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;

/*節点xを根とする部分木の中で最小のキーを持つ節点を返す*/
Node treeMinimum(Node x){
while (x->left != NIL) { x = x->left;}
return x;
}
Node treeSearch(Node u, int k){
if (u == NIL || k == u->key) return u;
if(k < u->key) return treeSearch(u->left,k);
else return treeSearch(u->right,k);
}

/*２分探索木の節点xに次節点がある場合はその次節点を返す
ただし、木の中でxが最大のキーを持つ場合はNILを返す*/
Node treeSuccessor(Node x){
Node y;
if(x->right != NIL) return treeMinimum(x->right);
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
/*削除する節点yを決定する*/
if(z->left == NIL || z->right == NIL) y = z; /*zが子を最大１つ持つ場合は入力節点のz*/
else y = treeSuccessor(z); /*zが子を２つ持つ場合はzの次節点*/
/*xをyのNILではない子またはyが子を持たない場合はNILを設定*/
if(y->left != NIL) x = y->left;
else x = y->right;
/*yの親とxのポインタを変更しyを削除する*/
if(x != NIL) x->parent = y->parent; /*yが子を１つ持つ場合*/
if(y->parent == NIL) root = x;  /*yが根のときの境界条件の処理*/
else if(y == y->parent->left) y->parent->left = x; /*yが左の子の場合*/
else y->parent->right = x; /*yが右の子の場合*/
/*zの次節点が削除されたときにyの内容をzに移動する。*/
if(y != z) z->key = y->key; 
}

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

  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) root = z; //if 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);
}
}

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

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;
}