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>
#include <assert.h>
#define N 500001

typedef struct tree{
  int key;
  struct tree *parent;
  struct tree *left;
  struct tree *right;
} Tree;

Tree *createtree(int);
void insert(Tree *, int);
void find(Tree *, int);
void inorderwalk(Tree *);
void preorderwalk(Tree *);

Tree *root = NULL;

int main(){

  int m, x[N], i, j;
  char order[N][7];

  scanf("%d", &m);
  for(i = 0; i < m; i++){
    scanf(" %s", order[i]);
    if(order[i][0] != 'p') scanf("%d", &x[i]);
  }

  for(i = 0; i < m; i++){
    if(order[i][0] == 'i'){
      insert(root, x[i]);
    } 
    else if(order[i][0] == 'f'){
      find(root, x[i]);
    }
    else{
      assert(root!=NULL);
      inorderwalk(root);
      printf("\n");
      preorderwalk(root);
      printf("\n");
    }
   
  }

  return 0;
}

void insert(Tree *t, int v){
  Tree *x, *y, *z;
  z =  createtree(v);
  y = NULL;
  x = t;

  while(x != NULL){
    y = x;
    if(z->key < x->key) x = x->left;
    else x = x->right;
  }

  z->parent = y;

  if(y == NULL) root = z;
  else if(z->key < y->key) y->left = z;
  else y->right = z;  
}

void find(Tree *t, int v){
  Tree *x;
  int flag = 0;

  x = t;

 while(x != NULL){
   if(v == x->key){
     flag = 1;
     break;
   }
   if(v < x->key) x = x->left;
   else x = x->right;
  }

 if(flag == 1) printf("yes\n");
 else printf("no\n");
}

void inorderwalk(Tree *x){
  if(x->left != NULL) inorderwalk(x->left);
  printf(" %d",x->key);
  if(x->right != NULL) inorderwalk(x->right);
}

void preorderwalk(Tree *x){
  printf(" %d",x->key);
  if(x->left != NULL) preorderwalk(x->left);
  if(x->right != NULL) preorderwalk(x->right);
}

Tree *createtree(int key){
  Tree *tree = (Tree *)malloc( sizeof(Tree) );
  tree->key = key;
  tree->parent = NULL;
  tree->left = NULL;
  tree->right = NULL;
  return tree;
}