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>

struct Node {
  int key;
  struct Node *right, *left, *parent;
};
typedef struct Node Node;

Node *root, *NIL;

Node * treeMinimum(Node *x) {
  while(x->left != NIL)
    x = x->left;
  return x;
}

Node * find(Node *u, int k) {
  while(u != NIL && k != u->key) {
    if(k < u->key) u = u->left;
    else u = u->right;
  }
  return u;
}

Node * treeSuccessor(Node *x) {
  if(x->right != NIL) return treeMinimum(x->right);
  Node *y = x->parent;
  while(y != NIL && x == y->right) {
    x = y;
    y = y->parent;
  }
  return y;

}

void treeDelete(Node *z) {
  Node *y; // 削除する対象
  Node *x; // yの子

  // 削除する節点を決める
  if(z->left == NIL || z->right == NIL) y = z;
  else y = treeSuccessor(z);

  // yの子xを決める
  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;
  }
}

void insert(int k) {
  Node *y = NIL;
  Node *x = root;
  Node *z;
  
  z = (Node *)malloc(sizeof(Node));
  z->key   = k;
  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;
    }
  }
}

void inorder(Node *u) {
  if(u == NIL) return;
  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);
}

void preorder(Node *u) {
  if(u == NIL) return;
  printf(" %d",u->key);
  preorder(u->left);
  preorder(u->right);
}
  
int main(void) {
  int n, i, x;
  char com[16];
  scanf("%d",&n);
  
  for(i=0;i<n;i++) {
    scanf("%s",com);
    if(!strcmp(com,"find")) {
      scanf("%d",&x);
      Node *t = find(root,x);
      if(t != NIL) printf("yes\n");
      else printf("no\n");
    } else if(!strcmp(com,"insert")) {
      scanf("%d",&x);
      insert(x);
    } else if(!strcmp(com,"print")) {
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    } else if(!strcmp(com,"delete")) {
      scanf("%d",&x);
      treeDelete(find(root,x));
    }
  }

  return 0;
}