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 NIL NULL
struct node{
  struct node *r;
  struct node *l;
  struct node *p;
  int key;
};
typedef struct node * Node;
Node treeMinimum(Node x);
Node treeSearch(Node u, int k);
Node treeSuccessor(Node x);
void treeDelete(Node z);
void insert(int k);
void inorder(Node u);
void preorder(Node u);
Node root;
Node T;
int main(){
  int n, i, x;
  char str[7];
  scanf("%d", &n);
 
  for ( i = 0; i < n; i++ ){
    scanf("%s", str);
    if ( str[0] == 'f' ){
      scanf("%d", &x);
      T = treeSearch(root, x);
      if ( T != NIL ) printf("yes\n");
      else printf("no\n");
    } else if ( str[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( str[0] == 'p' ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    } else if ( str[0] == 'd' ){
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }
  }
  return 0;
}
Node treeMinimum(Node x){
  while(x->l != NIL)
    x = x->l;
  return x;
}
Node treeSearch(Node u, int k){
  while(u != NIL && k != u->key){
    if(k < u->key) u = u->l;
    else u = u->r;
  }
  return u;
}
 
Node treeSuccessor(Node x){
  Node y;
  if(x->r != NIL) return treeMinimum(x->r);
  y = x->p;
  while(y != NIL && x == y->r){
    x = y;
    x = y->p;
  }
  return y;
}
 
void treeDelete(Node z){
  Node y;
  Node x;
  if(z->l == NIL || z->r == NIL) y = z;
  else y = treeSuccessor(z);
  if(y->l != NIL) x = y->l;
  else x = y->r;
  if(x != NIL) x->p = y->p;
  if(y->p == NIL) root = x;
  else if(y == y->p->l) y->p->l = x;
  else y->p->r = x;
  if(y != z) z->key = y->key;
  }
 
void insert(int k){
  Node y = NIL;
  Node x = root;
  Node z;
 
  z = malloc(sizeof(struct node));
  z->key = k;
  z->l = NIL;
  z->r = NIL;
 
  while(x != NIL){
    y = x;
    if(z->key < x->key) x = x->l;
    else  x = x->r;   
  }
  z->p = y;
  if(y == NIL) root = z;
  else if(z->key < y->key) y->l = z;
  else y->r = z; 
}
 
void inorder(Node u){
  if(u == NIL) return;
  inorder(u->l);
  printf(" %d", u->key);
  inorder(u->r);
}
void preorder(Node u){ 
  if(u == NIL) return;
  printf(" %d", u->key);
  preorder(u->l);
  preorder(u->r);
}