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

struct node{
  int key;
  struct node *right;
  struct node *left;
  struct node *parent;
};

typedef struct node *NodePointer;

NodePointer root;
NodePointer nil;

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

void insert(int k){
  NodePointer y,x,z;
  y=nil;
  x=root;
  z=(NodePointer)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(NodePointer u){
  if(u==nil)return;
  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);
}

void preorder(NodePointer u){
  if(u==nil)return;
  printf(" %d",u->key);
  preorder(u->left);  
  preorder(u->right);
}

int main(){
int n,i,x;
  char c[7];
  NodePointer t;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%s",c);
    if(strcmp(c,"find")==0){
      scanf("%d",&x);
      t=find(root,x);
      if(t!=nil)printf("yes\n");
      else printf("no\n");
    }
    else if(strcmp(c,"insert")==0){
      scanf("%d",&x);
      insert(x);
    }
    else if(strcmp(c,"print")==0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }
  return 0;
}