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<h2 class="index-header">
<a href="/2025/04/10/OpenGL%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/" target="_self">
OpenGL学习笔记
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</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2025/04/10/OpenGL%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/" target="_self">
<div>
一、简介OpenGL（Open Graphics Library）是一个跨编程语言、跨平台的编程图形程序接口，它将计算机的资源抽象称为一个个OpenGL的对象，对这些资源的操作抽象为一个个的OpenGL指令。 OpenGL有着以下主要特性: 1. 低层次的渲染 APIOpenGL 提供了直接与图形硬件进行交互的能力。这使得它非常强大，因为它可以充分利用图形处理器（GPU）的性能。然而，这
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<i class="iconfont icon-date"></i>
<time datetime="2025-04-10 21:19" pubdate>
2025-04-10
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<a href="/2024/12/12/Graham-Pollak%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E/" target="_self">
Graham-Pollak定理的证明
</a>
</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2024/12/12/Graham-Pollak%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E/" target="_self">
<div>
一、定理陈述Graham - Pollak定理：任何$K_n$（完全图，有$n$个顶点）的分解中至少需要$n - 1$个完全二部图。 二、符号定义 对于图中的每个顶点$v_i \in V$，定义一个实变量$x_i$，其中$V$是图中所有顶点的集合。 对于第$k$个二部图，将其左侧顶点集记为$L_k$，右侧顶点集记为$R_k$。 对于任意顶点集$S$，定义$X(S)=\sum_{v_i
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<i class="iconfont icon-date"></i>
<time datetime="2024-12-12 11:00" pubdate>
2024-12-12
</time>
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<h2 class="index-header">
<a href="/2024/12/12/Mantel%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E/" target="_self">
Mantel定理的证明
</a>
</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2024/12/12/Mantel%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E/" target="_self">
<div>
一、定理陈述Mantel定理：对于一个具有 $n$ 个顶点的简单无向图 $G$，其边数 $m$ 满足 $m\leq\frac{n^2}{4}$，当且仅当图 $G$ 是一个完全二部图 $K_{\lfloor\frac{n}{2}\rfloor,\lceil\frac{n}{2}\rceil}$ 时等号成立。 二、证明过程（一）基本设定和握手引理的应用 设 $xy$ 是图 $G$ 的一条边，其中
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<div class="post-meta mr-3">
<i class="iconfont icon-date"></i>
<time datetime="2024-12-12 10:38" pubdate>
2024-12-12
</time>
</div>
</div>
</article>
</div>
<div class="row mx-auto index-card">
<article class="col-12 col-md-12 mx-auto index-info">
<h2 class="index-header">
<a href="/2024/12/11/%E6%9F%AF%E8%A5%BF%E4%BA%A4%E9%94%99%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E/" target="_self">
柯西交错定理的证明
</a>
</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2024/12/11/%E6%9F%AF%E8%A5%BF%E4%BA%A4%E9%94%99%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E/" target="_self">
<div>
一、定理陈述柯西交错定理： 设 $A=\begin{bmatrix}a & y^{*} \ y & B\end{bmatrix}$ 是 $n$ 阶 Hermitian 矩阵，$B$ 是 $A$ 的 $n - 1$ 阶主子矩阵，$\mu_{2} \leq \mu_{3} \leq \cdots \leq \mu_{n}$ 是 $B$ 的特征值，$\lambda_{1}
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<i class="iconfont icon-date"></i>
<time datetime="2024-12-11 20:53" pubdate>
2024-12-11
</time>
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<h2 class="index-header">
<a href="/2024/11/17/%E6%B5%85%E8%B0%88A-%E7%AE%97%E6%B3%95/" target="_self">
浅谈A*算法
</a>
</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2024/11/17/%E6%B5%85%E8%B0%88A-%E7%AE%97%E6%B3%95/" target="_self">
<div>
1. 算法思想A* 算法是一种启发式搜索算法，常用于在图中寻找从起始节点到目标节点的最短路径。它结合了 Dijkstra 算法（保证能找到最优解的广度优先搜索拓展）的特点以及启发式函数来引导搜索方向，以减少搜索空间。 算法维护两个集合，一个是已探索的节点集合，另一个是待探索的节点集合（通常用优先队列实现，按照节点的评估函数值排序）。每个节点都有一个评估函数 `f(n)`，它由两部分组成：从起始
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<i class="iconfont icon-date"></i>
<time datetime="2024-11-17 22:09" pubdate>
2024-11-17
</time>
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</article>
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<h2 class="index-header">
<a href="/2024/11/17/%E6%B5%85%E8%B0%88Johnson%E7%AE%97%E6%B3%95/" target="_self">
浅谈 Johnson 算法
</a>
</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2024/11/17/%E6%B5%85%E8%B0%88Johnson%E7%AE%97%E6%B3%95/" target="_self">
<div>
1. 算法思想Johnson 算法用于解决带权有向图中所有节点对之间的最短路径问题，它结合了 Bellman-Ford 算法和 Dijkstra 算法的优点。首先，通过添加一个虚拟节点 s 到图中，将所有边的权重进行重新赋值（重赋权技巧），使得图中不存在负权环的同时，利用 Bellman-Ford 算法计算出从虚拟节点 s 到图中每个节点的最短距离 h(v)。然后，对于图中的每一对节点 u 和
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<i class="iconfont icon-date"></i>
<time datetime="2024-11-17 22:09" pubdate>
2024-11-17
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<a href="/2024/11/17/hello-world/" target="_self">
Hello World
</a>
</h2>
<a class="index-excerpt index-excerpt__noimg" href="/2024/11/17/hello-world/" target="_self">
<div>
Welcome to Hexo! This is your very first post. Check documentation for more info. If you get any problems when using Hexo, you can find the answer in troubleshooting or you can ask me on GitHub. Quick
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<time datetime="2024-11-17 22:00" pubdate>
2024-11-17
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