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>
#define N 500000

struct BiT_Node{
  int key;
  struct BiT_Node *p;
  struct BiT_Node *left;
  struct BiT_Node *right;
};

typedef struct BiT_Node *Node;

Node root;

Node getMinimum(Node x){
  while(x->left != NULL) x = x->left;
  return x;
}

void insert (int v){
  Node y = NULL;
  Node x = root;
  Node z;
  z = malloc(sizeof(struct BiT_Node));
  z->key = v;
  z->left = NULL;
  z->right = NULL;
  y = NULL;
  while(x != NULL){
    y = x;
    if(z->key < x->key) x = x->left;
    else x = x->right;
  }
  
  z->p = y;

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

Node treeSuccessor(Node u){
  if(u->right != NULL)  return getMinimum(u->right);
  Node v = u->p;
  while(v != NULL && u == v->right ){
    u = v;
    v = v->p;
  }
  return v;
}

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

void pre_walk(Node u){
  if(u == NULL) return;
  printf(" %d",u->key);
  if(u->left != NULL) pre_walk(u->left);
  if(u->right != NULL) pre_walk(u->right);
}

Node find(int key){
  Node u;
  u = root;
  while(u != NULL && key != u->key){
    if(key < u->key) u = u->left;
    else u = u->right;
  }
  return u;
}

void delete(Node u){
  Node y;
  Node x;
  if(u->left == NULL || u->right == NULL) y = u;
  else y = treeSuccessor(u);
  if(y->left != NULL){
    x = y->left;
  }
  else x = y->right;

  if(x != NULL) x->p = y->p;
  if(y->p == NULL) root = x;
  else {
    if(y == y->p->left){
      y->p->left = x;
    }
    else y->p->right = x;
  }

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

  free(y);
}

int main()
{
  int n,i,tmp;
  char buf[20];
  scanf("%d",&n);
  for(i = 0 ; i < n; i++){
    scanf("%s",buf);
    if(buf[0] == 'i'){
      scanf("%d",&tmp);
      insert(tmp);
    }
    else if(buf[0] == 'f') {
      scanf("%d",&tmp);
      if(find(tmp) != NULL) printf("yes\n");
      else printf("no\n");
    }
    else if(buf[0] == 'd'){
      scanf("%d",&tmp);
      delete(find(tmp));
    }
    else if(buf[0] == 'p') {
      in_walk(root);
      printf("\n");
      pre_walk(root);
      printf("\n");
    }
  }
  return 0;
}