1. 最大堆
代码语言：javascript复制class MaxHeap:
def __init__(self):
self.heap = []
def parent(self, i):
return (i - 1) // 2
def left_child(self, i):
return 2 * i 1
def right_child(self, i):
return 2 * i 2
def get_max(self):
if not self.heap:
return None
return self.heap[0]
def insert(self, item):
self.heap.append(item)
self._heapify_up(len(self.heap) - 1)
def extract_max(self):
if not self.heap:
return None
max_item = self.heap[0]
last_item = self.heap.pop()
if self.heap:
self.heap[0] = last_item
self._heapify_down(0)
return max_item
def _heapify_up(self, i):
while i > 0 and self.heap[i] > self.heap[self.parent(i)]:
self.heap[i], self.heap[self.parent(i)] = self.heap[self.parent(i)], self.heap[i]
i = self.parent(i)
def _heapify_down(self, i):
max_index = i
left = self.left_child(i)
if left < len(self.heap) and self.heap[left] > self.heap[max_index]:
max_index = left
right = self.right_child(i)
if right < len(self.heap) and self.heap[right] > self.heap[max_index]:
max_index = right
if i != max_index:
self.heap[i], self.heap[max_index] = self.heap[max_index], self.heap[i]
self._heapify_down(max_index)
if __name__ == '__main__':
max_heap = MaxHeap()
max_heap.insert(1)
max_heap.insert(2)
max_heap.insert(0)
max_heap.insert(8)
print(max_heap.get_max())2. 最小堆
代码语言：javascript复制class MinHeap:
def __init__(self):
self.heap = []
def parent(self, i):
return (i - 1) // 2
def left_child(self, i):
return 2 * i 1
def right_child(self, i):
return 2 * i 2
def get_min(self):
if not self.heap:
return None
return self.heap[0]
def insert(self, item):
self.heap.append(item)
self._heapify_up(len(self.heap) - 1)
def extract_min(self):
if not self.heap:
return None
min_item = self.heap[0]
last_item = self.heap.pop()
if self.heap:
self.heap[0] = last_item
self._heapify_down(0)
return min_item
def _heapify_up(self, i):
while i > 0 and self.heap[i] < self.heap[self.parent(i)]:
self.heap[i], self.heap[self.parent(i)] = self.heap[self.parent(i)], self.heap[i]
i = self.parent(i)
def _heapify_down(self, i):
min_index = i
left = self.left_child(i)
if left < len(self.heap) and self.heap[left] < self.heap[min_index]:
min_index = left
right = self.right_child(i)
if right < len(self.heap) and self.heap[right] < self.heap[min_index]:
min_index = right
if i != min_index:
self.heap[i], self.heap[min_index] = self.heap[min_index], self.heap[i]
self._heapify_down(min_index)3. 最小-最大堆
最小-最大堆的性质是：树中偶数层的每个节点都小于它的所有后代，而树中奇数层的每个节点都大于它的所有后代。
用途 双端优先级队列
代码语言：javascript复制class MinMaxHeap:
def __init__(self):
self.heap = []
def parent(self, i):
return (i - 1) // 2
def left_child(self, i):
return 2 * i 1
def right_child(self, i):
return 2 * i 2
def get_min(self):
if not self.heap:
return None
return self.heap[0]
def get_max(self):
if not self.heap:
return None
if len(self.heap) == 1:
return self.heap[0]
if len(self.heap) == 2:
return self.heap[1] if self.heap[1] > self.heap[0] else self.heap[0]
return self.heap[1] if self.heap[1] > self.heap[2] else self.heap[2]
def insert(self, item):
self.heap.append(item)
self._heapify_up(len(self.heap) - 1)
def extract_min(self):
if not self.heap:
return None
min_item = self.heap[0]
last_item = self.heap.pop()
if self.heap:
self.heap[0] = last_item
self._heapify_down_min(0)
return min_item
def extract_max(self):
if not self.heap:
return None
max_item = self.get_max()
max_index = self.heap.index(max_item)
self.heap[max_index] = self.heap[-1]
self.heap.pop()
if max_index < len(self.heap):
self._heapify_down_max(max_index)
return max_item
def _heapify_up(self, i):
if i == 0:
return
parent = self.parent(i)
if self.heap[i] < self.heap[parent]:
self.heap[i], self.heap[parent] = self.heap[parent], self.heap[i]
self._heapify_up_max(parent)
else:
self._heapify_up_min(i)
def _heapify_up_min(self, i):
grandparent = self.parent(self.parent(i))
if i > 2 and self.heap[i] < self.heap[grandparent]:
self.heap[i], self.heap[grandparent] = self.heap[grandparent], self.heap[i]
self._heapify_up_min(grandparent)
def _heapify_up_max(self, i):
grandparent = self.parent(self.parent(i))
if i > 2 and self.heap[i] > self.heap[grandparent]:
self.heap[i], self.heap[grandparent] = self.heap[grandparent], self.heap[i]
self._heapify_up_max(grandparent)
def _heapify_down_min(self, i):
while True:
min_index = i
left = self.left_child(i)
if left < len(self.heap) and self.heap[left] < self.heap[min_index]:
min_index = left
right = self.right_child(i)
if right < len(self.heap) and self.heap[right] < self.heap[min_index]:
min_index = right
if i != min_index:
self.heap[i], self.heap[min_index] = self.heap[min_index], self.heap[i]
i = min_index
else:
break
def _heapify_down_max(self, i):
while True:
max_index = i
left = self.left_child(i)
if left < len(self.heap) and self.heap[left] > self.heap[max_index]:
max_index = left
right = self.right_child(i)
if right < len(self.heap) and self.heap[right] > self.heap[max_index]:
max_index = right
if i != max_index:
self.heap[i], self.heap[max_index] = self.heap[max_index], self.heap[i]
i = max_index
else:
break在这个实现中，MinMaxHeap类代表一个min-max堆，包含一个list堆，用于存放堆中的元素。 parent、left_child 和right_child 方法分别返回节点的父节点、左子节点和右子节点的索引。 get_min 方法返回堆中的最小元素，get_max 方法返回堆中的最大元素。 insert 方法将一个元素插入到堆中并维护堆属性。 extract_min 方法从堆中移除最小元素并保持堆属性。 extract_max 方法从堆中移除最大元素并保持堆属性。
_heapify_up、_heapify_up_min、_heapify_up_max、_heapify_down_min 和 _heapify_down_max 方法用于维护最小-最大堆属性。 _heapify_up 在向堆中插入元素后调用，以确保元素位于正确的位置。 _heapify_up_min 和 _heapify_up_max 由 _heapify_up 调用以维护最小-最大堆属性。 _heapify_down_min 和 _heapify_down_max 分别被 extract_min 和 extract_max 调用，以维护 min-max 堆属性。
