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10 changes: 10 additions & 0 deletions src/content/blog/2025-06-20/index.md
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---
title: "Placeholder"
author: "Unknown"
date: "Jun 20, 2025"
description: "Placeholder content"
latex: true
pdf: true
---

Content coming soon.
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二叉堆的平衡性使其成为工业级应用的首选,尤其适合高频数据更新场景。

## 手撕二叉堆实现(代码核心部分)
二叉堆本质是完全二叉树,满足堆序性:父节点值始终大于或等于子节点值(最大堆)。其底层使用数组存储,索引映射关系为:父节点索引 $parent(i) = \lfloor (i-1)/2 \rfloor$,左子节点 $left\\_child(i) = 2i+1$,右子节点 $right\\_child(i) = 2i+2$。这种结构避免了指针开销,内存访问高效。
二叉堆本质是完全二叉树,满足堆序性:父节点值始终大于或等于子节点值(最大堆)。其底层使用数组存储,索引映射关系为:父节点索引 \( parent(i) = \lfloor (i-1)/2 \rfloor \),左子节点 \( \text{left\_child}(i) = 2i+1 \),右子节点 \( \text{right\_child}(i) = 2i+2 \)。这种结构避免了指针开销,内存访问高效。

关键操作包括上浮(Heapify Up)和下沉(Heapify Down)。上浮用于插入后维护堆结构,从新元素位置向上比较并交换,直至满足堆性质。以下 Python 代码实现上浮逻辑:

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