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>

struct node{
    struct node *right;
    struct node *left;
    struct node *parent;
    int key;
};
typedef struct node * Node;
#define NIL NULL

Node root;
/*
Node treeMinimum(Node x){


}

Node treeMaximum(Node x){


}

Node treeSearch(Node u, int k){


}

Node treeSuccessor(Node x){


}

void treeDelete(Node z){
    Node y; // node to be deleted
    Node x; // child of y



}
*/

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 = 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){
        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;
    char com[20];
    scanf("%d", &n);

    for ( i = 0; i < n; i++ ){
        scanf("%s", 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[0] == 'i' ){
            scanf("%d", &x);
            insert(x);
        } else if ( com[0] == 'p' ){
            inorder(root);
            printf("\n");
            preorder(root);
            printf("\n");
        } else if ( com[0] == 'd' ){
            scanf("%d", &x);
            //treeDelete(treeSearch(root, x));
        }
    }

    return 0;
}