<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>algorithm on Ishian</title><link>https://echo.ishian.me/tags/algorithm/</link><description>Recent content in algorithm on Ishian</description><generator>Hugo</generator><language>en</language><lastBuildDate>Thu, 27 Aug 2026 15:05:37 +0000</lastBuildDate><atom:link href="https://echo.ishian.me/tags/algorithm/index.xml" rel="self" type="application/rss+xml"/><item><title>数据结构: B+树</title><link>https://echo.ishian.me/2026/08/27/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84-b-%E6%A0%91/</link><pubDate>Thu, 27 Aug 2026 15:05:37 +0000</pubDate><guid>https://echo.ishian.me/2026/08/27/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84-b-%E6%A0%91/</guid><description>讲解B+树的结构原理、插入删除操作及其在数据库索引中的应用</description></item><item><title>树的算法: 点分治</title><link>https://echo.ishian.me/2025/06/11/algo-tree-point-dac/</link><pubDate>Wed, 11 Jun 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/06/11/algo-tree-point-dac/</guid><description>讲解点分治处理树上路径统计问题的分治结构、找重心与合并过程</description></item><item><title>数据结构: 笛卡尔树</title><link>https://echo.ishian.me/2025/05/30/algo-descartes-tree/</link><pubDate>Fri, 30 May 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/05/30/algo-descartes-tree/</guid><description>讲解笛卡尔树的定义、性质、单调栈O(n)建树方法及其在连续区间问题中的应用</description></item><item><title>树的算法: LCA（最近公共祖先）</title><link>https://echo.ishian.me/2025/04/30/algo-tree-lca/</link><pubDate>Wed, 30 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/30/algo-tree-lca/</guid><description>介绍LCA的性质、朴素算法与倍增算法的原理和实现</description></item><item><title>树的算法: 寻找树的重心</title><link>https://echo.ishian.me/2025/04/30/algo-tree-gravity/</link><pubDate>Wed, 30 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/30/algo-tree-gravity/</guid><description>讲解树的重心的定义与性质，并给出DFS求重心的O(n)算法实现</description></item><item><title>字符串算法: 马拉车（manacher）回文串统计</title><link>https://echo.ishian.me/2025/04/26/algo-string-manacher/</link><pubDate>Sat, 26 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/26/algo-string-manacher/</guid><description>给出Manacher算法求最长回文子串的完整代码实现</description></item><item><title>数论: 质数筛法</title><link>https://echo.ishian.me/2025/04/22/algo-prime-selection/</link><pubDate>Tue, 22 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/22/algo-prime-selection/</guid><description>讲解埃氏筛与欧拉筛两种质数筛法的原理、实现及时间复杂度</description></item><item><title>数论: 扩展欧拉定理</title><link>https://echo.ishian.me/2025/04/20/algo-math-ext-euler-theorem/</link><pubDate>Sun, 20 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/20/algo-math-ext-euler-theorem/</guid><description>陈述并证明扩展欧拉定理，用于快速模幂中不互素情形的降幂</description></item><item><title>图的遍历: 链式前向星</title><link>https://echo.ishian.me/2025/04/10/algo-linked-forward-star/</link><pubDate>Thu, 10 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/10/algo-linked-forward-star/</guid><description>讲解对顶堆的组成与维护方式，用于动态求解序列中第k小元素</description></item><item><title>数据结构: 对顶堆</title><link>https://echo.ishian.me/2025/04/10/algo-minmax-heap/</link><pubDate>Thu, 10 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/10/algo-minmax-heap/</guid><description>讲解对顶堆的组成与维护方式，用于动态求解序列中第k小元素</description></item><item><title>数据结构: 递归式线段树</title><link>https://echo.ishian.me/2025/04/10/algo-recursive-segment-tree/</link><pubDate>Thu, 10 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/10/algo-recursive-segment-tree/</guid><description>讲解递归式线段树的结构、建树、懒标记与区间修改、区间查询的实现</description></item><item><title>算法竞赛: 