n皇后问题，C++代码解决，要求随机输入正整数n，输出n后问题的解法个数，以及输出至少两种二维图形

以下是解决 n 皇后问题的 C++ 代码：

#include <iostream>
#include <vector>
#include <cmath>
#include <cstdlib>
using namespace std;

void nQueens(int n, vector<int>& pos, int& count) {
    if (pos.size() == n) {
        count++;
        return;
    }
    for (int i = 0; i < n; i++) {
        bool legal = true;
        for (int j = 0; j < pos.size(); j++) {
            if (pos[j] == i || abs(pos.size()-j) == abs(i-pos[j])) {
                legal = false;
                break;
            }
        }
        if (legal) {
            pos.push_back(i);
            nQueens(n, pos, count);
            pos.pop_back();
        }
    }
}

int main() {
    int n;
    cout << "Please input n: ";
    cin >> n;

    int count = 0;
    vector<int> pos;
    nQueens(n, pos, count);

    cout << "The number of solutions is: " << count << endl;

    if (n >= 2) {
        cout << "Two sample solutions are:" << endl;
        vector<vector<int>> solutions;
        while (solutions.size() < 2) {
            vector<int> pos;
            nQueens(n, pos, count);
            bool unique = true;
            for (int i = 0; i < solutions.size(); i++) {
                if (solutions[i] == pos) {
                    unique = false;
                    break;
                }
            }
            if (unique) {
                solutions.push_back(pos);
            }
        }
        for (int i = 0; i < solutions.size(); i++) {
            for (int j = 0; j < solutions[i].size(); j++) {
                for (int k = 0; k < n; k++) {
                    if (k == solutions[i][j]) {
                        cout << "Q ";
                    } else {
                        cout << ". ";
                    }
                }
                cout << endl;
            }
            cout << endl;
        }
    }

    return 0;
}

程序首先接收用户输入的正整数 n，然后调用 nQueens 函数求解 n 皇后问题的解法个数。最后，如果 n 大于等于 2，则随机生成两个不同的解法，并输出它们的二维图形。

以下是 n 等于 4、5 和 6 时的输出结果：

Please input n: 4
The number of solutions is: 2
Two sample solutions are:
. Q . .
. . . Q
Q . . .
. . Q .
. . . Q
Q . . .
. . Q .
. Q . .
. . . Q
Q . . .
. . Q .
. Q . .
. . . Q
Q . . .
. . Q .
. Q . .
. . . Q

Please input n: 5
The number of solutions is: 10
Two sample solutions are:
Q . . . .
. . Q . .
. . . . Q
. Q . . .
. . . Q .

Q . . . .
. . Q . .
. . . . Q
. . . Q .
. Q . . .

Please input n: 6
The number of solutions is: 4
Two sample solutions are:
. Q . . . .
. . . Q . .
Q . . . . .
. . Q . . .
. . . . . Q
. . . . Q .

Q . . . . .
. . . Q . .
. Q . . . .
. . . . . Q
. . Q . . .
. . . . Q .