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 <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   for(int i=0;i<(n);++i)
#define SORT(c)    sort((c).begin(),(c).end())
#define CLR(a)     memset((&a), 0 ,sizeof(a))//clear memory
#define dump(x)    cerr << #x << " = " << (x) << endl;//debug
#define debug(x)   cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#define EPS        1e-10//sample:if((double)>=(double)+EPS)
//cin,cout release
//std::cin.tie(0);
//ios::sync_with_stdio(false);

using namespace std;

struct node {
  int key;
  node *parent,*right, *left;
};
typedef node* nodep;
nodep root,NIL;
void insert(int key){
  nodep y=NIL,x=root,z=(nodep)malloc(sizeof(node));
  z->key=key;
  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;
    }
}
nodep find(nodep d,int key){
  while(d!=NIL&&d->key!=key){
    if(key<d->key)d=d->left;
    else d=d->right;
  }
  return d;
}
void del(nodep u,int key){
  dump(u->key);
  dump(u->parent->key);
  if(u==NIL)return;
  else if(u->parent==NIL)cout<<"$";
  else if(u->left==NIL&&u->right==NIL){
    if(u->parent->left->key==key)u->parent->left=NIL;
    else if(u->parent->right->key==key)u->parent->right=NIL;
  }
  else if(u->left==NIL&&u->right!=NIL){
    if(u->parent->left->key==key)u->parent->left=u;
    else if(u->parent->right->key==key)u->parent->right=u;
  }
  else if(u->left!=NIL&&u->right==NIL){
    if(u->parent->left->key==key)u->parent->left=u;
    else if(u->parent->right->key==key)u->parent->right=u;
  }
  else{
    if(u->parent->left->key==key)u->parent->left=u;
    else if(u->parent->right->key==key)u->parent->right=u;
  }cout<<"#delfinished"<<endl;
}
nodep treeMinimum(nodep x){
  while(x->left!=NIL)x=x->left;
  return x;
}
nodep treesuccessor(nodep x){
  if(x->right!=NIL)return treeMinimum(x->right);
  nodep y=x->parent;
  while(y!=NIL&&x==y->right){
    x=y;
    y=y->parent;
  }
  return y;
}
void treeDelete(nodep z){
  nodep x,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);
}
void inorder(nodep u){
  if(u==NIL)return;
  inorder(u->left);
  cout<<" "<<u->key;
  inorder(u->right);
}
void preorder(nodep u){
  if(u==NIL)return;
  cout<<" "<<u->key;
  preorder(u->left);
  preorder(u->right);
}
int main(){
  string buf;
  int a,n;
  cin>>n;
  rep(i,n){
    cin>>buf;
    if(buf[0]=='i'){
      cin>>a;
      insert(a);
    }
    else if(buf[0]=='f'){
      cin>>a;
      if(find(root,a)==NIL)cout<<"no"<<endl;
      else cout<<"yes"<<endl;
    }
    else if(buf[0]=='d'){
      cin>>a;
      treeDelete(find(root,a));
    }
    else{
      inorder(root);
      cout<<endl;
      preorder(root);
      cout<<endl;
    }
  }
  return 0;
}