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 <Find> */
#include <stdio.h>
#include <stdlib.h>

struct node
{
    struct node *right;
    int key;
    struct node *left;
};

typedef struct node * NodePointer;

void init(void);
NodePointer makenode(int);
void insert(int, NodePointer);
void preorder(NodePointer);
void inorder(NodePointer);
int find(int, NodePointer);

NodePointer head, tail;

int main()
{
    char str[7];
    int i, n, k;

    init();
    scanf("%d", &n);
    for(i=0; i<n; i++){
        scanf("%s", str);
        if(str[0] == 'i'){
            scanf("%d", &k);
            insert(k, head);
        } else if(str[0] == 'p'){
            inorder(head -> right);
            printf("\n");
            preorder(head -> right);
            printf("\n");
        } else{
            scanf("%d", &k);
            if(find(k, head -> right)){
                printf("yes\n");
            } else{
                printf("no\n");
            }
        }
    }
    return 0;
}

void init(void)
{
    head = makenode(-1);
    tail = makenode(-1);
    head -> right = tail;
    head -> left = tail;
}

NodePointer makenode(int k)
{
    NodePointer x;

    x = malloc(sizeof(struct node));
    x -> key = k;
    x -> left = x -> right = tail;

    return x;
}

void insert(int k, NodePointer p)
{
    if(k < p -> key){
        if(p -> left == tail){
            p -> left = makenode(k);
        } else{
            insert(k, p -> left);
        }
    } else{
        if(p -> right == tail){
            p -> right = makenode(k);
        } else{
            insert(k, p -> right);
        }
    }
}

void preorder(NodePointer node)
{
    if(node != tail){
        printf(" %d", node -> key);
        preorder(node -> left);
        preorder(node -> right);
    }
}

void inorder(NodePointer node)
{
    if(node != tail){
        inorder(node -> left);
        printf(" %d", node -> key);
        inorder(node -> right);
    }
}

int find(int k, NodePointer node)
{
    if(node == tail){
        return 0;
    }

    if(node -> key == k){
        return 1;
    } else if(node -> key < k){
        return find(k, node -> right);
    } else{
        return find(k, node -> left);
    }
}