LeetCode-51.N-Queens

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..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]

public class Solution 
{
    public IList<IList<string>> SolveNQueens(int n)
        {
            IList<IList<string>> res = new List<IList<string>>();
            IList<string> list = new List<string>();
            string s = "";
            for (int i = 0; i < n; i++)
                s += ".";
            for (int i = 0; i < n; i++)
                list.Add(s);
            PlaceQ(res, list, n, 0);
            return res;
        }

        private void PlaceQ(IList<IList<string>> res, IList<string> list,int n,int row)
        {
            if (row == n)
            {
                res.Add(new List<string>(list));
                return;
            }    

            for (int col = 0; col < n; col++)
                if (isValid(list,n,row,col))
                {
                    list[row]=list[row].Remove(col,1).Insert(col, "Q");
                    PlaceQ(res, list, n, row + 1);
                    list[row] = list[row].Remove(col,1).Insert(col, ".");
                }
        }

        private static bool isValid(IList<string> list, int n, int row, int col)
        {
            for (int i = 0; i < row; i++)
                if (list[i][col] == 'Q')
                    return false;
            for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--)
                if (list[i][j] == 'Q')
                    return false;
            for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++)
                if (list[i][j] == 'Q')
                    return false;
            return true;
        }
}