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 *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;

Node root;

Node treeMinimum(Node x);
Node treeMaximum(Node x);
Node treeSuccessor(Node x);
void treeDelete(Node z);
void inorder( Node );
void preorder( Node );
void insert( int );
Node treeSearch( Node, int );

//-----------------------------------------------------------
int main(){
  int n, i, x;
  char com[20];
  scanf("%d", &n);

  for ( i = 0; i < n; i++ ){
    scanf("%s", com);
    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] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( com[0] == 'p' ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    } else if ( com[0] == 'd' ){
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }
  }

  return 0;
}
//----------------------------------------------------------
Node treeMinimum(Node x){
    while( x->left != NIL ) 
	x = x->left;
    return x;
}

//------------------------------------------------------------
Node treeMaximum(Node x){
    while( x->right != NIL ) 
	x = x->right;
    return x;
}

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

//----------------------------------------------------------
Node treeSuccessor(Node x){
    Node y;
    
    if( x->right != NIL ) return treeMinimum(x->right); //case 1

    y = x->parent;
    while( y != NIL && x == y->right ){
	x = y;
	y = y->parent;
    }
    return y; //case 2
}

//----------------------------------------------------------
void treeDelete(Node z){
    Node y; // node to be deleted
    Node x; // child of y

    if( z->left == NIL || z->right == NIL ) y = z;
    else y = treeSuccessor( 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;
}

//-----------------------------------------------------------
void insert(int k){
  Node y = NIL;   //y is parent of the k 
  Node x = root;   //x is the root node
  Node z;   //z is new node for the k

  //initialization
  z = malloc(sizeof(struct node));
  z->key = k;
  z->left = NIL;
  z->right = NIL;
  //decide where to place the z node
  while(x != NIL){  //when Binary Tree T is not empty.
      y = x;  //substitute x for y as a parent
      if(z->key < x->key) x = x->left;
      else  x = x->right;
  }
  z->parent = y;
  //connect them
  if(y == NIL) root = z;//when Binary Tree T is empty
  else if(z->key < y->key) y->left = z;
  else y->right = z;
}

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

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