最小化DFAc++代码

最小化DFA（Deterministic Finite Automaton）是一种将给定的DFA转化为具有最少状态数的等价DFA的过程。下面是一个用C++实现最小化DFA的代码示例：

#include <iostream>
#include <vector>
#include <queue>
#include <map>
using namespace std;

// DFA状态
struct State {
    bool isFinal;  // 是否是终止状态
    map<char, int> transitions;  // 状态转移表
};

// 最小化DFA函数
vector<State> minimizeDFA(const vector<State>& dfa) {
    int numStates = dfa.size();
    vector<vector<bool>> distinguishable(numStates, vector<bool>(numStates, true));

    // 标记终止状态和非终止状态为不可区分
    for (int i = 0; i < numStates; i++) {
        for (int j = 0; j < numStates; j++) {
            if ((dfa[i].isFinal && !dfa[j].isFinal) || (!dfa[i].isFinal && dfa[j].isFinal)) {
                distinguishable[i][j] = false;
            }
        }
    }

    // 使用BFS算法进行状态可区分性检测
    queue<pair<int, int>> q;
    for (int i = 0; i < numStates - 1; i++) {
        for (int j = i + 1; j < numStates; j++) {
            if (!distinguishable[i][j]) {
                q.push({i, j});
            }
        }
    }

    while (!q.empty()) {
        pair<int, int> p = q.front();
        q.pop();
        int state1 = p.first;
        int state2 = p.second;

        for (const auto& transition : dfa[state1].transitions) {
            char symbol = transition.first;
            int nextState1 = transition.second;
            int nextState2 = dfa[state2].transitions[symbol];

            if (!distinguishable[nextState1][nextState2]) {
                distinguishable[state1][state2] = false;
                break;
            }

            if (!distinguishable[state1][state2]) {
                q.push({state1, state2});
                break;
            }
        }
    }

    // 构建最小化DFA
    vector<State> minimizedDFA;
    vector<int> newState(numStates, -1);
    int nextState = 0;

    for (int i = 0; i < numStates; i++) {
        if (newState[i] == -1) {
            newState[i] = nextState++;
            minimizedDFA.push_back(dfa[i]);
        }

        for (int j = i + 1; j < numStates; j++) {
            if (!distinguishable[i][j]) {
                newState[j] = newState[i];
            }
        }
    }

    // 更新状态转移表
    for (auto& state : minimizedDFA) {
        for (auto& transition : state.transitions) {
            transition.second = newState[transition.second];
        }
    }

    return minimizedDFA;
}

int main() {
    // 构建原始DFA
    vector<State> dfa(4);
    dfa[0].isFinal = false;
    dfa[0].transitions['a'] = 1;
    dfa[0].transitions['b'] = 3;
    dfa[1].isFinal = true;
    dfa[1].transitions['a'] = 2;
    dfa[1].transitions['b'] = 3;
    dfa[2].isFinal = false;
    dfa[2].transitions['a'] = 1;
    dfa[2].transitions['b'] = 3;
    dfa[3].isFinal = false;
    dfa[3].transitions['a'] = 3;
    dfa[3].transitions['b'] = 3;

    // 最小化DFA
    vector<State> minimizedDFA = minimizeDFA(dfa);

    // 输出最小化DFA
    for (int i = 0; i < minimizedDFA.size(); i++) {
        cout << "State " << i << ": ";
        if (minimizedDFA[i].isFinal) {
            cout << "Final State";
        } else {
            cout << "Non-final State";
        }
        cout << endl;

        for (const auto& transition : minimizedDFA[i].transitions) {
            cout << "Transition on '" << transition.first << "' to State " << transition.second << endl;
        }

        cout << endl;
    }

    return 0;
}

这段代码实现了一个最小化DFA的函数`minimizeDFA`，它接受一个原始DFA的状态列表作为输入，并返回一个最小化后的DFA的状态列表。在`main`函数中，我们构建了一个简单的原始DFA，并调用`minimizeDFA`函数进行最小化操作。最后，输出最小化后的DFA的状态信息。