用C++写：输入公式，例如（pVq）→→r，输出该公式的真值表及其主析取、合 取范式。

为了实现这个任务，我们可以使用C++编写一个程序来生成给定命题公式的真值表，并计算其主析取范式和主合取范式。以下是一个示例代码：

#include <iostream>
#include <string>
#include <map>
#include <vector>

using namespace std;

// 计算命题的真值
bool evaluate(const string& formula, const map<char, bool>& values) {
    for (char c : formula) {
        if (c == 'T') return true;
        if (c == 'F') return false;
    }

    // 替换变量为对应的真值
    string newFormula = formula;
    for (auto& pair : values) {
        char var = pair.first;
        bool val = pair.second;
        for (size_t i = 0; i < newFormula.size(); ++i) {
            if (newFormula[i] == var) {
                newFormula[i] = val ? 'T' : 'F';
            }
        }
    }

    // 计算真值表
    while (true) {
        size_t pos = newFormula.find("->");
        if (pos == string::npos) break;
        bool p = newFormula[pos - 1] == 'T';
        bool q = newFormula[pos + 2] == 'T';
        newFormula.replace(pos - 1, 4, p && !q ? "F" : "T");
    }

    while (true) {
        size_t pos = newFormula.find("V");
        if (pos == string::npos) break;
        bool p = newFormula[pos - 1] == 'T';
        bool q = newFormula[pos + 1] == 'T';
        newFormula.replace(pos - 1, 3, p || q ? "T" : "F");
    }

    while (true) {
        size_t pos = newFormula.find("^");
        if (pos == string::npos) break;
        bool p = newFormula[pos - 1] == 'T';
        bool q = newFormula[pos + 1] == 'T';
        newFormula.replace(pos - 1, 3, p && q ? "T" : "F");
    }

    return newFormula[0] == 'T';
}

// 生成真值表
void generateTruthTable(const string& formula) {
    vector<char> variables;
    for (char c : formula) {
        if (isalpha(c) && find(variables.begin(), variables.end(), c) == variables.end()) {
            variables.push_back(c);
        }
    }

    int n = variables.size();
    int rows = 1 << n;
    vector<vector<bool>> truthTable(rows, vector<bool>(n));

    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < n; ++j) {
            truthTable[i][j] = (i >> (n - j - 1)) & 1;
        }
    }

    cout << "真值表:" << endl;
    for (int j = 0; j < n; ++j) {
        cout << variables[j] << "\t";
    }
    cout << formula << endl;

    for (int i = 0; i < rows; ++i) {
        map<char, bool> values;
        for (int j = 0; j < n; ++j) {
            values[variables[j]] = truthTable[i][j];
            cout << (truthTable[i][j] ? "T" : "F") << "\t";
        }
        bool result = evaluate(formula, values);
        cout << (result ? "T" : "F") << endl;
    }
}

// 计算主析取范式和主合取范式
void calculateMintermsAndMaxterms(const string& formula) {
    vector<char> variables;
    for (char c : formula) {
        if (isalpha(c) && find(variables.begin(), variables.end(), c) == variables.end()) {
            variables.push_back(c);
        }
    }

    int n = variables.size();
    int rows = 1 << n;
    vector<vector<bool>> truthTable(rows, vector<bool>(n));
    vector<bool> results(rows);

    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < n; ++j) {
            truthTable[i][j] = (i >> (n - 1)) & 1;
        }
        map<char, bool> values;
        for (int j = 0; j < n; ++j) {
            values[variables[j]] = truthTable[i][j];
        }
        results[i] = evaluate(formula, values);
    }

    vector<string> minterms;
    vector<string> maxterms;

    for (int i = 0; i < rows; ++i) {
        if (results[i]) {
            string minterm;
            for (int j = 0; j < n; ++j) {
                if (truthTable[i][j]) {
                    minterm += variables[j];
                } else {
                    minterm += '~' + variables[j];
                }
                if (j < n - 1) minterm += " ^ ";
            }
            minterms.push_back(minterm);
        } else {
            string maxterm;
            for (int j = 0; j < n; ++j) {
                if (!truthTable[i][j]) {
                    maxterm += variables[j];
                } else {
                    maxterm += '~' + variables[j];
                }
                if (j < n - 1) maxterm += " V ";
            }
            maxterms.push_back(maxterm);
        }
    }

    cout << "主析取范式: " << (minterms.empty() ? "F" : "") << endl;
    for (const auto& term : minterms) {
        cout << "(" << term << ") V ";
    }
    if (!minterms.empty()) cout << "\b\b";

    cout << "\n主合取范式: " << (maxterms.empty() ? "T" : "") << endl;
    for (const auto& term : maxterms) {
        cout << "(" << term << ") ^ ";
    }
    if (!maxterms.empty()) cout << "\b\b";
}

int main() {
    string formula;
    cout << "请输入公式（例如 (p V q) -> r）: ";
    cin >> formula;

    generateTruthTable(formula);
    calculateMintermsAndMaxterms(formula);

    return 0;
}

### 说明
1. **evaluate** 函数用于计算给定命题公式的真值。
2. **generateTruthTable** 函数生成并打印真值表。
3. **calculateMintermsAndMaxterms** 函数计算并打印主析取范式和主合取范式。
4. **main** 函数读取用户输入的公式，并调用上述函数进行处理。

### 使用方法
运行程序后，输入公式（例如 `(p V q) -> r`），程序将输出该公式的真值表及其主析取范式和主合取范式。