Day 3

% Our backpacks

backpack('vJrwpWtwJgWrhcsFMMfFFhFp').
backpack('jqHRNqRjqzjGDLGLrsFMfFZSrLrFZsSL').
backpack('PmmdzqPrVvPwwTWBwg').
backpack('wMqvLMZHhHMvwLHjbvcjnnSBnvTQFn').
backpack('ttgJtRGJQctTZtZT').
backpack('CrZsJsPPZsGzwwsLwLmpwMDw').

% Split a backpacks into two lists of equal length
sections(Backpack, SectionOne, SectionTwo) :- atom_length(Backpack, BackpackSize), Length is BackpackSize // 2, sub_atom(Backpack, 0, Length, Length, SectionOneChars), sub_atom(Backpack, Length, Length, _, SectionTwoChars), atom_chars(SectionOneChars, SectionOne), atom_chars(SectionTwoChars, SectionTwo).

% Check for items that occur in both lists
common_items(SectionOne, SectionTwo, Common) :- setof(X, member(X, SectionOne), OneUnique), setof(Y, (member(Y, OneUnique), memberchk(Y, SectionTwo)), Common).

% Find all common items on a backpack. Result is a list of lists
all_common(CommonListOfLists) :- findall(Common, (backpack(Backpack), sections(Backpack, SectionOne, SectionTwo), common_items(SectionOne, SectionTwo, Common)), CommonListOfLists).

% Find the values in a list of lists
% Empty list has no values
find_values([], 0).
find_values([CommonList|RestListOfLists], SumValue) :- find_item_values(CommonList, ItemValues), find_values(RestListOfLists, RestSum), SumValue is ItemValues + RestSum.

% Find values in a list
find_item_values([], 0).
find_item_values([Item|Rest], SumValue) :- item_value(Item, ItemValue), find_item_values(Rest, RestSum), SumValue is ItemValue + RestSum.

% Determine the value of a single item
item_value(Item, ItemValue) :- name(Item, AsciiValue), AsciiValue < 97, ItemValue is AsciiValue - 38.
item_value(Item, ItemValue) :- name(Item, AsciiValue), AsciiValue > 96, ItemValue is AsciiValue - 96.

% Solve the puzzle
solve(SumValue) :- all_common(CommonListOfLists), find_values(CommonListOfLists, SumValue).