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137 lines
3.8 KiB
137 lines
3.8 KiB
"""
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File: my_heap.py
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Created Time: 2023-02-23
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Author: Krahets (krahets@163.com)
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"""
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import sys, os.path as osp
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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from modules import *
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class MaxHeap:
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"""大顶堆"""
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def __init__(self, nums: list[int]):
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"""构造方法，根据输入列表建堆"""
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# 将列表元素原封不动添加进堆
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self.max_heap = nums
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# 堆化除叶节点以外的其他所有节点
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for i in range(self.parent(self.size() - 1), -1, -1):
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self.sift_down(i)
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def left(self, i: int) -> int:
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"""获取左子节点索引"""
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return 2 * i + 1
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def right(self, i: int) -> int:
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"""获取右子节点索引"""
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return 2 * i + 2
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def parent(self, i: int) -> int:
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"""获取父节点索引"""
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return (i - 1) // 2 # 向下整除
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def swap(self, i: int, j: int):
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"""交换元素"""
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self.max_heap[i], self.max_heap[j] = self.max_heap[j], self.max_heap[i]
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def size(self) -> int:
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"""获取堆大小"""
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return len(self.max_heap)
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def is_empty(self) -> bool:
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"""判断堆是否为空"""
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return self.size() == 0
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def peek(self) -> int:
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"""访问堆顶元素"""
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return self.max_heap[0]
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def push(self, val: int):
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"""元素入堆"""
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# 添加节点
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self.max_heap.append(val)
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# 从底至顶堆化
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self.sift_up(self.size() - 1)
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def sift_up(self, i: int):
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"""从节点 i 开始，从底至顶堆化"""
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while True:
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# 获取节点 i 的父节点
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p = self.parent(i)
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# 当“越过根节点”或“节点无需修复”时，结束堆化
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if p < 0 or self.max_heap[i] <= self.max_heap[p]:
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break
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# 交换两节点
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self.swap(i, p)
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# 循环向上堆化
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i = p
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def pop(self) -> int:
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"""元素出堆"""
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# 判空处理
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if self.is_empty():
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raise IndexError("堆为空")
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# 交换根节点与最右叶节点（即交换首元素与尾元素）
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self.swap(0, self.size() - 1)
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# 删除节点
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val = self.max_heap.pop()
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# 从顶至底堆化
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self.sift_down(0)
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# 返回堆顶元素
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return val
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def sift_down(self, i: int):
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"""从节点 i 开始，从顶至底堆化"""
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while True:
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# 判断节点 i, l, r 中值最大的节点，记为 ma
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l, r, ma = self.left(i), self.right(i), i
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if l < self.size() and self.max_heap[l] > self.max_heap[ma]:
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ma = l
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if r < self.size() and self.max_heap[r] > self.max_heap[ma]:
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ma = r
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# 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出
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if ma == i:
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break
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# 交换两节点
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self.swap(i, ma)
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# 循环向下堆化
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i = ma
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def print(self):
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"""打印堆（二叉树）"""
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print_heap(self.max_heap)
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"""Driver Code"""
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if __name__ == "__main__":
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# 初始化大顶堆
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max_heap = MaxHeap([9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2])
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print("\n输入列表并建堆后")
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max_heap.print()
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# 获取堆顶元素
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peek = max_heap.peek()
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print(f"\n堆顶元素为 {peek}")
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# 元素入堆
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val = 7
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max_heap.push(val)
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print(f"\n元素 {val} 入堆后")
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max_heap.print()
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# 堆顶元素出堆
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peek = max_heap.pop()
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print(f"\n堆顶元素 {peek} 出堆后")
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max_heap.print()
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# 获取堆大小
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size = max_heap.size()
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print(f"\n堆元素数量为 {size}")
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# 判断堆是否为空
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is_empty = max_heap.is_empty()
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print(f"\n堆是否为空 {is_empty}")
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