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 <stdlib.h>

struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
#define NIL NULL

Node root;

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

Node treeMaximum(Node x){
  while (x->right!=NIL) x=x->right;
  return x;
}

Node treeSearch(Node u, int k){
  Node ret = NIL;
  if (u->key==k) return u;
  else if (u->key>k) {
    if (u->left!=NIL)
      return treeSearch(u->left, k);
  } else if (u->right!=NIL)
    return treeSearch(u->right, k);
  return ret;
}

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

void treeDelete(Node z){
  Node y; // node to be deleted
  Node x; // child of y

  if (z->left==NIL && z->right==NIL) { // has no child
    if (z->parent->left==z)  z->parent->left=NIL;
    else                     z->parent->right=NIL;
    free(z);
  } else  if (z->left!=NIL && z->right!=NIL) { // has two children
    y = treeSuccessor(z);
    z->key=y->key;
    treeDelete(y);
  } else { // if (z->left!=NIL || z->right!=NIL) { //  has just one child
    x = (z->left!=NIL) ? z->left : z->right;
    if (z->parent->left==z)   z->parent->left=x;
    else                      z->parent->right=x;
    x->parent = z->parent;
    free(z);
    return;
  }
}

void insert(int k){
  Node y = NIL;
  Node x = root;
  Node z = malloc(sizeof(struct node));
  z->key = k;
  z->left = NIL;
  z->right = NIL;

  while (x!=NIL) {
    y = x;
    if (z->key < x->key)
      x = x->left;
    else
      x = x->right;
  }
  z->parent = y;

  if (y==NIL)
    root = z;
  else if (z->key < y->key)
    y->left = z;
  else
    y->right = z;
}

void inorder(Node u){
  if (u->left!=NIL) inorder(u->left);
  printf(" %d", u->key);
  if (u->right!=NIL) inorder(u->right);
}
void preorder(Node u){
  printf(" %d", u->key);
  if (u->left!=NIL) preorder(u->left);
  if (u->right!=NIL) preorder(u->right);
}

void print()
{
  if (root==NIL) return;
  preorder(root);
  printf("\n");
  inorder(root);
  printf("\n");
}

int main(){
  int n, i, x;
  char com[20];
  scanf("%d", &n);
  
  for (i = 0; i < n; i++){
    scanf("%s", com);
    switch (com[0]) {
    case 'f':
      scanf("%d", &x);
      Node t = treeSearch(root, x);
      if (t != NIL) printf("yes\n");
      else printf("no\n");
      break;
    case 'i':
      scanf("%d", &x);
      insert(x);
      break;
    case 'p':
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
      break;
    case 'd':
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }
  }
  return 0;
}