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>
#define MAX 500000
typedef struct pp{
    int num;
    struct pp *right, *left, *parent;
}PO;
PO *root, *nothing;
int n,input, anum = 0, fnum;
char command[7];
int finder[MAX];

void ins(int n)
{
    PO *x = root;
    PO *y = nothing;
    PO *v;//what i want to put as x;
    v = (PO *)malloc(sizeof(PO));
    v->num = n;
    v->left = nothing;
    v->right = nothing;
    while(1)
    {
        if(x == nothing) break;
        y = x;
        if(v->num < x->num) x = x->left;
        else x = x->right;
    }
    v->parent = y;
    if(y == nothing) root = v;
    else
    {
        if(v->num < y->num) y->left = v;
        else y->right = v;
    }
}

void no2find(PO *r)
{
    if(r == nothing) return;
    if(r->num == input)
    {
        fnum =1;
        return;
    }
    if(input>=r->num) no2find(r->right);
    else no2find(r->left);
}

int find(PO *r)
{
    fnum =0;
    no2find(r);//get datas
    return fnum;
}

void ino(PO *r)
{
    if(r == nothing) return;
    ino(r->left);
    printf(" %d", r->num);
    ino(r->right);
}

void pre(PO *r)
{
    if(r == nothing) return;
    printf(" %d", r->num);
    pre(r->left);
    pre(r->right);
}

int main()
{
    scanf("%d", &n);
    for(int i=0; i<n; i++)
    {
        scanf("%s", command);
        if(command[0] == 'i')
        {
            scanf("%d", &input);
            ins(input);
            anum++;
        }
        else if(command[0] == 'p')
        {
            ino(root);
            printf("\n");
            pre(root);
            printf("\n");
        }
        else
        {
            scanf("%d", &input);
            if(find(root) == 0) printf("no\n");
            else printf("yes\n");
        }
    }
    return 0;
}