# Advent Of Code 2021, Day 3: Binary Diagnostic

by Abigail ## Challenge

We are given a diagnostic report, with binary numbers like:

00100
11110
10110
10111
10101
01111
00111
11100
10000
11001
00010
01010


#### Part One

For Part One, we first have to calculate the gamma rate and the epsilon rate. For the gamma rate, we have to find the most common bit on each position. For the epsilone rate, we have to find the least common bit on each position.

So, for the example file above, the gamma rate is 10110, or 22 in decimal while the epsilon rate is 01001, or 9 in decimal.

The wanted result is the produce of both numbers, so 198.

#### Part Two

In Part Two, we need to calculate the oxygen generator rating, and the CO2 scrubber rating.

The ratings don't need to be calculated — they need to be found in the list. We do this repeatedly as follows:

• Find the most common bit and least common bit in the current position.
• For the oxygen generator rating, keep the values where the bit in the current position equals the most common bit in that position.
• For the CO2 scrubber rating, keep the values where the bit in the current position equals the least common bit in that position.
• Stop filtering when there is one value left.
• Increment the current position.

If 1 and 0 occur equally often, we break the tie by considering 1 to be the most frequent bit.

For the example file above, the oxygen generator rating is 10111, or 23 in decimal. The CO2 scrubber rating is 01010, or 10 in decimal.

The wanted result is the product of the two numbers, so 230.

## Solution

If the most occuring bit in a column is b, then the least occuring bit is 1 - b.

### Perl

First, we need to read the input, and put it into a datastructure. We'll use a 2-dimensional array: each value of the input we split into individual characters (hence, bits):

my $input = [map {chomp; [split //]} <>];  <> reads in the data; since it's in list context, it splits the input, returning a list of strings, each string a line of input. Each string is fed into the map. chomp removes the newline, and then we split the string into indivual characters, storing them into an array. So, the map returns a list of array(refs), making $input a reference to a two-dimensional array.

All input values have the same number of bits, so we can get the number of bits by just looking at the first entry:

my $nr_bits = @{$$input };  Evaluating an array in scalar context gives use the number of elements in the array. Next, we define a subroutine taking two arguments, a position and a reference to an array. It will return which bit (1 or 0) occurs most frequently on the given position. We find out which bit is used most often by summing the values of each of the bits (using sum0 from List::Util. This sum equals the number of 1 bits. If the sum equals or exceeds half the size of the input array, the most frequent bit is 1, else it is 0. If there is a tie, 1 will be returned. sub most_used (pos, list) { my ones = sum0 map {$$_ [$pos]} @$list;$ones >= @$list / 2 ? 1 : 0 }  We can now calculate the bits for the gamma rate of Part One: we just find out which bit is used most frequently on each position: my @max = map {most_used$_, $input} 0 ..$nr_bits - 1;


For the bits of the epsilon rate, we just flip the bits:

my @min = map {1 - $_} @max;  To turn those arrays of bits into integers, we use string interpolation and oct: local$" = "";
my $gamma = oct "0b@max"; my$epsilon = oct "0b@min";


For Part Two, we copy the input array, then repeatedly find the most/least used bit on a particular position, and filter out the values with those bits, until we are left with just one value:

my @oxygen    = @$input; my @co2 = @$input;
for (my $pos = 0;$pos < $nr_bits;$pos ++) {
my $o_bit = most_used$pos, \@oxygen;
my $c_bit = 1 - most_used$pos, \@co2;
@oxygen   = grep {$$_ [pos] == o_bit} @oxygen if @oxygen > 1; @co2 = grep {$$_ [$pos] ==$c_bit} @co2    if @co2    > 1;
}


Now, @oxygen and @co2 will contain exactly one element (each element an array of bits). We can turn those into integers in the same way as we did above:

local $" = ""; my$oxygen  = oct "0b@{$oxygen }"; my$co2     = oct "0b@{$co2 }";  All that is left is to print the answers: say "Solution 1: ",$gamma  * $epsilon; say "Solution 2: ",$oxygen * \$co2;


Find the full program on GitHub.