I have no idea why I would want to solve sudoku in PostgreSQL PL/pgSQL. My guess would be just for the fun of it. I’m also hoping that it can serve as a tutorial example in programming PostgreSQL PL/pgSQL.

So what is sudoku? It is basically a number puzzle where the objective is to fill 9×9 grid so that the columns, rows, and the smaller 3×3 squares, called blocks, doesn’t have the same number repeated. If you’re not familiar with sudoku, this Wikipedia page on sudoku may be helpful.

Now that you’re familiar with sudoku, there are many algorithms for solving sudoku. For this solution, I’ve decided to use brute force algorithm.

If you’re just interested in the end result, please jump to last page.

Table structure for sudoku

The table to represent sudoku is pretty straight forward. It’s basically 4 columns that describe:

• The x and y coordinate for each sudoku cell
• The value of the cell
• A marker to identify whether the value is given. I call this is_permanent

CREATE TABLE sudoku (
	x_col integer NOT NULL,
	y_col integer NOT NULL,
	val integer,
	is_permanent boolean NOT NULL DEFAULT false,
	CONSTRAINT sudoku_pkey PRIMARY KEY (x_col, y_col)
) WITHOUT OIDS;

In addition to sudoku table, I I’ll need to get a list of possible values. So rather than typing it every time in query string, I thought it would be convenient to have a table with a list of legal values.

CREATE TABLE nums (
	num integer NOT NULL DEFAULT 1,
	CONSTRAINT nums_pkey PRIMARY KEY (num)
) WITHOUT OIDS;

INSERT INTO nums VALUES (1),(2),(3),(4),(5),(6),(7),(8),(9);

Test case sudoku puzzle

For the purpose of testing the solution, let’s start with a rather easy to solve by hand. The puzzle and the solution is as below:

Populating sudoku table

Now that we have the puzzle to solve, let’s insert the known values into our sudoku table.

INSERT INTO sudoku (x_col, y_col, val, is_permanent) VALUES
	('1','3','5', TRUE), ('1','4','1', TRUE), ('1','6','9', TRUE),
	('1','7','4', TRUE), ('1','8','7', TRUE), ('1','9','3', TRUE),
	('2','3','9', TRUE), ('2','4','5', TRUE), ('2','7','8', TRUE),
	('2','9','6', TRUE), ('3','1','1', TRUE), ('3','2','4', TRUE),
	('3','4','8', TRUE), ('3','7','2', TRUE), ('4','1','4', TRUE),
	('4','8','6', TRUE), ('5','3','6', TRUE), ('5','4','7', TRUE),
	('5','6','2', TRUE), ('5','7','5', TRUE), ('6','2','8', TRUE),
	('6','9','1', TRUE), ('7','3','4', TRUE), ('7','6','1', TRUE),
	('7','8','2', TRUE), ('7','9','8', TRUE), ('8','1','5', TRUE),
	('8','3','2', TRUE), ('8','6','8', TRUE), ('8','7','6', TRUE),
	('9','1','3', TRUE), ('9','2','9', TRUE), ('9','3','8', TRUE),
	('9','4','2', TRUE), ('9','6','7', TRUE), ('9','7','1', TRUE)
;

On the next page, we’ll discuss on how to determine valid values for a given cell.