1import heapq
2 
3# HEAP: find top-K largest numbers
4def top_k_largest(nums: list, k: int) -> list:
5    min_heap = []                          # min-heap of size k
A min-heap of size K naturally tracks the K largest elements: any element larger than the heap minimum (the Kth largest seen so far) displaces it. The minimum of the heap is always the Kth largest.
6    for num in nums:
7        heapq.heappush(min_heap, num)      # push each number
8        if len(min_heap) > k:
Pop AFTER pushing, not before. Push first ensures the new element is considered. If it is too small, popping removes it immediately. The heap always holds exactly K elements.
9            heapq.heappop(min_heap)        # remove smallest if over k
10    return sorted(min_heap, reverse=True)  # result is top-k largest
11 
12# TRIE: insert and search
13class TrieNode:
14    def __init__(self):
Each TrieNode has a children dict (not a fixed-size array). This handles any alphabet without pre-allocating 26 slots. For a 26-character alphabet, an array is faster but uses more memory.
15        self.children = {}                 # char -> TrieNode
16        self.is_end = False                # marks end of a word
17 
18class Trie:
19    def __init__(self):
20        self.root = TrieNode()
21 
22    def insert(self, word: str):
23        node = self.root
24        for char in word:
is_end marks where a word terminates. Without it, "car" and "card" would be indistinguishable — traversing to "r" would find the same node whether you inserted "car" or only "card".
25            if char not in node.children:
26                node.children[char] = TrieNode()
27            node = node.children[char]
28        node.is_end = True                 # mark end of word
29 
30    def search(self, word: str) -> bool:
31        node = self.root
32        for char in word:
33            if char not in node.children:
34                return False
35            node = node.children[char]
36        return node.is_end