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 *r,*l,*p;
  int key;
};

typedef struct node * Node;

Node root, NIL;

Node treeSearch(Node u, int k)
{
  while((u != NIL) && (k != u->key)){
    if(k < u->key)
      u = u->l;
    else
      u = u->r;
  }
  return u;
}

void insert(int k)
{
  int H;
  Node x,y,z;

  x = root;
  y = NIL;
  z = malloc(sizeof(struct node));

  z->key = k;
  z->l = NIL;
  z->r = NIL;

  while(x != NIL){
    y = x;
    if(z->key < x->key)
      x = x->l;
    else
      x = x->r;
  }

  z->p = y;

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

void inorder(Node u)
{
  if(u == NIL)
    return;

  inorder(u->l);

  printf(" %d",u->key);

  inorder(u->r);
}

void preorder(Node u)
{
  if(u == NIL)
    return;

  printf(" %d",u->key);

  preorder(u->l);

  preorder(u->r);
}

int main()
{
  int n,i,a;
  char C[20];

  scanf("%d",&n);

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

    if(C[0] == 'f'){
      scanf("%d",&a);

      Node t = treeSearch(root, a);

      if(t != NIL)
        printf("yes\n");
      else
        printf("no\n");
    }

    else if(C[0] == 'i'){
      scanf("%d",&a);
      insert(a);
    }

    else if(C[0] == 'p'){

      inorder(root);

      printf("\n");

      preorder(root);

      printf("\n");
    }

  }

  return 0;
}