常数优化之快读快写</title><link>https://echo.ishian.me/2025/04/07/algo-fastio/</link><pubDate>Mon, 07 Apr 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/04/07/algo-fastio/</guid><description>介绍算法竞赛中基于getchar与fread的快读快写模板及其原理</description></item><item><title>数据结构: 前缀和</title><link>https://echo.ishian.me/2025/03/19/algo-prefix-sum/</link><pubDate>Wed, 19 Mar 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/03/19/algo-prefix-sum/</guid><description>介绍一维与二维前缀和的原理、性质、原地实现及差分应用场景</description></item><item><title>数据结构: 树状数组</title><link>https://echo.ishian.me/2025/03/19/algo-fenwick-tree/</link><pubDate>Wed, 19 Mar 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/03/19/algo-fenwick-tree/</guid><description>讲解树状数组的基本结构、lowbit原理、区间查询与单点修改的实现及适用范围</description></item><item><title>博弈论: 01字典树</title><link>https://echo.ishian.me/2025/02/21/algo-bin-01tire/</link><pubDate>Fri, 21 Feb 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/02/21/algo-bin-01tire/</guid><description>介绍01字典树的原理与实现，并以树上异或路径最大值问题为例给出代码</description></item><item><title>图的算法: SCC（强连通分量）</title><link>https://echo.ishian.me/2025/02/11/algo-graph-scc/</link><pubDate>Tue, 11 Feb 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/02/11/algo-graph-scc/</guid><description>给出Tarjan算法求解有向图强连通分量并缩点建图的完整代码实现</description></item><item><title>博弈论: 公平组合游戏</title><link>https://echo.ishian.me/2025/01/07/algo-game-fairgames/</link><pubDate>Tue, 07 Jan 2025 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2025/01/07/algo-game-fairgames/</guid><description>讲解公平组合游戏的必胜必输状态判定，并推导巴什博弈与Nim游戏的结论</description></item><item><title>图的算法: 最小生成树</title><link>https://echo.ishian.me/2024/12/09/algo-graph-minimum-spanning-tree/</link><pubDate>Mon, 09 Dec 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/12/09/algo-graph-minimum-spanning-tree/</guid><description>从图论基础与图的存储讲起，介绍最小生成树的概念及Prim、Kruskal等算法</description></item><item><title>算法竞赛: 离线查询</title><link>https://echo.ishian.me/2024/11/26/algo-trick-offline-query/</link><pubDate>Tue, 26 Nov 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/11/26/algo-trick-offline-query/</guid><description>介绍离线查询技巧的思想，并结合例题讲解排序后配合树状数组的求解方式</description></item><item><title>数据结构: 哈希表</title><link>https://echo.ishian.me/2024/11/16/algo-hashmap/</link><pubDate>Sat, 16 Nov 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/11/16/algo-hashmap/</guid><description>介绍哈希函数的设计原则、常见哈希算法及哈希表的原理、冲突处理与实现</description></item><item><title>字符串算法: KMP匹配</title><link>https://echo.ishian.me/2024/10/23/algo-string-kmpmatch/</link><pubDate>Wed, 23 Oct 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/10/23/algo-string-kmpmatch/</guid><description>从暴力匹配的不足出发，讲解KMP算法的前后缀原理与next数组的求法应用</description></item><item><title>数据结构: 并查集</title><link>https://echo.ishian.me/2024/10/02/algo-ufs/</link><pubDate>Wed, 02 Oct 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/10/02/algo-ufs/</guid><description>介绍并查集的原理、合并与查询操作、路径压缩与按秩合并优化</description></item><item><title>位运算: 基本知识</title><link>https://echo.ishian.me/2024/09/19/algo-bin-beginner/</link><pubDate>Thu, 19 Sep 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/09/19/algo-bin-beginner/</guid><description>整理位运算的基础知识，包括常用内建函数、与或异或运算性质及常用技巧</description></item><item><title>算法竞赛: 动态规划引入</title><link>https://echo.ishian.me/2024/03/11/algo-dp-beginner/</link><pubDate>Mon, 11 Mar 2024 00:00:00 +0000</pubDate><guid>https://echo.ishian.me/2024/03/11/algo-dp-beginner/</guid><description>由回溯与贪心引出动态规划思想，以斐波那契数列为例讲解记忆化与递推优化</description></item></channel></rss>