253 lines
13 KiB
C++
253 lines
13 KiB
C++
#include "nfa.h"
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class Partition {
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public:
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set<State*, StatePtrCompare> states;
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Partition(set<State*, StatePtrCompare> states) : states(states) {}
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};
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/*
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最小化算法步骤：
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首先把所有节点分为N和A两个集合，集非结束态和结束态
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S = {N,A}，然后遍历所有字符，去看每个字符都否对S中的状态集进行划分，每轮遍历下来，如果S仍然在扩大，则从头再来一轮。直到S不再扩大，即没有状态集可分为止。
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c can split s这里s指的是S中的一个状态集
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1.遍历s中每个状态，记录每个状态吃了字符c之后到达的状态，吃不了的不管。
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2.把到达的状态分类，分类依据：把属于同一个状态集的合在一起。这里的同一个状态集指的是S中现在有的状态集。
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3.按照第二步的分法把s分割。
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注意：是从s中分割出去，s最后保留下来的是吃了字符c还在状态集s中的状态或者吃不了c字符的状态。
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*/
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// split 函数用于将给定的状态集合（group）根据转移函数进一步细分。
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// group: 要细分的状态集合
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// input: 当前考虑的输入字符类型
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// partitions: 存储所有分区的集合，如果需要细分，将在该集合中添加新分区
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void split(const set<State*, StatePtrCompare>& group, InputCharType input, set<Partition*>& partitions) {
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// 用于存储每个目标分区与对应新分组状态集合的映射
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map<Partition*, set<State*, StatePtrCompare>> targetPartitionsMap;
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for (State* state : group) {
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auto it = state->transitions.find(input);
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if (it != state->transitions.end()) {
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State* targetState = *(it->second.begin());//DFA状态转移具有唯一性
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// 在当前所有分区中查找包含目标状态的分区
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for (Partition* partition : partitions) {
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if (partition->states.find(targetState) != partition->states.end()) {
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// 在映射表中将当前状态添加到对应的目标分区
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targetPartitionsMap[partition].insert(state);
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break;
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}
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}
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}
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}
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// 经过上述操作，将在group里的状态根据到达目标Partiset<State*, StatePtrCompare>分到不同set<State*>
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// 遍历目标分区映射表，检查是否需要进一步细分，即将经过input输入状态转换后处于不同目标分区的集合内部拆分开
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for (auto& entry : targetPartitionsMap) {
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Partition* targetPartition = entry.first;
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//到达该targetPartition的group部分状态合集如下：
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set<State*, StatePtrCompare>& newGroupStates = entry.second;
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//等于的情况不拆分，不会出现大于的情况，将targetPartition拆分开来，也可以将到达不同割集的源状态分割开来，也可以分割目标状态，总之是状态转移结果在现存割集即可
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if (newGroupStates.size() < targetPartition->states.size()) {
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for (State* state : newGroupStates) {
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targetPartition->states.erase(state);
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}
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Partition* newGroup = new Partition(newGroupStates);
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partitions.insert(newGroup);
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}
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}
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}
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DFA minimizeDFA(const DFA& dfa) {
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set<Partition*> partitions;
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// 将所有非终止状态分成一组，将所有终止状态按照 WordType 分组
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/*
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* 不同 WordType 的终止状态表示的是不同的词法单元类型。
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* 这些状态在词法分析过程中具有不同的语义,不能被合并为同一个状态。
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*/
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map<WordType, set<State*, StatePtrCompare>> endStateGroups; //初始终态集合
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set<State*, StatePtrCompare> nonEndStates; //初始非终态集合
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for (State* state : dfa.states) {
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if (state->isFinalState) {
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endStateGroups[state->wordType].insert(state);//使用wordType对终态集合进一步拆分
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}
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else {
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nonEndStates.insert(state);
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}
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}
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//构造初始分割，是对{N,A}中A的扩展（即终态，加快算法速度，扩展原因见上）
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for (auto& entry : endStateGroups) {
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Partition* endStateGroup = new Partition(entry.second);
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partitions.insert(endStateGroup);
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}
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Partition* nonEndStateGroup = new Partition(nonEndStates);
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partitions.insert(nonEndStateGroup);
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//对现有分隔进行再分隔，以获得最小化分割
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size_t oldSize;//分割集初始大小
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do {
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oldSize = partitions.size();
