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

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

 什么时候跳过的改动

 if (!isValid(cols, colIndex)) {
                continue;
            }

 public List<List<String>> solveNQueens(int n) {
         List<List<String>> results = new ArrayList<>();
        if (n <= 0) {
            return results;
        }
        List<Integer> list = new ArrayList<Integer>();
        search(results, list, n);
        return results;
    }
    
    /*
     * results store all of the chessboards
     * cols store the column indices for each row
     */
    private void search(List<List<String>> results,
                        List<Integer> cols,
                        int n) {
        if (cols.size() == n) {
            results.add(drawChessboard(cols));
            return;
        }
        
        for (int colIndex = 0; colIndex < n; colIndex++) {
            if (!isValid(cols, colIndex)) {
                continue;
            }
            cols.add(colIndex);
            search(results, cols, n);
            cols.remove(cols.size() - 1);
        }
    }
    
    private ArrayList<String> drawChessboard(List<Integer> cols) {
        ArrayList<String> chessboard = new ArrayList<>();
        for (int i = 0; i < cols.size(); i++) {
            StringBuilder sb = new StringBuilder();
            for (int j = 0; j < cols.size(); j++) {
                sb.append(j == cols.get(i) ? 'Q' : '.');
            }
            chessboard.add(sb.toString());
        }
        return chessboard;
    }
    
    private boolean isValid(List<Integer> cols, int column) {
        int row = cols.size();
        for (int rowIndex = 0; rowIndex < cols.size(); rowIndex++) {
            if (cols.get(rowIndex) == column || rowIndex + cols.get(rowIndex) == row + column || 
                rowIndex - cols.get(rowIndex) == row - column) {
                return false;
            }
            
        }
        return true;

    }
}