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<string.h>
#include<stdlib.h>

typedef struct tree{
  int ki;
  struct tree *right,*left,*parent;
}tree;

tree *root,*nil;

tree* minimum(tree *);
tree * find(tree*,int);
tree* success(tree *);
void delete(tree *);
void insert(int);
void inwalk(tree *);
void prwalk(tree *);

tree* minimum(tree *a)
{
  while(a->left != nil)
    a = a->left;
  return a;
}

tree * find(tree *z,int k)
{
  while(z != nil && k != z->ki) {
    if(k < z->ki) {
      z = z->left;
    }else{
      z = z->right;
    }
  }
    return z;
}

tree* success(tree *b)
{
  if(b->right != nil)
    return minimum(b->right);
  tree *B = b->parent;
  while(B != nil && b == B->right) {
    b = B;
    B = B->parent;
  }
  return B;
}

void delete(tree *f)
{
  tree *d;
  tree *c;

  if(f->left == nil || f->right == nil)
    d = f;
  else
    d = success(f);

  if(d->left != nil) {
    c = d->left;
  }else{
    c = d->right;
  }

  if(c != nil) {
    c->parent = d->parent;
  }

  if(d->parent == nil) {
    root = c;
  }else{
    if(d == d->parent->left) {
      d->parent->left = c;
    }else{
      d->parent->right = c;
    }
  }

  if(d != f) {
    f->ki = d->ki;
  }

  free(d);
}


void insert(int k)
{
  struct tree *a=root,*b=nil,*c;

  c = (struct tree *)malloc(sizeof(struct tree));
  c->ki = k;
  c->left = nil;
  c->right = nil;

  while(a!=nil) {
    b = a;
    if(c->ki < a->ki) {
      a = a->left;
    }else{
      a = a->right;
    }
  }

  c->parent = b;
  if(b == nil) {
    root = c;
  }else{
    if(c->ki < b->ki) {
      b->left = c;
    }else{
      b->right = c;
    }
  }
}

void inwalk(tree *x)
{
  if(x == nil)
    return;
  inwalk(x->left);
  printf(" %d",x->ki);
  inwalk(x->right);
}

void prwalk(tree *y)
{
  if(y == nil)
    return;
  printf(" %d",y->ki);
  prwalk(y->left);
  prwalk(y->right);
}

int main()
{
  int m,k,i;
  char ins[10];

  scanf("%d",&m);

  for(i=0;i<m;i++) {
    scanf("%s",ins);
    if(ins[0] == 'f') { /*f = find*/
      scanf("%d",&k);
      tree *t = find(root,k);
      if(t != nil) {
	printf("yes\n");
      }else{
	printf("no\n");
      }
    }else if(ins[0] == 'i') { /*i = insert*/
      scanf("%d",&k);
      insert(k);
    }else if(ins[0] == 'p') { /*p = print*/
      inwalk(root);
      printf("\n");
      prwalk(root);
      printf("\n");
    }else if(ins[0] == 'd') {
      scanf("%d",&k);
      delete(find(root,k));
    }
  }

  return 0;
}