backtracing

5月10日

1 37  Sudoku Slover

 public void solveSudoku(char[][] board) {
        if(board == null || board.length == 0)
            return;
        slove(board);
    }
    public boolean slove(char[][] board){
        for (int i = 0; i < board.length; i++)
        {
            for (int j = 0; j < board[0].length; j++)
            {
                if (board[i][j] == ‘.‘)
                {
                    for (char c = ‘1‘; c <= ‘9‘; c++)
                    {
                        if (isValue(board, i, j, c))
                        {
                            board[i][j] = c;
                            if (slove(board))
                                return true;
                            else
                                board[i][j] = ‘.‘;
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }
    public boolean isValue(char[][] board, int row, int col, char c)
    {
        for (int i = 0; i < 9; i++)
        {
            if (board[i][col] != ‘.‘ && board[i][col] == c) return false;
             if (board[row][i] != ‘.‘ && board[row][i] == c) return false;
             if (board[3 * (row/3) + i/3][3 *(col/3) + i % 3] != ‘.‘ &&
             board[3 * (row/3) + i/3][3 *(col/3) + i % 3] == c) return false;
        }
        return true;
    }

2 51 N-Queens

  public List<List<String>> solveNQueens(int n) {
        List<List<String>> res = new ArrayList<>();
        help(n, 0, new int[n], res);
        return res;
    }
    public void help(int n, int row, int[] colforrow, List<List<String>> res)
    {
        if (row == n)
        {
            ArrayList<String> item = new ArrayList<>();
            for (int i = 0; i < n; i++)
            {
                StringBuilder sb = new StringBuilder();
                for (int j = 0; j < n; j++)
                {
                    if (colforrow[i] == j)
                        sb.append(‘Q‘);
                    else
                        sb.append(‘.‘);
                }
                item.add(sb.toString());
            }
            res.add(item);
            return;
        }
        for (int i = 0; i < n; i++)
        {
            colforrow[row] = i;
            if (check(row, colforrow))
            {
                help(n, row + 1, colforrow, res);
            }
        }
    }

3 52 N-Queens II

    public int totalNQueens(int n) {
        ArrayList<Integer> res = new ArrayList<>();
        res.add(0);
        help(n, 0, new int[n], res);
        return res.get(0);
    }
    private void help(int n, int row, int[] columnForRow, ArrayList<Integer> res)
   {
    if(row==n)
    {
        res.set(0,res.get(0)+1);
        return;
    }
    for(int i=0;i<n;i++)
    {
        columnForRow[row]=i;
        if(check(row,columnForRow))
        {
            help(n,row+1,columnForRow,res);
        }
    }
}
private boolean check(int row, int[] columnForRow)
{
    for(int i=0;i<row;i++)
    {
        if(columnForRow[i]==columnForRow[row] || Math.abs(columnForRow[row]-columnForRow[i])==row-i)
            return false;
    }
    return true;
} 

4 77  combinations  分子问题

    public List<List<Integer>> combine(int n, int k) {
        List<List<Integer>> res = new ArrayList<>();
        if (n <= 0 || n < k) return res;
        help(n, k, 1, new ArrayList<Integer>(), res);
        return res;
    }
    public void help(int n, int k, int start, ArrayList<Integer> item, List<List<Integer>> res)
    {
        if (item.size() == k)
        {
            res.add(new ArrayList<Integer>(item));
            return;
        }
        for (int i = start; i <= n; i++)
        {
            item.add(i);
            help(n, k, i + 1, item, res);
            item.remove(item.size() - 1);
        }
    }