mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 23:16:28 +08:00
136 lines
3.7 KiB
Python
136 lines
3.7 KiB
Python
"""
|
|
File: my_heap.py
|
|
Created Time: 2023-02-23
|
|
Author: Krahets (krahets@163.com)
|
|
"""
|
|
|
|
import sys, os.path as osp
|
|
|
|
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
|
|
from modules import *
|
|
|
|
|
|
class MaxHeap:
|
|
"""大顶堆"""
|
|
|
|
def __init__(self, nums: list[int]):
|
|
"""构造方法"""
|
|
# 将列表元素原封不动添加进堆
|
|
self.max_heap = nums
|
|
# 堆化除叶节点以外的其他所有节点
|
|
for i in range(self.parent(self.size() - 1), -1, -1):
|
|
self.sift_down(i)
|
|
|
|
def left(self, i: int) -> int:
|
|
"""获取左子节点索引"""
|
|
return 2 * i + 1
|
|
|
|
def right(self, i: int) -> int:
|
|
"""获取右子节点索引"""
|
|
return 2 * i + 2
|
|
|
|
def parent(self, i: int) -> int:
|
|
"""获取父节点索引"""
|
|
return (i - 1) // 2 # 向下整除
|
|
|
|
def swap(self, i: int, j: int):
|
|
"""交换元素"""
|
|
a, b = self.max_heap[i], self.max_heap[j]
|
|
self.max_heap[i], self.max_heap[j] = b, a
|
|
|
|
def size(self) -> int:
|
|
"""获取堆大小"""
|
|
return len(self.max_heap)
|
|
|
|
def is_empty(self) -> bool:
|
|
"""判断堆是否为空"""
|
|
return self.size() == 0
|
|
|
|
def peek(self) -> int:
|
|
"""访问堆顶元素"""
|
|
return self.max_heap[0]
|
|
|
|
def push(self, val: int):
|
|
"""元素入堆"""
|
|
# 添加节点
|
|
self.max_heap.append(val)
|
|
# 从底至顶堆化
|
|
self.sift_up(self.size() - 1)
|
|
|
|
def sift_up(self, i: int):
|
|
"""从节点 i 开始，从底至顶堆化"""
|
|
while True:
|
|
# 获取节点 i 的父节点
|
|
p = self.parent(i)
|
|
# 当“越过根节点”或“节点无需修复”时，结束堆化
|
|
if p < 0 or self.max_heap[i] <= self.max_heap[p]:
|
|
break
|
|
# 交换两节点
|
|
self.swap(i, p)
|
|
# 循环向上堆化
|
|
i = p
|
|
|
|
def pop(self) -> int:
|
|
"""元素出堆"""
|
|
# 判空处理
|
|
assert not self.is_empty()
|
|
# 交换根节点与最右叶节点（即交换首元素与尾元素）
|
|
self.swap(0, self.size() - 1)
|
|
# 删除节点
|
|
val = self.max_heap.pop()
|
|
# 从顶至底堆化
|
|
self.sift_down(0)
|
|
# 返回堆顶元素
|
|
return val
|
|
|
|
def sift_down(self, i: int):
|
|
"""从节点 i 开始，从顶至底堆化"""
|
|
while True:
|
|
# 判断节点 i, l, r 中值最大的节点，记为 ma
|
|
l, r, ma = self.left(i), self.right(i), i
|
|
if l < self.size() and self.max_heap[l] > self.max_heap[ma]:
|
|
ma = l
|
|
if r < self.size() and self.max_heap[r] > self.max_heap[ma]:
|
|
ma = r
|
|
# 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出
|
|
if ma == i:
|
|
break
|
|
# 交换两节点
|
|
self.swap(i, ma)
|
|
# 循环向下堆化
|
|
i = ma
|
|
|
|
def print(self):
|
|
"""打印堆（二叉树）"""
|
|
print_heap(self.max_heap)
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
# 初始化大顶堆
|
|
max_heap = MaxHeap([9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2])
|
|
print("\n输入列表并建堆后")
|
|
max_heap.print()
|
|
|
|
# 获取堆顶元素
|
|
peek = max_heap.peek()
|
|
print(f"\n堆顶元素为 {peek}")
|
|
|
|
# 元素入堆
|
|
val = 7
|
|
max_heap.push(val)
|
|
print(f"\n元素 {val} 入堆后")
|
|
max_heap.print()
|
|
|
|
# 堆顶元素出堆
|
|
peek = max_heap.pop()
|
|
print(f"\n堆顶元素 {peek} 出堆后")
|
|
max_heap.print()
|
|
|
|
# 获取堆大小
|
|
size = max_heap.size()
|
|
print(f"\n堆元素数量为 {size}")
|
|
|
|
# 判断堆是否为空
|
|
is_empty = max_heap.is_empty()
|
|
print(f"\n堆是否为空 {is_empty}")
|