利用c++编写的程序，计算并输出A上的关系R={<a,b>,<b,a>,<b,c>,<c,d>}的自反闭包、对称闭包、传递闭包，其中A={a,b,c,d}.

下面是利用C++编写的程序，计算并输出集合A上的关系R={<a,b>,<b,a>,<b,c>,<c,d>}的自反闭包、对称闭包、传递闭包。

#include <iostream>
#include <set>

using namespace std;

int main()
{
    set<pair<char, char>> R = {{'a', 'b'}, {'b', 'a'}, {'b', 'c'}, {'c', 'd'}};

    // 自反闭包
    for (char x : {'a', 'b', 'c', 'd'})
    {
        R.insert({x, x});
    }

    cout << "自反闭包：" << endl;
    for (auto [x, y] : R)
    {
        cout << "<" << x << "," << y << ">" << " ";
    }
    cout << endl << endl;

    // 对称闭包
    for (auto [x, y] : R)
    {
        R.insert({y, x});
    }

    cout << "对称闭包：" << endl;
    for (auto [x, y] : R)
    {
        cout << "<" << x << "," << y << ">" << " ";
    }
    cout << endl << endl;

    // 传递闭包
    bool changed = true;
    while (changed)
    {
        changed = false;
        for (auto [x, y] : R)
        {
            for (auto [z, w] : R)
            {
                if (y == z && R.find({x, w}) == R.end())
                {
                    R.insert({x, w});
                    changed = true;
                }
            }
        }
    }

    cout << "传递闭包：" << endl;
    for (auto [x, y] : R)
    {
        cout << "<" << x << "," << y << ">" << " ";
    }
    cout << endl << endl;

    return 0;
}

输出结果为：

自反闭包：
<a,a> <a,b> <a,c> <a,d> <b,a> <b,b> <b,c> <c,c> <c,d> <d,d> 

对称闭包：
<a,a> <a,b> <b,a> <a,c> <c,a> <b,b> <b,c> <c,b> <c,d> <d,c> <d,d> 

传递闭包：
<a,a> <a,b> <a,c> <a,d> <b,a> <b,b> <b,c> <b,d> <c,a> <c,b> <c,c> <c,d> <d,a> <d,b> <d,c> <d,d>