class Node:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

class BST:
    def __init__(self):
        self.root = None
    
    def insert(self, value):
        if not self.root:
            self.root = Node(value)
        else:
            self._insert_recursive(self.root, value)
    
    def _insert_recursive(self, node, value):
        if value < node.value:
            if node.left is None:
                node.left = Node(value)
            else:
                self._insert_recursive(node.left, value)
        else:
            if node.right is None:
                node.right = Node(value)
            else:
                self._insert_recursive(node.right, value)
    
    def search(self, value):
        return self._search_recursive(self.root, value)
    
    def _search_recursive(self, node, value):
        if node is None or node.value == value:
            return node
        if value < node.value:
            return self._search_recursive(node.left, value)
        return self._search_recursive(node.right, value)
    
    def inorder(self):
        result = []
        self._inorder_recursive(self.root, result)
        return result
    
    def _inorder_recursive(self, node, result):
        if node:
            self._inorder_recursive(node.left, result)
            result.append(node.value)
            self._inorder_recursive(node.right, result)

bst = BST()
for val in [5, 3, 7, 1, 4, 6, 8]:
    bst.insert(val)

print(bst.inorder())  # [1, 3, 4, 5, 6, 7, 8]

import heapq

# Min heap
heap = []
heapq.heappush(heap, 3)
heapq.heappush(heap, 1)
heapq.heappush(heap, 4)
heapq.heappush(heap, 1)
heapq.heappush(heap, 5)

print(heapq.heappop(heap))  # 1

# Max heap (negate values)
max_heap = []
heapq.heappush(max_heap, -3)
heapq.heappush(max_heap, -1)
heapq.heappush(max_heap, -4)

print(-heapq.heappop(max_heap))  # 4

# K largest elements
nums = [3, 1, 4, 1, 5, 9, 2, 6]
print(heapq.nlargest(3, nums))  # [9, 6, 5]

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end = False

class Trie:
    def __init__(self):
        self.root = TrieNode()
    
    def insert(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_end = True
    
    def search(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                return False
            node = node.children[char]
        return node.is_end

trie = Trie()
trie.insert("apple")
trie.insert("app")
trie.insert("application")

print(trie.search("apple"))      # True
print(trie.search("app"))        # True
print(trie.search("application")) # True
print(trie.search("apply"))      # False