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{
  long key;
  struct node *left;
  struct node *right;
  struct node *p;
}Node;

void print_tree(Node *x,int order) {
  if (order == 0) {
    printf(" %ld", x->key);    
  }
  if(x->left != NULL) print_tree(x->left,order);
  if (order == 1) {
    printf(" %ld", x->key);    
  }
  if(x->right != NULL) print_tree(x->right,order);
  if (order == 2) {
    printf(" %ld", x->key);    
  }
}

Node *insert(Node *root, long key) {
  Node *z = (Node*)malloc(sizeof(Node));
  z->key = key;
  z->p = NULL;
  z->left = NULL;
  z->right = NULL;
  Node *x,*y;
  y = NULL;
  x = root;
  while(x != NULL) {
    y = x;
    if(z->key < x->key) x = x->left;
    else x = x->right;
  }
  z->p = y;
  if(y  == NULL) return z;
  else if(z->key < y->key) y->left = z;
  else y->right = z;
  return root;
}

int search_tree(Node *root, long key) {
  Node *x = root;
  while(x != NULL) {
    if(x->key == key) return 1;
    else if(x->key > key) x = x->left;
    else if(x->key < key) x = x->right;
  }
  return 0;
}

Node *delete_node(Node *root, long key) {
  Node *x = root,*y = NULL;
  while(x != NULL) {
    if(x->key == key) break;
    y = x;
    if(x->key > key) x = x->left;
    else x = x->right;
  }
  if(x->left == NULL && x->right == NULL) {
    if(y == NULL) {
      free(x);
      return NULL;
    }
    if(y->key > key) y->left = NULL;
    else y->right = NULL;
    free(x);
    return root;
  }
  else if(x->left == NULL || x->right == NULL) {
    Node *z;
    if(x->left == NULL) z = x->right;
    if(x->right == NULL) z = x->left;
    if(y == NULL) {
      free(x);
      z->p = NULL;
      return z;
    }
    z->p = y;
    if(y->key > key) y->left = z;
    else x->p->right = z;
    free(x);
    return root; 
  }
  else{
    Node *z = x->right;
    while(z->left != NULL) z = z->left;
    long tmp = z->key;
    root = delete_node(root,tmp);
    x->key = tmp;
    return root;
  }
}

int main()
{
  long i,N,key;
  char command[7];
  Node *root = NULL;
  scanf("%ld",&N);
  for (i = 0; i < N; i++) {
    scanf("%s",command);
    if(strcmp(command,"insert") == 0) {
      scanf("%ld",&key);
      root = insert(root,key);
    }
    if(strcmp(command,"print") == 0) {
      print_tree(root,1);
      printf("\n");
      print_tree(root,0);
      printf("\n");
    }
    if(strcmp(command,"find") == 0) {
      scanf("%ld",&key);
      (search_tree(root,key) == 1) ? printf("yes\n") : printf("no\n");
    }
    if(strcmp(command,"delete") == 0) {
      scanf("%ld",&key);
      root = delete_node(root,key);
    }
  }

  return 0;
}