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>

typedef struct _tree_t {
	int id;
	struct _tree_t *p, *l, *r;
} tree_t;

tree_t* tree_insert(tree_t* root, int id){
	tree_t *y = NULL;
	tree_t *x = root;
	tree_t *z = (tree_t*)malloc(sizeof(tree_t));
	z->id = id;
	z->l = z->r = z->p = NULL;

	while(x != NULL) {
	    y = x;
	    if(z->id < x->id) {
	        x = x->l;
	    } else { 
	        x = x->r;
	    }
	}
	z->p = y;
	if(y == NULL) {
    	root = z;
	} else if(z->id < y->id) {
	    y->l = z;
	} else { 
	    y->r = z;
	}
	
	return root;
}

void print_find(tree_t *tree, int id) {
	if(tree==NULL) {
		printf("no\n");
		return;
	}
	
	if(id == tree->id) {
		printf("yes\n");
		return;
	} else if(id < tree->id) {
		print_find(tree->l, id);
	} else {
		print_find(tree->r, id);
	}
}

void print_preorder(tree_t *tree) {
    printf(" %d", tree->id);
    if(tree->l != NULL) print_preorder(tree->l);
    if(tree->r != NULL) print_preorder(tree->r);
}

void print_inorder(tree_t *tree) {
    if(tree->r == NULL && tree->l == NULL) {
        printf(" %d", tree->id);
    } else if(tree->r == NULL) {
        print_inorder(tree->l);
        printf(" %d", tree->id);
    } else if(tree->l == NULL) {
        printf(" %d", tree->id);
        print_inorder(tree->r);
    } else {
        print_inorder(tree->l);
        printf(" %d", tree->id);
        print_inorder(tree->r);
    }
}

int main(void) {
	int i, n, id;
	char buff[100];
	tree_t *root = NULL;
	scanf("%d\n", &n);
	for(i=0;i<n;i++) {
		scanf("%s %d\n", buff, &id);
		if(buff[0] == 'i') {
			root = tree_insert(root, id);
		} else if(buff[0] == 'f') {
			print_find(root, id);
		} else if(buff[0] == 'p') {
			print_inorder(root);
			printf("\n");
			print_preorder(root);
			printf("\n");
		}
	}
	
	return 0;
}