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
#define DEBUG

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

Node* tree;

void insert(int);
void inorder(Node*);
void preorder(Node*);
void delete(Node*);
Node* find(Node*,int);
Node* Minimum(Node*);
Node* Successor(Node*);

int main(){
  int m,i,k;
  char s[10];
  Node* f;

  scanf("%d",&m);

  for(i=0;i<m;i++){
    scanf("%s",s);
    if(s[0]=='i'){
      scanf("%d",&k);
      insert(k);
    }
    else if(s[0]=='p'){
      inorder(tree);
      printf("\n");
      preorder(tree);
      printf("\n");
    }
    else if(s[0]=='f'){
      scanf("%d",&k);
      f=find(tree,k);
      if(f!=NIL) printf("yes\n");
      else printf("no\n");
    }
    else if(s[0]=='d'){
      scanf("%d",&k);
      if((f=find(tree,k))!=NIL) delete(f);
    }
  }

  return 0;
}

void insert(int k){
  Node* y = NIL;
  Node* x = tree;
  Node* z;
  z=(Node *)malloc(sizeof(Node));
  z->k=k;
  z->left=NIL;
  z->right=NIL;

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

  if(y==NIL) tree=z;
  else if(z->k < y->k) y->left=z;
  else y->right=z;
  return;
}

void inorder(Node* tree){
  if(tree != NIL){
    inorder(tree->left);
    printf(" %d",tree->k);
    inorder(tree->right);
  }
  return;
}

void preorder(Node* tree){
  if(tree != NIL){
    printf(" %d",tree->k);
    preorder(tree->left);
    preorder(tree->right);
  }
  return;
}

Node* find(Node* tree,int f){
  if(tree != NIL){
    if(tree->k == f) return tree;
    if(tree->k > f) return find(tree->left,f);
    else return find(tree->right,f);
  }
  else return NIL;
}

void delete(Node* z){
  Node* y;
  Node* x;

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

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

  if(y->parent==NIL) tree=x;
  else if(y==y->parent->left) y->parent->left=x;
  else y->parent->right = x;

  if(y!=z){
    z->k = y->k;
  }

  return;
}

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

Node* Successor(Node* x){
  Node* y;

  if(x->right != NIL) return Minimum(x->right);

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