大根堆算法代码实现

下面是大根堆的算法代码实现，包括插入元素、删除堆顶元素和向下调整操作：

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

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

    def pop_max(self):
        if len(self.heap) == 0:
            return None
        elif len(self.heap) == 1:
            return self.heap.pop()
        else:
            max_val = self.heap[0]
            self.heap[0] = self.heap.pop()
            self._sift_down(0)
            return max_val

    def _sift_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._sift_up(parent)

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

其中，`insert` 方法用于插入元素，向上调整以满足大根堆的性质；`pop_max` 方法用于删除堆顶元素，将最后一个元素放到堆顶，然后向下调整以满足大根堆的性质；`_sift_up` 方法用于向上调整，`_sift_down` 方法用于向下调整。