How do I implement a binary heap in Python?

How do I implement a binary heap in Python?

To implement a binary heap in Python, you can use a list to represent the heap. Would you like to see a code example?

Yes, please provide a code example.

Here's a simple implementation of a min-heap:

class MinHeap:
    def __init__(self):
        self.heap = []

    def insert(self, val):
        self.heap.append(val)
        self._bubble_up(len(self.heap) - 1)

    def _bubble_up(self, index):
        parent = (index - 1) // 2
        if index > 0 and self.heap[index] < self.heap[parent]:
            self.heap[index], self.heap[parent] = self.heap[parent], self.heap[index]
            self._bubble_up(parent)

    def extract_min(self):
        if len(self.heap) == 0:
            return None
        if len(self.heap) == 1:
            return self.heap.pop()
        root = self.heap[0]
        self.heap[0] = self.heap.pop()
        self._bubble_down(0)
        return root

    def _bubble_down(self, index):
        smallest = index
        left = 2 * index + 1
        right = 2 * index + 2
        if left < len(self.heap) and self.heap[left] < self.heap[smallest]:
            smallest = left
        if right < len(self.heap) and self.heap[right] < self.heap[smallest]:
            smallest = right
        if smallest != index:
            self.heap[index], self.heap[smallest] = self.heap[smallest], self.heap[index]
            self._bubble_down(smallest)

What are the time complexities for insert and extract operations?

The time complexity for both insert and extract operations in a binary heap is O(log n), where n is the number of elements in the heap.