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, *left, *parent;
};

struct Node *root,*NIL;

void insert(int);
void inorder(struct Node *);
void preorder(struct Node *);
int search(struct Node *,int);

int main(){
  int m,i,z;
  char s[10];
  int *find,n;
  scanf("%d",&m);
  find = (int *)malloc(sizeof(int)*m);

  for(i=0; i<m; i++){
    scanf("%s",s);
    if(strcmp(s,"insert") == 0){
      scanf("%d",&z);
      insert(z);
    }
    else if(strcmp(s,"print") == 0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(strcmp(s,"find") == 0){
        scanf("%d",&n);
        if(search(root,n) == 0) printf("yes\n");
        else printf("no\n");
    }
  }
  return 0;
}

void insert(int k){
  struct Node *y = NIL;
  struct Node *x = root;
  struct Node *z;

  z = (struct Node *)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(struct Node *u){
  if(u == NIL) return;
  inorder(u->left);
  printf(" %d", u->key);
  inorder(u->right);
}

void preorder(struct Node *u){
  if(u == NIL) return;
  printf(" %d", u->key);
  preorder(u->left);
  preorder(u->right);
}

int search(struct Node *u, int n){
    while(u != NULL){
        if(n == u->key) return 0;
        else if(n < u->key) u = u->left;
        else u = u->right;
    }
    return -1;
}