[LeetCode] N-Queens

N-Queens

 

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The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.

For example,

There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

 

Solution:

//board is 0 for avaliable positons, 1 for the other

int board[100][100];

int queenPos[100];

int N;

int solutionNum = 0;

vector<vector<string> > result;





void dfs(int k)

{

    if(k == N)

    {//the last queen has been put properly

        solutionNum++;

        vector<string> cur;

        for(int i = 0;i < N;i++)

        {

            string column= "";

            for(int j = 0;j < N;j++)

            {

                if(queenPos[i] == j)

                    column += "Q";

                else

                    column += ".";

            }

    //        cout << column << endl;

            cur.push_back(column);

        }

    //    cout << endl << endl;

        result.push_back(cur);

        return;

    }



    for(int i = 0;i < N;i++)

    {

        //search for a postion for the current queen

        bool flag = true;



        if(board[i][k] == 0)

        {

            list<int> lastX, lastY;

            //this is a good postion for the k th column queen.

            queenPos[k] = i;//in the ith row, kth column

            //change the board state to mark its attark region.

            for(int j = 0;j < N;j++)

            {

                if(board[i][j] == 0)

                {

                    board[i][j] = 1;

                    lastX.push_back(i);

                    lastY.push_back(j);

                //    cout << i << " " << j << endl;

                }

                if(board[j][k] == 0)

                {

                    board[j][k] = 1;

                    lastX.push_back(j);

                    lastY.push_back(k);

                    //cout << j << " " << k << endl;

                }

                //

                if(i - j >= 0 && k - j >= 0 && board[i - j][k - j] == 0)

                {

                    //left up

                    lastX.push_back(i - j);

                    lastY.push_back(k - j);

                    board[i - j][k - j] = 1;



                    //cout << i -j  << " " << k - j << endl;

                }

                if(i - j >= 0 && k + j < N && board[i - j][k + j] == 0)

                {

                    lastX.push_back(i - j);

                    lastY.push_back(k + j);

                    board[i - j][k + j] = 1;

                    //cout << i -j  << " " << k + j << endl;

                }

                if(i + j < N && k - j >= 0 && board[i + j][k - j] == 0)

                {

                    lastX.push_back(i + j);

                    lastY.push_back(k - j);

                    board[i + j][k - j] = 1;

                //    cout << i + j  << " " << k - j << endl;

                }

                if(i + j < N && k + j < N && board[i + j][k + j] == 0)

                {

                    lastX.push_back(i + j);

                    lastY.push_back(k + j);

                    board[i + j][k + j] = 1;

                //    cout << i + j  << " " << k + j << endl;

                }

            }

            

            //cout << "put the " << k << " queen at " << i << " size = " << lastX.size() << endl;



            dfs(k + 1);

            

            //cout << "size = " << lastX.size() << endl;

            //back to the previous state.

            int num = lastX.size();

            for(int t = 0;t < num;t++)

            {

                int x = lastX.front();

                lastX.pop_front();

                int y = lastY.front();

                lastY.pop_front();

                board[x][y] = 0;

        //        cout << x << " " << y << endl;

            }    

        }

        else

            continue;

    }



}



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

        N = n;

    solutionNum = 0;

    for(int i = 0;i < 100;i++)

    {

        for(int j = 0;j < 100;j++)

            board[i][j] = 0;

        queenPos[i] = 0;

    }

    dfs(0);

    return result;    

    }

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