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>
#include<string.h>

struct node {
  int key;
  struct node *right;
  struct node *left;
  struct node *parent;
};

typedef struct node* Nodepointer;
Nodepointer nil, root;

Nodepointer treeMinimum(Nodepointer x){
  while( x->left != nil ) x = x->left;
  return x;
}

Nodepointer find(Nodepointer u, int k){
  while( u != nil && k != u->key ){
    if( k < u->key ) u = u->left;
    else u = u->right;
  }
  return u;
}

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

void treeDelete(Nodepointer z){
  Nodepointer y;
  Nodepointer x;

  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->parent = y->parent;
  if( y->parent ==nil ) root = x;
  else {
    if( y == y->parent->left) y->parent->left = x;
    else y->parent->right = x;
  }

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

  free(y);
}

void insert(int k){
  Nodepointer x, y, z;
  y = nil;
  x = root;

  z = (Nodepointer)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(Nodepointer u){
  if( u == nil ) return;
  inorder(u->left);
  printf(" %d", u->key);
  inorder(u->right);
}

void preorder(Nodepointer u){
  if( u == nil ) return;
  printf(" %d", u->key);
  preorder(u->left);
  preorder(u->right);
}

int main(){
  int n, i, x;
  char com[7];

  scanf("%d", &n);

  for( i = 0 ; i < n ; i++ ){
    scanf("%s",com);
    if( com[0] == 'f' ){
      scanf("%d", &x);
      Nodepointer t = find(root, x);
      if( t != nil ) printf("yes\n");
      else printf("no\n");
    }
    else if( strcmp("insert",com) == 0 ){
      scanf("%d", &x);
      insert(x);
    }
    else if( strcmp("print",com) == 0 ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if( strcmp("delete", com) == 0 ){
      scanf("%d", &x);
      treeDelete(find(root, x));
    }
  }
  return 0;

}