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<string.h>
#include<stdlib.h>

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

Node *root;

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

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

void insert(int k){
  Node *y = NIL;
  Node *x = root;
  Node *z;

  z=(Node*)malloc(sizeof(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);
}

Node * getminimum(Node *n){
  while(n->left!=NULL)n=n->left;
  return n;
}

Node * getsuccessor(Node *z){
  Node* y;

  if(z->right!=NULL)return getminimum(z->right);
  y=z->parent;
  while(z!=NULL&&z==y->right){
    z=y;
    y=y->parent;
  }
  return y;
}

void delete(Node* z){
  Node *x,*y;
  if((z->left!=NULL)&&(z->right!=NULL))y=getsuccessor(z);
  else y=z;

  if(y->left!=NULL)x=y->left;
  else x=y->right;

  if(x!=NULL)x->parent=y->parent;

  if(y->parent==NULL)root=x;
  else if(y==y->parent->left)y->parent->left=x;
  else y->parent->right=x;

  if(y!=z)z->key=y->key;

}

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);
      delete(treeSearch(root,x));
    }

  }

  return 0;
}