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)

/**
  * BInary Search tree (insert & search)
  * output 1)node_number, 2)parent_number, 3)depth, 4)kind_of_node, 5)child_list
  */

/* inclution */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>

/* Definition */
#define MAX 500000
#define LEN 10

/* Global Variables */
struct Node {
  int key;
  struct Node *right, *left, *parent;
};

/* Prototype */
void insert(int);
struct Node* find(struct Node*, int);
void inOrderWalk(struct Node*);
void preOrderWalk(struct Node*);

struct Node *root, *NIL;

int n;

/* main */
int main(){
  int i,x; //n: length of input, z: insert node key
  char str[LEN]; //insert???????´?
  
  /* input the number of A[] */
  scanf("%d",&n);
  
  /* input datas */
  for(i=0;i<n;i++){
    scanf("%s", str);
    if(!strcmp(str, "find")) {
      scanf("%d", &x);
      struct Node *result = find(root, x);
      if(result!=NIL) {
        printf("yes\n");
      }else {
        printf("no\n");
      }
    }else if(!strcmp(str, "insert")) {
      scanf("%d", &x);
      insert(x);
    }else if(!strcmp(str, "print")) {
      inOrderWalk(root);
      printf("\n");
      preOrderWalk(root);
      printf("\n");
    }
  }

  return 0;
}

/* insertion */
void insert(int k) {
  struct Node *y = NIL; //x ??? ???
  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) { // T ???????????´???
    root = z;
  }else if (z->key < y->key) {
    y->left = z; // z ??? y ?????????????????????
  }else {
    y->right = z; // z ??? y ?????????????????????
  }
}

struct Node *find(struct Node *v, int k) {
  while(v!=NIL && k!=v->key) {
    if(k<v->key) {
      v = v->left;
    }else {
      v = v->right;
    }
  }
  return v;
}

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

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