->left);
  if(node->key != TREE_VALUE) printf(" %d", node->key);
  if(node->right != NIL) printInorder(node->right);
}

void printPreorder(NodePointer node) {
  if(node->key != TREE_VALUE) printf(" %d", node->key);
  if(node->left  != NIL) printPreorder(node->left);
  if(node->right != NIL) printPreorder(node->right);
}

NodePointer find(NodePointer node, int key) {
  if(node == NIL) return NIL;
  if(node->key == key) return node;
  else if(key < node->key)
    return find(node->left, key);
  else
    return find(node->right, key);
}

NodePointer treeMinimum(NodePointer x) {
  while(x->left != NIL) {
    x = x->left;
  }
  return x;
}

NodePointer treeSuccessor(NodePointer x) {
  NodePointer y;
  if(x->right != NIL)
    return treeMinimum(x->right);
  y = x->p;
  while(y != NIL && x == y->right) {
    x = y;
    y = y->p;
  }
  return y;
}

void treeDelete(Tree T, NodePointer z) {
  NodePointer x, y;

  if(z->left == NIL || z->right == NIL)
    y = z;
  else
    y = treeSuccessor(z);

  if(y->left != NIL)
    x = y->left;
  else
    x = y->right;

  if(x != NIL)
    x->p = y->p;

  if(y->p == NIL)
    T->left = x;
  else if(y == y->p->left)
    y->p->left = x;
  else
    y->p->right = x;

  if(y != z)
    z->key = y->key;

}

int main() {
  int N, key;
  char str[10];
  Tree tree;

  // initialize tree
  tree = makeNode(TREE_VALUE);

  scanf("%d", &N);
  while(N--) {
    scanf("%s", str);
    if(str[0] == 'i') {
      scanf("%d", &key);
      treeInsert(tree, makeNode(key));
    } else if(str[0] == 'p') {
      printInorder(tree);
      printf("\n");
      printPreorder(tree);
      printf("\n");
    } else if(str[0] == 'f') {
      scanf("%d", &key);
      printf(find(tree,key)?"yes\n":"no\n");
    } else {
      scanf("%d", &key);
      treeDelete(tree, find(tree,key));
    }
  }
  return 0;
}