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<bits/stdc++.h>
using namespace std;

struct Node
{
    int key;
    Node *parent,*left,*right;
};
Node *root,*NIL;

Node* Find(Node *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)
{
    Node *y=NIL;
    Node *x=root;
    Node *z;

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

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

int main()
{
    int n,i,x;
    string com;

    scanf("%d",&n);

    for(i=0;i<n;i++)
    {
        cin>>com;
        if(com[0]=='f')
        {
            scanf("%d",&x);
            Node *t=Find(root,x);
            if(t!=NIL)printf("yes\n");
            else printf("no\n");
        }
        else if(com=="insert")
        {
            scanf("%d",&x);
            Insert(x);
        }
        else if(com=="print")
        {
            inorder(root);
            printf("\n");
            preorder(root);
            printf("\n");
        }
    }

 	return 0;
}