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>

struct node{
  
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;

};

typedef struct node * Node;
#define NIL NULL

Node root;



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



int main(){

  int n, i, x;
  char com[20];

  scanf("%d", &n);

  //  maxh = 0;

  for ( i = 0; i < n; i++ ){
    
    scanf("%s", com);
    
    if ( strcmp(com, "find") == 0 ){
      
      scanf("%d", &x);

      Node t = treeSearch(root, x);
      if ( strcmp(com, "findMin") == 0 ){
	Node minn = treeMinimum(t);
	printf("%d\n", minn->key);
      }
      else if ( strcmp(com, "findMax") == 0 ){
	Node maxn = treeMaximum(t);
	printf("%d\n", maxn->key);
      }
      else {

	if ( t != NIL ) printf("yes\n");
	else printf("no\n");

      }
    }
    else if ( com[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    }
    else if ( strcmp(com, "print") == 0 ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if ( strcmp(com, "delete") == 0 ){
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }

  }
    /*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));
      }*/
  
  /*
  for ( i = 0; i < n; i++ ){

    scanf("%s", com);

    if ( strcmp(com, "insert") == 0 ){

      scanf("%d", &x);

      insert(x);
    }
    else if ( strcmp(com, "print") == 0 ){

      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");

    }
  }*/

  return 0;
}

void insert(int k){
  
  int H;
  Node y;
  Node x;
  Node z;

  y = NIL; // x ??????
  x = root; // T??????

  z = 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 ){ // T ???????????´???

    root = z;

  }
  
  else {
    if (z->key < y->key) {

      y->left = z; // z ??? y ?????????????????????
    }
    else {

      y->right = z;// z ??? y ?????????????????????

    }
  }
}

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);

}



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;
}

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

  Node y = x->parent;

  while( y != NIL && x == y->right ){

    x = y;
    y = y->parent;

  }
  return y;

}

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;

  }

  free(y);


}