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for (InputCharType input = static_cast<InputCharType>(0); input < EPSILON; input = static_cast<InputCharType>(input + 1)) {//类似于求Ia,Ib等
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for (Partition* partition : set<Partition*>(partitions)) {//遍历现存分割的每一个割集，看是否可再分割
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if (partition->states.size() > 1) {//为1的集合不可再分割
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split(partition->states, input, partitions);//核心分割函数
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}
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}
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}
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} while (partitions.size() != oldSize);//当割集集合大小不再变化时停止
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// 创建新的最小化 DFA，即重新映射dfa，重新编号状态
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// 构造DFA参数为DFA(State* set<State*, StatePtrCompare> set<State*>set<State*, StatePtrCompare> set<State*> states)
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set<State*, StatePtrCompare> minimizedStates;
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set<State*, StatePtrCompare> minimizedEndStates;
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State* minimizedStartState = nullptr;
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map<State*, State*> stateMap;
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for (Partition* partition : partitions) {//遍历获得的每个割集
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State* newState = new State(minimizedStates.size());//编号
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// 检查当前划分是否包含旧DFA的开始状态，如果是，则将新状态设置为最小化DFA的开始状态
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if (partition->states.find(dfa.startState) != partition->states.end()) {
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minimizedStartState = newState;
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}
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// 如果划分的状态集合不为空，选择一个代表状态
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if (!partition->states.empty()) {
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State* representative = *(partition->states.begin());//因为在前面终止状态都分到了不同割集，且大小为1，所以如果是终止状态begin已经可以代表了
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//在分割状态集合的过程中，已经确保了一个划分中所有状态具有相同的属性,要么所有状态都是终止状态，要么都不是终止状态。所以我们只需要检查一个状态来确定新状态是否应该是终止状态。
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// 如果代表状态是终止状态，则设置新状态为终止状态，并保留相应的单词类型
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if (representative->isFinalState) {
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newState->setFinalState(true, representative->wordType);
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minimizedEndStates.insert(newState);
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}
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}
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// 将集合里面所有旧状态映射到同一个新状态
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for (State* state : partition->states)
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{
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stateMap[state] = newState;
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}
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// 将新状态插入到最小化DFA的状态集合中
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minimizedStates.insert(newState);
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}
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// 遍历旧DFA中的所有状态
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for (State* oldState : dfa.states) {
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// 通过映射找到与旧状态对应的新状态
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State* newState = stateMap[oldState];
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for (const auto& transition : oldState->transitions) {
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InputCharType input = transition.first;
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State* oldTargetState = *(transition.second.begin());//dfa每个状态只有一个转移状态，沿用了nfa的结构，所以集合大小<=1
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State* newTargetState = stateMap[oldTargetState];// 获取旧状态的目标状态
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newState->addTransition(input, newTargetState);// 通过映射找到新的目标状态
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}
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}
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// 清理并删除原始分区
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for (Partition* partition : partitions) {
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delete partition;
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}
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return DFA(minimizedStartState, minimizedEndStates, minimizedStates);
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}
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void removeUnreachableStates(DFA& dfa) {
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set<State*> reachableStates; //可达状态集合
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queue<State*> statesQueue; //状态队列
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//将初始状态加入可达状态集合和队列
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reachableStates.insert(dfa.startState);
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statesQueue.push(dfa.startState);
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// BFS 遍历 DFA，找出所有可达状态
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while (!statesQueue.empty()) {
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State* currentState = statesQueue.front();
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statesQueue.pop();
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for (const auto& transition : currentState->transitions) {
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State* targetState = *(transition.second.begin());//dfa每个状态只有一个转移状态，沿用了nfa的结构，所以集合大小<=1
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if (reachableStates.find(targetState) == reachableStates.end()) {//若未访问
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reachableStates.insert(targetState);
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statesQueue.push(targetState);
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}
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}
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}
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// 删除所有不可达状态
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for (auto it = dfa.states.begin(); it != dfa.states.end();) {
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State* state = *it;
