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>
#define N 500000
#define DUMMY 2000000001

struct Node{
  int key;
  struct Node *left,*right;
};

struct Node *make_node(int x){
  struct Node *node = malloc(sizeof(struct Node));
  if(node != NULL){
    node->key = x;
    node->left = NULL;
    node->right = NULL;
  }
  return node;
}

struct Node *root;

int search_min(struct Node*);
struct Node *delete_min(struct Node *node);

struct Node *insert(int,struct Node*);
void insort(struct Node*);
void presort(struct Node*);
void find(int,struct Node*);
struct Node *Delete(int,struct Node*);

int main(void){
  int m,n=0;
  int i;
  int k;
  char order[7];

  root = NULL;

  scanf("%d",&m);

  for(i=0;i<m;i++){
    scanf("%s",order);
    if(strcmp(order,"insert") == 0){
      scanf("%d",&k);
      root = insert(k,root);
    }else if(strcmp(order,"print") == 0){
      insort(root);
      printf("\n");
      presort(root);
      printf("\n");
    }else if(strcmp(order,"find") == 0){
      scanf("%d",&k);
      find(k,root);
    }else if(strcmp(order,"delete") == 0){
      scanf("%d",&k);
      Delete(k,root);
    }
  }
}

struct Node *insert(int key,struct Node *node){
  if (node == NULL)
    return make_node(key);
  else if (key < node->key)
    node->left = insert(key, node->left);
  else if (key > node->key)
    node->right = insert(key, node->right);
  return node;
}

void find(int key,struct Node *node){
  while (node != NULL) {
    if (node->key == key){
      printf("yes\n");
      return;
    }
    else if(key < node->key)
      node = node->left;
    else
      node = node->right;
  }
  printf("no\n");
  return;
}

int search_min(struct Node *node){
  while (node->left != NULL) node = node->left;
  return node->key;
}

struct Node *delete_min(struct Node *node){
  if (node->left == NULL) {
    struct Node *temp = node->right;
    free(node);
    return temp;
  }
  node->left = delete_min(node->left);
  return node;
}

struct Node *Delete(int key,struct Node *node){
  if (node == NULL) return NULL;
  if (key == node->key) {
    if (node->left == NULL) {
      struct Node *temp = node->right;
      free(node);
      return temp;
    }
    if (node->right == NULL) {
      struct Node *temp = node->left;
      free(node);
      return temp;
    }
    node->key = search_min(node->right);
    node->right = delete_min(node->right);
  } else if (key < node->key)
    node->left = Delete(key, node->left);
  else
    node->right = Delete(key, node->right);
  return node;
}

void insort(struct Node *node){

  if(node == NULL) return;

  insort(node->left);

  printf(" %d",node->key);

  insort(node->right);
}

void presort(struct Node *node){

  if(node == NULL) return;

  printf(" %d",node->key);
  
  presort(node->left);
  presort(node->right);
}