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>
#include<string.h>
typedef struct node{
  int key;
  struct node *r,*l,*par;
}Node;

Node *root,*NIL;

Node* treemin(Node *value){
  while(value->l != NIL)value=value->l;
  return value;
}
Node* find(Node *value,int k){
  while(value!=NIL&&k!=value->key){
    if(k<value->key)value=value->l;
    else value=value->r;
  }
  return value;
}
Node* treesuccess(Node *value1){
  if(value1->r!=NIL)return treemin(value1->r);
  Node *value2=value1->par;
  while(value2!=NIL&&value1==value2->r){
    value1=value2;
    value2=value2->par;
  }
  return value2;
}
void treedel(Node *z){
  Node *x,*y;
  if(z->l==NIL||z->r==NIL)y=z;
  else y=treesuccess(z);
  if(y->l!=NIL){
    x=y->l;
  }
  else{
    x=y->r;
  }
  if(x!=NIL){
    x->par=y->par;
  }
  if(y->par==NIL){
    root=x;
  }
  else{
    if(y==y->par->l){
      y->par->l=x;
    }
    else{
      y->par->r=x;
    }
  }
  if(y!=z){
    z->key=y->key;
  }
  free(y);
}
void insert(int value){
  Node *y=NIL;
  Node *x=root;
  Node *z;

  z=(Node *)malloc(sizeof(Node));
  z->key=value;
  z->l=NIL;
  z->r=NIL;
  while(x!=NIL){
    y=x;
    if(z->key<x->key){
      x=x->l;
    }
    else{
      x=x->r;
    }
  }

  z->par=y;
  if(y==NIL){
    root=z;
  }
  else{
    if(z->key<y->key){
      y->l=z;
    }
    else{
      y->r=z;
    }
  }
}
void inorder(Node *u){
  if(u==NIL)return;
  inorder(u->l);
  printf(" %d",u->key);
  inorder(u->r);
}

void preorder(Node *u){
  if(u==NIL)return;
  printf(" %d",u->key);
  preorder(u->l);
  preorder(u->r);
}
int main(){
  int n,i,a;
  char ary[10];

  scanf("%d",&n);

  for(i=0;i<n;i++){
    scanf("%s",ary);
    if(strncmp(ary,"f",1)==0){
      scanf("%d",&a);
      Node *v=find(root,a);
      if(v!=NIL)printf("yes\n");
      else printf("no\n");
    }
    else if(strcmp(ary,"insert")==0){
      scanf("%d",&a);
      insert(a);
    }
    else if(strcmp(ary,"print")==0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(strcmp(ary,"delete")==0){
      scanf("%d",&a);
      treedel(find(root,a));
    }
  }
  return 0;
}