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if (reachableStates.find(state) == reachableStates.end()) {//若当前状态不可达，删除
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it = dfa.states.erase(it);
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delete state;
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}
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else {
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++it;
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}
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}
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}
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vector<string> recognize(const DFA& dfa, const string& input, const string& output) {
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State* currentState = dfa.startState;
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State* nextState = nullptr;
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string buffer;
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vector<string> tokens; // 用于收集识别到的Token
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//打开结果输出文件
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ofstream file(output);
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if (!file.is_open()) {
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cout << "Error opening file!" << endl;
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return tokens;
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}
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for (size_t i = 0; i < input.length(); ++i) {
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char c = input[i];
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if (c == ' '||c=='\n'||c=='\r\n'||c==' ')// 如果是空格、换行等分隔符，则跳过
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{continue; }
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InputCharType inputCharType = getInputCharType(c);
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auto it = currentState->transitions.find(inputCharType);
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if (it != currentState->transitions.end()) {
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nextState = *(it->second.begin());
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buffer.push_back(c);
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if (nextState->isFinalState && i + 1 < input.length()) {// 如果下一个状态是终止状态并且还有剩余字符
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char nextChar = input[i + 1];
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InputCharType nextInputCharType = getInputCharType(nextChar);
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auto nextIt = nextState->transitions.find(nextInputCharType);// 查找下一个状态的转换表中是否有对应的输入字符类型
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if (nextIt == nextState->transitions.end()) {// 如果没有更多匹配的转换
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// 输出识别到的单词符号和对应的类型
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cout << buffer << "\t<" << getWordTypeName(nextState->wordType,buffer)<<","<<getWordAttribute(nextState->wordType,buffer) << ">" << endl;
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file << buffer << "\t<" << getWordTypeName(nextState->wordType, buffer)<<","<<getWordAttribute(nextState->wordType,buffer) << ">" << endl;
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tokens.push_back(getGrammarName(nextState->wordType, buffer));
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buffer.clear();
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currentState = dfa.startState;
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}
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else {
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currentState = nextState;// 更新当前状态为下一个状态
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}
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}
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else {
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currentState = nextState;// 更新当前状态为下一个状态
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}
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}
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else {// 如果没有找到匹配的转换
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if (currentState->isFinalState) {// 如果当前状态是终止状态
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// 输出识别到的单词符号和对应的类型
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cout << buffer << "\t<" << getWordTypeName(currentState->wordType,buffer) <<","<<getWordAttribute(nextState->wordType,buffer) << ">" << endl;
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file << buffer << "\t<" << getWordTypeName(currentState->wordType, buffer) << ","<<getWordAttribute(nextState->wordType,buffer) << ">" << endl;
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tokens.push_back(getGrammarName(currentState->wordType, buffer) );
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buffer.clear();
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}
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else {
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// 如果当前状态不是终止状态
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// 输出无法识别的字符信息
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cout << "Unrecognized characters: " << c << endl;
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file << "Unrecognized characters: " << c << endl;
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buffer.clear();
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}
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currentState = dfa.startState;// 回到起始状态
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//--i;// 重新处理当前字符,还是跳过吧，这里可以添加错误处理
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}
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}
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// 处理最后一个字符，如果缓冲区不为空且当前状态是终止状态,对应第一个if里面的else
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if (!buffer.empty() && currentState->isFinalState) {
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cout << buffer << "\t<" << getWordTypeName(currentState->wordType,buffer) << ","<<getWordAttribute(nextState->wordType,buffer) << ">" << endl;
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file << buffer << "\t<" << getWordTypeName(currentState->wordType, buffer) << ","<<getWordAttribute(nextState->wordType,buffer) << ">" << endl;
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tokens.push_back(getGrammarName(currentState->wordType, buffer));
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}
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file.close();//关闭文件
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return tokens;
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} |