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>
#include<string.h>

#define YOSHI 1000000

struct Node{
    int key;
    struct Node *left;
    struct Node *right;
    struct Node *parent;
};

struct Node *root,*NIL;

void insert(int k){
    struct Node *y = NIL;
    struct Node *x = root;
    struct Node *z;
    
    z = (struct Node *)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(struct Node *u){
    if(u == NIL){
        return;
    }
    inorder(u -> left);
    printf(" %d",u -> key);
    inorder(u -> right);
}

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

void *find(struct Node *u,int k){
    while((u != NIL) && (k != u -> key)){
        if(k < u -> key){
            u = u -> left;
        }
        else{
            u = u -> right;
        }
    }
    return u;
}

int main(){
    int m,i,x;
    char com[6];
    struct Node *t;
    scanf("%d",&m);
    
    for(i = 0;i < m;i++){
        scanf("%s",com);
        if(strcmp(com,"insert") == 0){
            scanf("%d",&x);
            insert(x);
        }
        else if(strcmp(com,"print") == 0){
            inorder(root);
            printf("\n");
            preorder(root);
            printf("\n");
        }
        else if(strcmp(com,"find") == 0){
            scanf("%d",&x);
            t = find(root,x);
            if(t != NIL){
                printf("yes\n");
            }
            else{
                printf("no\n");
            }
        }
    }
    return 0;
}