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 k;
  struct Node *right;
  struct Node *left;
  struct Node *parent;
}T;

T *root, *NIL;

void Insert(int);
void Inorder(T *);
void Preorder(T *);
T * Find(T *, int);
void Delete(T *);
T * Minimum(T *);
T * Successor(T *);

int main(){
  int i,n,value,findnum;
  char com[10];

  scanf("%d",&n);

  for(i = 0 ; i < n ; i++){
    scanf("%s",com);

    if(strcmp(com,"insert") == 0){
      scanf("%d",&value);
      Insert(value);
    }
    else if(strcmp(com,"print") == 0){
      Inorder(root);
      printf("\n");
      Preorder(root);
      printf("\n");
    }
    else if(strcmp(com,"find") == 0){
      scanf("%d",&value);
      struct Node *F = Find(root,value);
      if(F != NIL) printf("yes\n");
      else printf("no\n");
    }
    else if(strcmp(com,"delete") == 0){
      scanf("%d",&value);
      Delete(Find(root,value));
    }
  }

    return 0;
}

void Insert(int n){
T *p = root;
T *q = NIL;
T *r;

r = (T *)malloc(sizeof(struct Node));
r -> k = n;
r -> left = NIL;
r -> right = NIL;

while(p != NIL){
   q = p;
   if(r->k < p->k){
     p = p -> left;
   }
   else{
     p = p -> right;
   }
}

r -> parent = q;
  if(q == NIL){
    root = r;
  }
  else{
    if(r->k < q->k){
      q -> left = r;
    }
    else{
      q -> right = r;
    }
  }
}

void Inorder(T *x){
  if(x == NIL) return;
  Inorder(x -> left);
  printf(" %d",x -> k);
  Inorder(x -> right);
}

void Preorder(T *x){
  if(x == NIL) return;
  printf(" %d",x -> k);
  Preorder(x -> left);
  Preorder(x -> right);
}

T * Find(T *x, int n){
  while(x != NIL && n != x -> k){
    if(n < x -> k ) x = x -> left;
    else x = x -> right;
  }
  return x;
}

void Delete(T *x){
  struct Node *y;
  struct Node *z;

  if(x -> left == NIL || x -> right == NIL) y = x;
  else y = Successor(x);

  if(y -> left != NIL) z = y -> left;
  else z = y -> right;

  if(z != NIL) z -> parent = y -> parent;

  if(y -> parent == NIL){
    root = y;
  }
  else {
    if(y == y -> parent -> left) y -> parent -> left = z;
    else y -> parent -> right = z;
  }

  if(y != x) x -> k = y -> k;

  free(y);
}

T * Minimum(T *x){
  while(x -> left != NIL) x = x -> left;
  return x;
}

T * Successor(T *x){
  struct Node *y;

  if(x -> right != NIL) return Minimum(x -> right);

  y = x -> parent;
  while(y != NIL && x == y -> right){
    x = y;
    y = y -> parent;
  }
  return y;
}