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 tree{
  int key;
  struct tree *parent;
  struct tree *left;
  struct tree *right;
};
struct tree *T,*NIL;
void insert(struct tree *);
int find(int);
void inorder(struct tree *);
void preorder(struct tree *);
int main(){
  int n,k,i;
  char command[10],a;
  struct tree *A;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%s%c",command,&a);
    if(!strcmp(command,"insert")){
      scanf("%d",&k);
      A=malloc(sizeof(struct tree));
      A->key=k;
      A->left=NIL;
      A->right=NIL;
      insert(A);
    }
    else if(!strcmp(command,"print")){
      inorder(T);
      printf("\n");
      preorder(T);
      printf("\n");
    }
    else{
      scanf("%d",&k);
      if(find(k)==0)printf("yes\n");
      else printf("no\n");
    }
  }
  return 0;
}
    void insert(struct tree *z){
  struct tree *x,*y;
  x=T;
  y=NIL;
  while(x!=NIL){
    y=x;
    if(x->key>z->key) x=x->left;
    else x=x->right;
  }
  z->parent=y;
  if(y==NIL){
    T=z;
  }
  else {
    if(y->key<z->key)y->right=z;
    else y->left=z;
  }
}
void inorder(struct tree *A){
  if(A==NIL)return;
  inorder(A->left);
  printf(" %d",A->key);
  inorder(A->right);
}
void preorder(struct tree *A){
  if(A==NIL)return;
  printf(" %d",A->key);
  preorder(A->left);
  preorder(A->right);
}
int find(int k){
  struct tree *x=T;
  while(x!=NIL){
    if(x->key==k)return 0;
    else if(k<x->key)x=x->left;
    else x=x->right;
  }
  return 1;
}