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>

#define NIL NULL

struct node{
  int d;
  struct node *p;
  struct node *r;
  struct node *l;
};
typedef struct node *NP;

NP root;

void my_insert(NP);
void my_inorder_print(NP);
void my_preorder_print(NP);
NP my_find(NP,int);
NP my_successor(NP);
NP my_min(NP);
void my_delete(NP);
NP make_node(int);

int main(){
  int i,n,input;
  char in[7];
  NP z;
  scanf("%d",&n);
  for(i=0; i<n; i++){
    scanf("%s",in);
    if(strcmp(in,"insert")==0){
      scanf("%d",&input);
      //INSERT
      z=make_node(input);
      my_insert(z);
    }
    if(strcmp(in,"print")==0){
      //PRINT
      my_inorder_print(root);
      printf("\n");
      my_preorder_print(root);
      printf("\n");
    }
    if(strcmp(in,"find")==0){
      scanf("%d",&input);
      //FIND
      if(my_find(root,input)!=NIL) printf("yes\n");
      else printf("no\n");
    }
    if(strcmp(in,"delete")==0){
      scanf("%d",&input);
      //DELETE
      z=my_find(root,input);
      my_delete(z);
    }
  }
  return 0;
}

void my_insert(NP z){
  NP x,y;
  y=NIL;
  x=root;
  while(x!=NIL){
    y=x;
    if(z->d<x->d) x=x->l;
    else x=x->r;
  }
  z->p=y;

  if(y==NIL){
    root=z;
  }else if(z->d<y->d){
    y->l=z;
  }else{
    y->r=z;
  }
}

void my_inorder_print(NP p){
  if(p!=NIL){
    my_inorder_print(p->l);
    printf(" %d",p->d);
    my_inorder_print(p->r);
  }
}

void my_preorder_print(NP p){
  if(p!=NIL){
    printf(" %d",p->d);
    my_preorder_print(p->l);
    my_preorder_print(p->r);
  }
}

NP make_node(int key){
  NP p;
  p=(NP)malloc(sizeof(struct node));
  p->d=key;
  p->p=NIL;
  p->r=NIL;
  p->l=NIL;
  return p;
}

NP my_find(NP x,int k){
  if(x==NIL || x->d==k) return x;
  if(k<x->d) return my_find(x->l,k);
  else return my_find(x->r,k);
}

void my_delete(NP z){
  NP x,y;
  if(z->l==NIL || z->r==NIL) y=z;
  else y=my_successor(z);

  if(y->l!=NIL) x=y->l;
  else x=y->r;

  if(x!=NIL) x->p=y->p;

  if(y->p==NIL) root=x;
  else if(y==y->p->l) y->p->l=x;
  else y->p->r=x;

  if(y!=z) z->d=y->d;
}

NP my_successor(NP x){
  NP y;
  if(x->r!=NIL) return my_min(x->r);
  y=x->p;
  while(y!=NIL && x==y->r){
    x=y;
    y=y->p;
  }
  return y;
}

NP my_min(NP z){
  while(z->l!=NIL) z=z->l;
  return z;
}