Write an algorithm to prim all ways of arranging eight queens on an 8x8 chess board so that none of them share the same row, column or diagonal. In this case, "diagonal" means all diagonals, not just the two that bisect the board.

nQueens.cpp

#include <iostream>
#include <string>
#include <vector>
#include <math.h>
#include <map>
#include <fstream>
#include < ctime >
#include <algorithm>
#include <vector>
#include <iostream>
#include <set>
using namespace std;

bool valid( vector<vector<int>> &b, int x, int y){
    int w = b.size();
    int h = b[0].size();

    // column and row
    for( int i = 0; i < w; i++){         
        if( b[x][i] ) return false;
        if( b[i][y] ) return false;
    }

    // check diagonals
    int tx = x+1, ty = y+1;
    while( tx < w && ty < h ){
        if( b[tx++][ty++] ) return false;
    }
    tx = x-1, ty = y-1;
    while( tx >= 0 && ty >= 0 ){
        if( b[tx--][ty--] ) return false;
    }
    tx = x+1, ty = y-1;
    while( tx < w && ty >= 0 ){
        if( b[tx++][ty--] ) return false;
    }
    tx = x-1, ty = y+1;
    while( tx > 0 && ty < h ){
        if( b[tx--][ty++] ) return false;
    }

    return true;
}

bool placeQ( vector<vector<int>>& b, int col, set<vector<vector<int>>> &ans){

    if ( col >= b[0].size() )
        return true;
    for( int i = 0; i < b.size(); i++){
        if( valid(b, i, col) ){
            b[i][col] = 1;

            if( !placeQ(b, col+1, ans) )
                b[i][col] = 0;
            else{
                if( col == 0 ){
                    ans.insert(b);
                    std::fill(b.begin(),b.end(),vector<int>(b.size()));
                }
                else
                    return true;
            }
        }
    }
    return false;
}

int main(){
    int n = 8;
    vector<vector<int>> b(n, vector<int>(n,0));
    set<vector<vector<int>>> ans;
    placeQ(b, 0, ans);

    for( auto f = ans.begin(); f != ans.end(); ++f){
        for( auto i = f->begin(); i !=  f->end(); ++i){
            for( auto j = i->begin(); j != i->end(); ++j){
                cout << *j << " ";
            }
            cout << endl;
        }
        cout << endl << endl;
    }
    cout << endl << "Done." <<endl;
    cin.get();
    return 0;
}

Can you explain the intuition for this part:

 // column and row
    for( int i = 0; i < w; i++){         
        if( b[x][i] ) return false;
        if( b[i][y] ) return false;
    }

Are you essentially setting the checks for the rows and columns to false?