Heap Sort — Practice Tasks¶

class MinHeap:
    def __init__(self): self._h = []
    def push(self, x): pass  # TODO: append + sift-up
    def pop(self): pass      # TODO: swap root with last, pop, sift-down
    def peek(self): return self._h[0]

def heap_sort(arr):
    # TODO: build max-heap, repeatedly swap root to end and sift-down
    pass

import heapq
def heap_sort_builtin(arr):
    h = list(arr)
    heapq.heapify(h)  # O(n)
    return [heapq.heappop(h) for _ in range(len(h))]

def sift_down(heap, i, n):
    # TODO: iterative version (no recursion)
    pass

def kth_smallest(arr, k):
    # TODO: build min-heap, pop k-1 times, return next
    pass

def kth_largest(arr, k):
    # TODO: maintain min-heap of size k; smallest of top-k at root
    pass

def top_k_frequent(nums, k):
    # TODO: count frequencies, then heap of (-freq, num) → top k
    pass

import heapq
def merge_k_lists(lists):
    # TODO: heap with (head_val, list_idx, node)
    pass

import heapq
def priority_queue_demo():
    # TODO: store tuples (priority, item); push/pop in priority order
    pass

import heapq
def dijkstra(graph, start):
    # graph: {u: [(v, weight), ...]}
    dist = {start: 0}
    pq = [(0, start)]
    # TODO: pop min-distance node, relax edges, push updated distances
    return dist

import heapq
def huffman_codes(freqs):
    # freqs: {char: count}
    # TODO: build huffman tree using min-heap
    return {}

import heapq
def max_sliding_window_heap(nums, k):
    # TODO: max-heap (negate values); lazy deletion of out-of-window items
    pass

import heapq
class MedianFinder:
    def __init__(self):
        self.lo = []  # max-heap (negate)
        self.hi = []  # min-heap
    def add(self, num): pass    # TODO
    def median(self): pass       # O(1)

class IndexedMinHeap:
    """Supports decrease_key(item, new_priority) in O(log n)."""
    def __init__(self):
        self._h = []
        self._idx = {}  # item → position in _h
    def push(self, item, priority): pass  # TODO
    def pop(self): pass
    def decrease_key(self, item, new_priority): pass