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 <iostream>
#include <cstdlib>
//#include <vector>
using namespace std;
struct Node{
    int key;
    Node *l,*r;
};
//vector<int>p;
Node *T;
//int isn;
void insert(Node *z){

    if(T==NULL)
    {
        T=z;
        //cout<<T->key<<endl;
        return;
    }

    Node *p,*temp=T;
    while(temp!=NULL)
    {
        p=temp;
        if(z->key<temp->key)
            temp=temp->l;
        else
            temp=temp->r;
    }
    if(z->key<p->key)
        p->l=z;
    else
        p->r=z;
}
void preOrder(Node *T){
    if(T==NULL){
        //cout<<1<<endl;
        return;
    }
    cout<<' '<<T->key;
    preOrder(T->l);
    preOrder(T->r);
}
void inOrder(Node *T){
    if(T==NULL)return;
    inOrder(T->l);
    cout<<' '<<T->key;
    inOrder(T->r);
}
void find(int x){
    Node *temp=T;
    while(temp!=NULL){
        if(x<temp->key)
            temp=temp->l;
        else if(x>temp->key)
            temp=temp->r;
        else
        {
            cout<<"yes"<<endl;
            return;
        }
    }
    cout<<"no"<<endl;
}
int main(){
    int m,key;
    char com[20];
    T=NULL;
    //isn=0;
    cin>>m;
    for(int i=0;i<m;i++)
    {
        cin>>com;
        if(com[0]=='i')
        {
            cin>>key;
            Node *z=(Node* )malloc(sizeof(Node));
            z->key=key;
            z->l=NULL;
            z->r=NULL;
            insert(z);
            //cout<<1;
        }
        else if(com[0]=='p')
        {
            inOrder(T);
            cout<<endl;
            preOrder(T);
            cout<<endl;

        }
        else
        {
            cin>>key;
            find(key);
        }
    }
    return 0;
}