CodeSignal-Arrays(4):sudoku2

Question

Sudoku is a number-placement puzzle. The objective is to fill a 9 × 9 grid with numbers in such a way that each column, each row, and each of the nine 3 × 3 sub-grids that compose the grid all contain all of the numbers from 1 to 9 one time.

Implement an algorithm that will check whether the given grid of numbers represents a valid Sudoku puzzle according to the layout rules described above. Note that the puzzle represented by grid does not have to be solvable.

Example

• For

  grid = [['.', '.', '.', '1', '4', '.', '.', '2', '.'],
          ['.', '.', '6', '.', '.', '.', '.', '.', '.'],
          ['.', '.', '.', '.', '.', '.', '.', '.', '.'],
          ['.', '.', '1', '.', '.', '.', '.', '.', '.'],
          ['.', '6', '7', '.', '.', '.', '.', '.', '9'],
          ['.', '.', '.', '.', '.', '.', '8', '1', '.'],
          ['.', '3', '.', '.', '.', '.', '.', '.', '6'],
          ['.', '.', '.', '.', '.', '7', '.', '.', '.'],
          ['.', '.', '.', '5', '.', '.', '.', '7', '.']]
  

  the output should be
  solution(grid) = true;

• For

  grid = [['.', '.', '.', '.', '2', '.', '.', '9', '.'],
          ['.', '.', '.', '.', '6', '.', '.', '.', '.'],
          ['7', '1', '.', '.', '7', '5', '.', '.', '.'],
          ['.', '7', '.', '.', '.', '.', '.', '.', '.'],
          ['.', '.', '.', '.', '8', '3', '.', '.', '.'],
          ['.', '.', '8', '.', '.', '7', '.', '6', '.'],
          ['.', '.', '.', '.', '.', '2', '.', '.', '.'],
          ['.', '1', '.', '2', '.', '.', '.', '.', '.'],
          ['.', '2', '.', '.', '3', '.', '.', '.', '.']]
  

  the output should be
  solution(grid) = false.

  The given grid is not correct because there are two 1s in the second column. Each column, each row, and each 3 × 3 subgrid can only contain the numbers 1 through 9 one time.

Input/Output

• [execution time limit] 4 seconds (py3)

• [memory limit] 1 GB

• [input] array.array.char grid

  A 9 × 9 array of characters, in which each character is either a digit from '1' to '9' or a period '.'.

• [output] boolean

  Return true if grid represents a valid Sudoku puzzle, otherwise return false.

Answer python

def solution(grid):
    # Check rows
    for row in grid:
        if not is_valid(row):
            return False

    # Check columns
    for col in range(9):
        column = [grid[row][col] for row in range(9)]
        if not is_valid(column):
            return False

    # Check sub-grids
    for row in range(0, 9, 3):
        for col in range(0, 9, 3):
            subgrid = [
                grid[r][c]
                for r in range(row, row + 3)
                for c in range(col, col + 3)
            ]
            if not is_valid(subgrid):
                return False

    return True


def is_valid(group):
    numbers = set()
    for num in group:
        if num != '.':
            if num in numbers:
                return False
            numbers.add(num)
    return True