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>
#define N 500001

int key[N];
int left[N];
int right[N];
int root;
int head;

void printpre(int x){
    if(x == -1) return;
    printf(" %d", key[x]);
    printpre(left[x]);
    printpre(right[x]);
}

void printin(int x){
    if(x == -1) return;
    printin(left[x]);
    printf(" %d", key[x]);
    printin(right[x]);
}

int find(int x, int y){
    if(x == -1)
        return -1;
    if(y < key[x])
        return find(left[x], y);
    else if(y == key[x])
        return x;
    else
        return find(right[x], y);
}

void insert(int x){
    int y = -1;
    int z = root;
    while(z != -1){
        y = z;
        if(x < key[z])
            z = left[z];
        else
            z = right[z];
    }

    if(y == -1) {
        root = head;
    } else if(x < key[y]) {
        left[y] = head;
    } else {
        right[y] = head;
    }
    key[head] = x;
    left[head] = -1;
    right[head] = -1;
    head++;
}

int main(void){
    int n;
    scanf("%d", &n);
    root = -1;
    while(n--){
        char cmd[8];
        scanf("%s", cmd);
        if(cmd[0] == 'i'){
            int z;
            scanf("%d", &z);
            insert(z);
        } else if(cmd[0] == 'f') {
            int z;
            scanf("%d", &z);
            printf("%s\n", find(root, z) == -1 ? "no" : "yes");
        } else {
            printin(root);
            puts("");
            printpre(root);
            puts("");
        }
    }
}