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<string.h>
struct node{
  struct node *p;
  struct node *left;
  struct node *right;
  int key;
} ;

int flag = 0;
typedef struct node Node;
Node *root, *NIL;

void Insert(int);
void Inorder(Node *);
void Preorder(Node *);
void Find(Node *, int);

int main(){
  int n,i,m;
  char in[7],insert[7] = "insert",find[5] = "find",print[6] = "print";
  scanf("%d",&n);
  for(i = 0; i < n; i++){
    scanf("%s",in);
    (void)getchar();
    if(strcmp(in, insert) == 0) {
      scanf(" %d",&m);
      Insert(m);
    }
    else if(strcmp(find, in) == 0) {
      scanf("%d",&m);
      Find(root,m);
      if(flag == 1){
        printf("yes\n");
      }
      else{
        printf("no\n");
      }
      flag = 0;
    }
    else {
      Inorder(root);
      printf("\n");
      Preorder(root);
      printf("\n");
    }
  }
  return 0;
}
void Insert(int Ins) {
  Node *x = NIL;
  Node *y = root;
  Node *z;

  z = malloc(sizeof(Node));
  z -> key = Ins;
  z -> left = NIL;
  z -> right = NIL;
  while(y != NIL) {
    x = y;
    if(z -> key < y -> key){
      y = y -> left;
    }
    else{
      y = y -> right;
    }
  }

  z -> p = x;
  if(x == NIL){
    root = z;
  }
  else {
    if(z -> key < x -> key){
      x -> left = z;
    }
    else{
      x -> right = z;
    }
  }
}

void Inorder(Node *n) {
  if(n == NIL){
    return;
  }
  else {
    Inorder(n -> left);
    printf(" %d", n->key);
    Inorder(n -> right);
  }
}

void Preorder(Node *n) {
  if(n == NIL){
    return 0;
  }
  else {
    printf(" %d", n->key);
    Preorder(n -> left);
    Preorder(n -> right);
  }
}
void Find(Node *n, int k) {
    if(n == NIL){
      return;
    }
  else {
    if(n -> key == k) {
      flag = 1;
      return 0;
    }
  }
    if(n -> key > k) {
      Find(n -> left, k);
      return;
    }
    else {
      Find(n -> right, k);
      return 0;
    }
}