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>
typedef struct node{
  int key;
  struct node *p;       //親
  struct node *left;    //左の子
  struct node *right;   //右の子
} tree;
void insert(tree *);
void Inorder(tree *);
void Preorder(tree *);
void find(tree *,int);
void delete(int);
tree *Successor(tree *);
tree *t = NULL;

int main(){
  int n,i,k;
  char function[10];
  tree *new;
  
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%s",function);
    if(function[0] == 'f'){
      scanf("%d",&k);
      find(t,k);
    }
    else if(function[0] == 'p'){
      Inorder(t);
      printf("\n");
      Preorder(t);
      printf("\n");
    }
    else if(function[0] == 'i'){
      scanf("%d",&k);
      new=malloc(sizeof(struct node));
      new->key=k;
      insert(new);
    }
    else if(function[0] = 'd'){
      scanf("%d",&k);
      delete(k) ;
    }
  }
  return 0;
}

void Preorder(tree *x){
  if(x == NULL) return;
  else  printf(" %d",x->key);
  if(x->left != NULL) Preorder(x->left);
  if(x->right != NULL) Preorder(x->right);
}
void Inorder(tree *x){
  if(x == NULL) return;
  if(x->left != NULL) Inorder(x->left);
  if(x != NULL) printf(" %d",x->key);
  if(x->right != NULL) Inorder(x->right);
}

void insert(tree *new){
  tree *x;
  tree *y;
  
  y=NULL;
  x=t;
  
  while(x != NULL){
    y=x;
    if(x->key > new->key) x=x->left;
    else x=x->right;
  }
  new->p = y;
  
  if(y == NULL){
    t=new;
    new->left = NULL;
    new->right = NULL;
  }
  else if(y->key > new->key){
    y->left = new;
    new->left = NULL;
    new->right = NULL;
  }
  else{
    y->right = new;
    new->left = NULL;
    new->right = NULL;
  }
}

void find(tree *t,int key){
  if(t == NULL){
    printf("no\n");
    return;
  }
  if(t->key == key){
    printf("yes\n");
    return;
  }
  if(t->key > key){
    find(t->left,key);
    return;
  }
  else{
    find(t->right,key);
    return;
  }
}

void delete(int k){
  tree *x;  //目的の場所
  tree *y;  //消す場所
  tree *z;  //繋ぎ用
  x = t;
  while(1){
    if(x == NULL) return;
    if(x->key == k) break;
    else if(x->key > k) x=x->left;
    else x=x->right;
  }

  //子の数は？
  if(x->left == NULL || x->right == NULL) y=x;
  else y=Successor(x);
  //消すやつの子は？
  if(y->left != NULL) z=y->left;
  else z=y->right;
  //その子が空でないならその子の親は消すやつの親
  if(z != NULL) z->p = y->p;
  //親がいないならそれは頂点
  //自分が左の子なら親の左の子は自分の子
  //自分が右の子なら親の右の子は自分の子
  if(y->p == NULL) t=z;
  else if(y == y->p->left) y->p->left = z;
  else y->p->right = z;
  //子を２つもってる場合
  if(x != y) x->key=y->key;


  free(y);
}

tree *Successor(tree *x){
  tree *y;
  if(x->right != NULL){
    x=x->right;
    while(x->left != NULL) x=x->left;
    return x;
  }
  else{
    y=x->p;
    while(y != NULL && y->right == x){
      x=y;
      y=y->p;
    }
    return y;
  }
}