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>
typedef struct node{
  int key;
  struct node *p,*left,*right;
}node;
typedef struct node* Node;
void insert(int);
Node find(int);
void delNode(Node);
void inorder(Node);
void preorder(Node);
Node minimum(Node);
Node successor(Node);
Node root,NIL;

int main(){
  int i,m,k;
  char string[8];
  scanf("%d",&m);
  for(i = 0; i < m; i++){
    scanf("%s",string);
   if(strcmp(string,"insert") == 0){
      scanf("%d",&k);
      insert(k);
    }
    else if(strcmp(string,"find") == 0){
      scanf("%d",&k);
      if(NIL == find(k))printf("no\n");
      else printf("yes\n");
    }
    else if(strcmp(string,"print") == 0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(strcmp(string,"delete") == 0){
      scanf("%d",&k);
      delNode(find(k));
    }
  }
  return 0;
}

void insert(int k){
  Node y = NIL;
  Node x = root;
  Node z;

  z = (Node)malloc(sizeof(node));
  z->left = NIL;
  z->right = NIL;
  z->key = k;

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

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

void delNode(Node z){
  Node del,x;
  if(z->left == NIL || z->right == NIL) del = z;
  else del = successor(z);

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

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

  if(del->p == NIL) root = x;
  else if(del == del->p->left) del->p->left = x;
  else if(del == del->p->right) del->p->right = x;

  if(del != z) z->key = del->key;
}

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

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

Node successor(Node x){
  Node y;
  if(x->right != NIL) return minimum(x->right);

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

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