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138 lines
3.9 KiB
138 lines
3.9 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
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from pathlib import Path
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sys.path.append(str(Path(__file__).parent.parent))
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from modules import print_heap
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class MaxHeap:
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"""大頂堆積"""
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def __init__(self, nums: list[int]):
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"""建構子，根據輸入串列建堆積"""
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# 將串列元素原封不動新增進堆積
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self.max_heap = nums
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# 堆積化除葉節點以外的其他所有節點
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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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"""獲取左子節點的索引"""
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return 2 * i + 1
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def right(self, i: int) -> int:
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"""獲取右子節點的索引"""
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return 2 * i + 2
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def parent(self, i: int) -> int:
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"""獲取父節點的索引"""
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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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"""交換元素"""
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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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"""獲取堆積大小"""
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return len(self.max_heap)
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def is_empty(self) -> bool:
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"""判斷堆積是否為空"""
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return self.size() == 0
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def peek(self) -> int:
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"""訪問堆積頂元素"""
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return self.max_heap[0]
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def push(self, val: int):
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"""元素入堆積"""
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# 新增節點
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self.max_heap.append(val)
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# 從底至頂堆積化
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self.sift_up(self.size() - 1)
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def sift_up(self, i: int):
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"""從節點 i 開始，從底至頂堆積化"""
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while True:
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# 獲取節點 i 的父節點
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p = self.parent(i)
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# 當“越過根節點”或“節點無須修復”時，結束堆積化
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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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# 交換兩節點
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self.swap(i, p)
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# 迴圈向上堆積化
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i = p
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def pop(self) -> int:
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"""元素出堆積"""
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# 判空處理
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if self.is_empty():
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raise IndexError("堆積為空")
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# 交換根節點與最右葉節點（交換首元素與尾元素）
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self.swap(0, self.size() - 1)
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# 刪除節點
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val = self.max_heap.pop()
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# 從頂至底堆積化
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self.sift_down(0)
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# 返回堆積頂元素
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return val
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def sift_down(self, i: int):
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"""從節點 i 開始，從頂至底堆積化"""
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while True:
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# 判斷節點 i, l, r 中值最大的節點，記為 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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# 若節點 i 最大或索引 l, r 越界，則無須繼續堆積化，跳出
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if ma == i:
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break
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# 交換兩節點
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self.swap(i, ma)
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# 迴圈向下堆積化
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i = ma
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def print(self):
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"""列印堆積（二元樹）"""
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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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# 初始化大頂堆積
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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輸入串列並建堆積後")
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max_heap.print()
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# 獲取堆積頂元素
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peek = max_heap.peek()
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print(f"\n堆積頂元素為 {peek}")
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# 元素入堆積
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val = 7
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max_heap.push(val)
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print(f"\n元素 {val} 入堆積後")
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max_heap.print()
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# 堆積頂元素出堆積
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peek = max_heap.pop()
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print(f"\n堆積頂元素 {peek} 出堆積後")
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max_heap.print()
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# 獲取堆積大小
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size = max_heap.size()
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print(f"\n堆積元素數量為 {size}")
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# 判斷堆積是否為空
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is_empty = max_heap.is_empty()
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print(f"\n堆積是否為空 {is_empty}")
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