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 <cstdio>
#include <cstring>
#include <cstdlib>

typedef struct tree_{
    int value;
    struct tree_ *left;
    struct tree_ *right;
}tree;

void preorder(tree *p){
    if(p==NULL)return;
    printf(" %d",p->value);
    preorder(p->left);
    preorder(p->right);
}

void inorder(tree *p){
    if(p==NULL)return;
    inorder(p->left);
    printf(" %d",p->value);
    inorder(p->right);
}

tree *insert(tree *p, int x){
    if(p==NULL){
        p = (tree *)malloc(sizeof(tree));
        p->value = x;
        p->left = NULL;
        p->right = NULL;
    }else{
        if(p->value>x)p->left = insert(p->left, x);
        else if(p->value<x)p->right = insert(p->right, x);
    }
    return p;
}

bool find(tree *p, int x){
    bool ans;
    if(p==NULL)ans = false;
    else if(p->value>x)ans = find(p->left, x);
    else if(p->value<x)ans = find(p->right, x);
    else ans = true;
    return ans;
}

int main(){
    int i, n, x;
    char cmd[7];
    tree *root = NULL;
    scanf("%d",&n);
    for(i=0;i<n;i++){
        scanf("%s",cmd);
        if(strcmp(cmd,"insert")==0){
            scanf("%d",&x);
            root = insert(root, x);
        }else if(strcmp(cmd,"print")==0){
            inorder(root);
            printf("\n");
            preorder(root);
            printf("\n");
        }else if(strcmp(cmd,"find")==0){
            scanf("%d",&x);
            if(find(root, x))printf("yes\n");
            else printf("no\n");
        }else return -1;
    }
    return 0;
}