Question

I’m writing an algorithm in PHP to solve a given Sudoku puzzle. I’ve set up a somewhat object-oriented implementation with two classes: a Square class for each individual tile on the 9×9 board, and a Sudoku class, which has a matrix of Squares to represent the board.

The implementation of the algorithm I’m using is a sort of triple-tier approach. The first step, which will solve only the most basic puzzles (but is the most efficient), is to fill in any squares which can only take a single value based on the board’s initial setup, and to adjust the constraints accordingly on the rest of the unsolved squares.

Usually, this process of ‘constant propagation’ doesn’t solve the board entirely, but it does solve a sizable chunk. The second tier will then kick in. This parses each unit (or 9 squares which must all have unique number assignments, e.g. a row or column) for the ‘possible’ values of each unsolved square. This list of possible values is represented as a string in the Square class:

class Square {  private $name;                // 00, 01, 02, ... , 86, 87, 88 private $peers;               // All squares in same row, col, and box private $number;              // Assigned value (0 if not assigned) private $possibles;           // String of possible numbers (1-9)  public function __construct($name, $p = 0) {   $this->name = $name;   $this->setNumber($p);   if ($p == 0) {     $this->possibles = '123456789';   } }  // ... other functions 

Given a whole array of unsolved squares in a unit (as described in the second tier above), the second tier will concatenate all the strings of ‘possibles’ into a single string. It will then search through that single string for any unique character values – values which do not repeat themselves. This will indicate that, within the unit of squares, there is only one square that can take on that particular value.

My question is: for implementing this second tier, how can I parse this string of all the possible values in a unit and easily detect the unique value(s)? I know I could create an array where each index is represented by the numbers 1-9, and I could increment the value at the corresponding index by 1 for each possible-value of that number that I find, then scan the array again for any values of 1, but this seems extremely inefficient, requiring two linear scans of an array for each unit, and in a Sudoku puzzle there are 27 units.

Answer 1

This is somewhat like what you have already ruled out as ‘extremely inefficient’, but with builtin functions so it might be quite efficient:

$all_possibilities = '1234567891234'; $unique = array(); foreach (count_chars($all_possibilities, 1) as $c => $occurrences) {   if ($occurrences == 1)     $unique[] = chr($c); } print join('', $unique) . '\n'; 

Prints: ‘56789’