Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ 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

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

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>

struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
#define NIL NULL

Node root;

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

Node treeMaximum(Node x){
  while(x -> right != NIL) {
    x = x -> right;
  }
  return x;
}

Node treeSearch(Node u, int k){
  if(u == NIL || k == u -> key) {
    return u;
  }else if(k < u -> key) {
    return treeSearch(u -> left, k);
  }else{
    return treeSearch(u -> right, k);
  }
}

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

void treeDelete(Node z){
  Node y; // node to be deleted
  Node x; // child of y
  if(z -> left == NIL || z -> right == NIL) {
    y = z;
  }else{
    y = treeSuccessor(z);
  }

  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;
  }
  free(y);
}

void insert(int k){
  Node y = NIL;
  Node x = root;
  Node z;

  z = malloc(sizeof(struct 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);
}

void search(int x) {
  Node b;
  b = treeSearch(root, x);
  if(b != NIL) {
    printf("yes\n");
  }else{
    printf("no\n");
  }
}

int main(){
  int n, i, x;
  char com[20];
  scanf("%d", &n);

  for ( i = 0; i < n; i++ ){
    scanf("%s", com);
    if ( com[0] == 'f' ){
      scanf("%d", &x);
      Node t = treeSearch(root, x);
      if ( t != NIL ) printf("yes\n");
      else printf("no\n");
    } else if ( com[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( com[0] == 'p' ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    } else if ( com[0] == 'd' ){
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }
  }

  return 0;
}