N-Queens Solutions in C++

// Source : https://oj.leetcode.com/problems/n-queens/
// Author : Hao Chen
// Date   : 2014-08-22



#include <stdlib.h>
#include <iostream>
#include <vector>
#include <string>
using namespace std;

vector< vector<string> > solveNQueens(int n); 
void solveNQueensRecursive(int n, int currentRow, vector<int>& solution, vector< vector<string> >& result); 
bool isValid(int attemptedColumn, int attemptedRow, vector<int> &queenInColumn); 


vector< vector<string> > solveNQueens(int n) {
    vector< vector<string> > result;
    vector<int> solution(n);

    solveNQueensRecursive(n, 0, solution, result);

    return result;    
}

//The following recursion is easy to understand. Nothing's tricky.
//  1) recursively find all of possible columns row by row.
//  2) solution[] array only stores the columns index. `solution[row] = col;` 
void solveNQueensRecursive(int n, int currentRow, vector<int>& solution, vector< vector<string> >& result) {
    //if no more row need to do, shape the result
    if (currentRow == n){
        vector<string> s;
        vector<string> s(n, string(n, '.'));
        for (int row = 0; row < n; row++) {
            s[row][solution[row]] = 'Q';
        }
        result.push_back(s);
        return;
    }

    //for each column
    for (int col = 0; col < n; col++) {
        //if the current column is valid
        if (isValid(col, currentRow, solution) ) {
            //place the Queue
            solution[currentRow] = col;
            //recursively put the Queen in next row
            solveNQueensRecursive(n, currentRow+1, solution, result);
        }
    } 
}

//Attempting to put the Queen into [row, col], check it is valid or not
//Notes: 
//  1) we just checking the Column not Row, because the row cannot be conflicted
//  2) to check the diagonal, we just check |x'-x| == |y'-y|, (x',y') is a Queen will be placed
bool isValid(int attemptedColumn, int attemptedRow, vector<int> &queenInColumn) {

    for(int i=0; i<attemptedRow; i++) {
        if (attemptedColumn == queenInColumn[i]  || 
            abs(attemptedColumn - queenInColumn[i]) == abs(attemptedRow - i)) {
            return false;
        } 
    }
    return true;
}





void printMatrix(vector< vector<string> >& matrix ){
    for (int i = 0; i < matrix.size(); i++) {
        cout << "-----------" << endl;
        for (int j = 0; j < matrix[i].size(); j++) {
            cout << matrix[i][j] << endl;
        }
    }
}


int main(int argc, char** argv)
{
    int n = 8;
    if (argc>1){
        n = atoi(argv[1]);
    }
    
    vector< vector<string> > result = solveNQueens(n);
    printMatrix(result);
    
    return 0;
}

#include <vector>
#include <string>

using std::vector; using std::string;

class Solution {
    vector<vector<string>> ret;
public:
    vector<vector<string> > solveNQueens(int n) {
        vector<int> queens(n, 0);
        solveNQueens(0, queens);
        return ret;
    }
    
    void solveNQueens(int row, vector<int> queens) {
        int size = queens.size();
        if (row == size) {
            vector<string> solution(size, string(size, '.'));
            for (int r=0; r<size; ++r)
                solution[r][queens[r]] = 'Q';
            ret.push_back(solution);
        } else for (int col=0; col<size; ++col) {
            queens[row] = col;
            if (isValid(row, col, queens)) solveNQueens(row+1, queens);
        }
    }
    
    bool isValid(int row, int col, const vector<int> &queens) {
        for (int queen_col=0, r=row-1, lc=col-1, rc=col+1; r>=0; --r, --lc, ++rc) {
            queen_col = queens[r];
            if (queen_col == col || queen_col == lc || queen_col == rc) return false;
        }
        return true;
    }
};

/// Source : https://leetcode.com/problems/n-queens/description/
/// Author : liuyubobobo
/// Time   : 2017-11-18

#include <iostream>
#include <vector>
#include <cassert>

using namespace std;

/// Basic Recursive
/// Time Complexity: O(n^n)
/// Space Complexity: O(n)
class Solution {
private:
    vector<bool> col, dia1, dia2;
    vector<vector<string>> res;

    // 尝试在一个n皇后问题中, 摆放第index行的皇后位置
    void putQueen(int n, int index, vector<int> &row){

        if(index == n){
            res.push_back(generateBoard(n, row));
            return;
        }

        for(int i = 0 ; i < n ; i ++)
            // 尝试将第index行的皇后摆放在第i列
            if(!col[i] && !dia1[index + i] && !dia2[index - i + n - 1]){
                row.push_back(i);
                col[i] = true;
                dia1[index + i] = true;
                dia2[index - i + n - 1] = true;
                putQueen(n, index + 1, row);
                col[i] = false;
                dia1[index + i] = false;
                dia2[index - i + n - 1] = false;
                row.pop_back();
            }

        return;
    }

    vector<string> generateBoard(int n, vector<int> &row){
        assert(row.size() == n);
        vector<string> board(n, string(n, '.'));
        for(int i = 0 ; i < n ; i ++)
            board[i][row[i]] = 'Q';
        return board;
    }

public:
    vector<vector<string>> solveNQueens(int n) {

        res.clear();

        col.clear();
        for(int i = 0 ; i < n ; i ++)
            col.push_back(false);

        dia1.clear();
        dia2.clear();
        for(int i = 0 ; i < 2 * n - 1 ; i ++){
            dia1.push_back(false);
            dia2.push_back(false);
        }

        vector<int> row;
        putQueen(n, 0, row);

        return res;
    }
};


void printBoard(const vector<string>& board){
    for(string row: board)
        cout << row << endl;
    cout << endl;
}

int main() {

    int n = 4;
    vector<vector<string>> res = Solution().solveNQueens(n);
    for(vector<string> board: res)
        printBoard(board);

    return 0;
}