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>

struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
#define NIL NULL
Node root;

void treeDelete(Node z){
  Node x;
  Node y;
  if( z->left == NIL || z->right == NIL ) y = z;
  else y = getSuccessor(z);
  if( y->left != NIL ) x = y->left;
  else x = y->right;
  if( x != NIL ) x->parent = y->parent;
  if( y->parent == NIL) root = x;
  else if(y == y->parent->left) y->parent->left = x;
  else y->parent->right = x;
  if( y != z ) z->key = y->key;
  free(y);
}

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

getSuccessor(Node x){
  if( x->right != NIL ) return getMinimum( x->right );
  Node y = x->parent;
  while ( y != NIL && x == y->right ){
    x = y;
    y = y->parent;
  }
  return y;
}

Node treeSearch( Node u, int k ){
  while( u != NIL && k != u->key ){
    if( k < u->key ) u = u->left;
    else u = u->right;
  }
  return u;
}

void insert(int k){
  Node y=NIL;
  Node x=root;
  Node z;
  
  z=(Node)malloc(sizeof(struct node));

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

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

int main (){
    int n,i,x;
    char com[20];
    scanf( "%d", &n );
    root = NIL;
    for(i=0;i<n;i++){
        scanf( "%s", com );
        if( com[0] == 'i' ){
        scanf( "%d", &x );
        insert(x);
        }
        else if(com[0] == 'p'){
        inorder(root);
        printf("\n");
        preorder(root);
        printf("\n");
        }
        else if( com[0] == 'f'){
        scanf( "%d", &x);
        Node t = treeSearch(root,x);
        if( t != NIL )printf("yes\n");
        else printf("no\n");
        }
        else if(com[0] == 'd'){
        scanf( "%d", &x);
        treeDelete(treeSearch(root,x));
        }
    }
    return 0;
    }