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 data{
  int key;
  struct data *right,*left,*parent;
};

struct data *root,*NIL;

struct data * find(struct data *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){
  struct data *y = NIL;
  struct data *x = root;
  struct data *z;

  z = (struct data *)malloc(sizeof(struct data));
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 data *cin){
  if(cin == NIL){
    return;
  }
  inorder(cin -> left);
  printf(" %d",cin -> key);
  inorder(cin -> right);
}

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

int main(){
  int num,i,x;
  char mozi[1000];

scanf("%d",&num);
for(i = 0;i < num;i++){
  scanf("%s",mozi);
  if(mozi[0] == 'f'){
    scanf("%d",&x);
    struct data *t = find(root,x);
    if(t != NIL){
      printf("yes\n");
    }
    else{
      printf("no\n");
    }
  }
  else if(strcmp(mozi,"insert") == 0){
    scanf("%d",&x);
    insert(x);
  }
  else if(strcmp(mozi,"print") == 0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }
    return 0;
}