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‎lab-05/2025-05-FSA/README.md‎

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# FSA
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## Description
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As learned in the lecture, FSA can be used to solve string matching problems. Here you are given a string S, and you are required to output it's transition function according to the FSA algorithm.
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## Input
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One line, indicating the input string $S: (1 \leq |S| \leq 10^5)$
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The string contains only lowercase letters.
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## Output
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$|S|$ lines, each containing 26 integers, indicating the transition function.
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### Sample Input
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``` log
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aabaaabb
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```
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### Sample Output
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``` log
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1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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2 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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```
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### 算法分析
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本题要求构建字符串的有限状态自动机(FSA)转移表, 用于高效匹配
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核心思路是先用 KMP 算法求出前缀函数, 然后对每个状态和每个字母, 递归回退到最长可匹配前缀, 若匹配则状态加一, 否则回退
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这样可在 $O(n\cdot|\Sigma|)$ 时间内预处理出所有转移, 其中 $n$ 为模式串长度, $|\Sigma|=26$
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输出每个状态下 26 个字母的转移结果, 可直接用于自动机匹配

‎lab-05/2025-05-FSA/pom.xml‎

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<?xml version="1.0" encoding="UTF-8"?>
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<project xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://maven.apache.org/POM/4.0.0"
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xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 https://maven.apache.org/xsd/maven-4.0.0.xsd">
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<modelVersion>4.0.0</modelVersion>
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<parent>
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<groupId>nanoseeds.algorithm-template</groupId>
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<artifactId>2025fall-lab-05</artifactId>
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<version>${revision}</version>
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<relativePath>./../pom.xml</relativePath>
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</parent>
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<groupId>nanoseeds.algorithm-template.2025fall-lab-05</groupId>
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<artifactId>2025-05-FSA</artifactId>
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<version>${revision}</version>
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<name>${project.groupId}.${project.artifactId}</name>
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<description>${project.groupId}.${project.artifactId}</description>
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<build>
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<sourceDirectory>${project.basedir}/src</sourceDirectory>
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<testSourceDirectory>${project.basedir}/test</testSourceDirectory>
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</build>
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</project>

‎lab-05/2025-05-FSA/resources/01.data.in‎

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