传统办法-回溯法

#include<iostream>
#include<math.h>
using namespace std;

int n=8;
int total=0;
int *c=new int(n);

bool is_ok(int row){
    for(int j=0;j!=row;j++){
        if(c[row]==c[j] || row-c[row]==j-c[j] || row+c[row]==j+c[j])
            return false;
    }
    return true;
}

void queen(int row){
    if(row==n)
        total++;
    else
        for(int col=0;col!=n;col++){
            c[row]=col;
            if(is_ok(row))
                queen(row+1);
        }       
}

int main(){
    queen(0);
    cout<<total<<endl;
    return 1;
}

新版方法

#include <iostream>
#include <vector>
#include <algorithm>

using  namespace std;


void  N_Queue(vector<int> colum_index, vector<vector<int>>& result, int start);

int main()
{
    int n;
    cin >> n;
    vector<int> colum_index;
    for (int i = 0; i < n; ++i) {
        colum_index.push_back(i);
    }
    vector<vector<int>> res;
    N_Queue(colum_index, res, 0);
    cout << res.size() << endl;
    return 0;
}

void  N_Queue(vector<int> colum_index, vector<vector<int>>& result, int start)
{
    if (start == colum_index.size() - 1)
    {
        bool res = true;
        for (int i = 0; i < colum_index.size(); i++)
        {
            for (int j = i + 1; j < colum_index.size(); ++j) {
                if (i - j == colum_index[i] - colum_index[j] || i - j == colum_index[j] - colum_index[i])
                {
                    res = false;
                    break;
                }
            }
            if (!res)
            {
                break;
            }
        }
        if (res)
        {
            result.push_back(colum_index);
        }
    } else{
        for (int i = start; i < colum_index.size(); i++)
        {
            swap(colum_index[i], colum_index[start]);
            N_Queue(colum_index, result, start + 1);
            swap(colum_index[i], colum_index[start]);
        }
    }
}

参考

回溯法
排列法