# Sudoku and Recursion - Perl Weekly Challenge #86

I solved Challenge #2 in Perl Weekly Challenge #2 with **Recursion!**

You are given Sudoku puzzle (9x9).

Write a script to complete the puzzle and must respect the following rules:

- Each row must have the numbers 1-9 occuring just once.
- Each column must have the numbers 1-9 occuring just once.
- The numbers 1-9 must occur just once in each of the 9 sub-boxes (3x3) of the grid.

So, just Sudoku like we know it. This is the sample puzzle:

```
_ _ _ 2 6 _ 7 _ 1
6 8 _ _ 7 _ _ 9 _
1 9 _ _ _ 4 5 _ _
8 2 _ 1 _ _ _ 4 _
_ _ 4 6 _ 2 9 _ _
_ 5 _ _ _ 3 _ 2 8
_ _ 9 3 _ _ _ 7 4
_ 4 _ _ 5 _ _ 3 6
7 _ 3 _ 1 8 _ _ _
```

We can start with the upper-left corner, which we’ll call `0,0`

. We can iterate through `1..9`

, and find that `1`

is a no-go for the first row and first column and first block, `2`

is a no-go for the first row, and `3`

is the first one that can possibly work.

```
3 _ _ 2 6 _ 7 _ 1
6 8 _ _ 7 _ _ 9 _
1 9 _ _ _ 4 5 _ _
8 2 _ 1 _ _ _ 4 _
_ _ 4 6 _ 2 9 _ _
_ 5 _ _ _ 3 _ 2 8
_ _ 9 3 _ _ _ 7 4
_ 4 _ _ 5 _ _ 3 6
7 _ 3 _ 1 8 _ _ _
```

And then start by testing `0,1`

and `0,2`

and find `0,3`

already has `2`

set, and so on. We go forward, accepting the pre-existing values and inserting values when necessary. Going through all possible choices like this is what we call **brute force**, and, at the level we’re at with Sudoki, with a 9x9 grid and only 9 possible choices for each position, taking only a fraction of a second on my laptop, this is valid.

A more clever way would go through and find out that, for `1,5`

, the only possible solution is `1`

, mark that, then find every other only-possible solutions, until it is all solved. This is how I solve them when I solve Sudoku puzzles by hand.

```
#!/usr/bin/env perl
use strict;
use warnings;
use feature qw{ say signatures state };
no warnings qw{ experimental };
my $puzzle = '
_ _ _ 2 6 _ 7 _ 1
6 8 _ _ 7 _ _ 9 _
1 9 _ _ _ 4 5 _ _
8 2 _ 1 _ _ _ 4 _
_ _ 4 6 _ 2 9 _ _
_ 5 _ _ _ 3 _ 2 8
_ _ 9 3 _ _ _ 7 4
_ 4 _ _ 5 _ _ 3 6
7 _ 3 _ 1 8 _ _ _
';
my @puzzle;
for my $row ( grep { /\S/ } split /\s?\n\s?/, $puzzle ) {
my @row = split /\s/mx, $row;
push @puzzle, \@row;
}
say 'BEFORE';
display_puzzle(@puzzle);
solve_puzzle( 0, 0, \@puzzle );
sub solve_puzzle ( $x, $y, $puzzle ) {
return unless $puzzle->[$x][$y];
my $n = $puzzle->[$x][$y];
my $nx = $x;
my $ny = $y;
$nx++;
if ( $nx > 8 ) {
$ny++;
$nx = 0;
}
if ( $n eq '_' ) {
for my $i ( 1 .. 9 ) {
$puzzle->[$x][$y] = $i;
next unless test_puzzle($puzzle);
if ( $x == 8 && $y == 8 ) {
say 'SOLVED';
display_puzzle($puzzle->@*);
}
else {
solve_puzzle( $nx, $ny, $puzzle );
}
}
$puzzle->[$x][$y] = '_';
}
else {
solve_puzzle( $nx, $ny, $puzzle );
}
}
sub test_puzzle( $puzzle) {
my @puzzle = $puzzle->@*;
my $yardstick = join ' ', 1 .. 9;
# rows
for my $x ( 0 .. 8 ) {
my @row = $puzzle[$x]->@*;
# I repeat this code, which makes it a good candidate,
# if not toy code, to be pulled into another function
# so i can use it for columns, rows and blocks
for my $k ( 1 .. 9 ) {
my @c = grep { /$k/ } @row;
my $c = scalar @c;
return 0 if $c > 1;
}
}
# columns
for my $x ( 0 .. 8 ) {
my @col = map { $puzzle->[$_][$x] } 0 .. 8;
for my $k ( 1 .. 9 ) {
my @c = grep { /$k/ } @col;
my $c = scalar @c;
return 0 if $c > 1;
}
}
# blocks
for my $xa ( 0 .. 2 ) {
for my $ya ( 0 .. 2 ) {
my @block;
for my $xb ( 0 .. 2 ) {
for my $yb ( 0 .. 2 ) {
my $x = $xa * 3 + $xb;
my $y = $ya * 3 + $yb;
push @block, $puzzle[$x][$y];
}
}
for my $k ( 1 .. 9 ) {
my @c = grep { /$k/ } @block;
my $c = scalar @c;
return 0 if $c > 1;
}
}
}
return 1;
}
sub display_puzzle ( @puzzle ) {
say '-' x 27;
for my $x ( 0 .. 8 ) {
if ( $x % 3 == 0 && $x ne 0 ) { say '' }
for my $y ( 0 .. 8 ) {
print ' ' if $y % 3 == 0;
print $puzzle[$x][$y] || '=';
print ' ';
}
say '';
}
say '-' x 27;
say '';
}
```

```
BEFORE
---------------------------
_ _ _ 2 6 _ 7 _ 1
6 8 _ _ 7 _ _ 9 _
1 9 _ _ _ 4 5 _ _
8 2 _ 1 _ _ _ 4 _
_ _ 4 6 _ 2 9 _ _
_ 5 _ _ _ 3 _ 2 8
_ _ 9 3 _ _ _ 7 4
_ 4 _ _ 5 _ _ 3 6
7 _ 3 _ 1 8 _ _ _
---------------------------
SOLVED
---------------------------
4 3 5 2 6 9 7 8 1
6 8 2 5 7 1 4 9 3
1 9 7 8 3 4 5 6 2
8 2 6 1 9 5 3 4 7
3 7 4 6 8 2 9 1 5
9 5 1 7 4 3 6 2 8
5 1 9 3 2 6 8 7 4
2 4 8 9 5 7 1 3 6
7 6 3 4 1 8 2 5 9
---------------------------
```