From 0378b27aedf31a060c004e5e80fead505e6ab8a4 Mon Sep 17 00:00:00 2001
From: Dory <dory@dory.moe>
Date: Mon, 4 Dec 2023 09:21:56 -0800
Subject: [PATCH] make part2 clearer

---
 04/part2.pl | 40 +++++++++++++++++++---------------------
 1 file changed, 19 insertions(+), 21 deletions(-)

diff --git a/04/part2.pl b/04/part2.pl
index 1bc2c7c..4e9c10b 100644
--- a/04/part2.pl
+++ b/04/part2.pl
@@ -1,27 +1,6 @@
 :- table match/3.
 :- table sum/5.
 
-% match1(WinningNums, CardNums, NMatches)
-match1(_, [], 0).
-match1(Wins, [X|Nums], N) :- member(X, Wins), match1(Wins, Nums, N1), N is N1 + 1.
-match1(Wins, [X|Nums], N) :- \+ member(X, Wins), match1(Wins, Nums, N).
-
-match(Input, Nth, NMatches) :-
-    nth1(Nth, Input, [Wins|CardNums]),
-    match1(Wins, CardNums, NMatches).
-
-% sum(Cards, X, StuffToSum, Indices, Sum).
-sum(_, _, [], [0], 0).
-sum(Cards, X, [Element|Rest], [I,INext|IRest], Sum) :-
-    sum(Cards, X, Rest, [INext|IRest], SumOfRest),
-    Sum is Element + SumOfRest,
-    I is INext + 1,
-    match(Cards, I, NMatches_i), NMatches_i >= X - I.
-sum(Cards, X, [_|Rest], [I,INext|IRest], SumOfRest) :-
-    sum(Cards, X, Rest, [INext|IRest], SumOfRest),
-    I is INext + 1,
-    match(Cards, I, NMatches_i), NMatches_i < X - I.
-
 % Number of card X = Nx = 1 + sum(Ni*(matches(i) >= x-i), i=1->x-1)
 ncards([], []).
 ncards([_|RestOfCards], [Nx|NRest]) :-
@@ -30,6 +9,25 @@ ncards([_|RestOfCards], [Nx|NRest]) :-
     reverse(RestOfCards, ReversedRestOfCards),
     sum(ReversedRestOfCards, X, NRest, _, Nx_minus_1), Nx is Nx_minus_1 + 1.
 
+% sum(Cards, X, StuffToSum, Indices, Sum).
+% This calculates the "sum(Ni*(matches(i) >= x-i), i=1->x-1)" part of Nx
+sum(_, _, [], [0], 0).
+sum(Cards, X, [Element|Rest], [I,INext|IRest], Sum) :-
+    sum(Cards, X, Rest, [INext|IRest], SumOfRest),
+    match(Cards, I, NMatches_i),
+    I is INext + 1,
+    (NMatches_i >= X - I -> Sum is Element + SumOfRest; Sum is SumOfRest).
+
+% match binds the number of matches that card Nth in the list has
+match(Cards, Nth, NMatches) :-
+    nth1(Nth, Cards, [Wins|CardNums]),
+    match1(Wins, CardNums, NMatches).
+
+% match1(WinningNums, CardNums, NMatches) binds number of matches for a card.
+match1(_, [], 0).
+match1(Wins, [X|Nums], M) :- member(X, Wins), match1(Wins, Nums, M1), M is M1 + 1.
+match1(Wins, [X|Nums], M) :- \+ member(X, Wins), match1(Wins, Nums, M).
+
 % this is a more normal sum of a list
 sum([], 0).
 sum([Element|Rest], Sum) :- sum(Rest, RestOfSum), Sum is Element + RestOfSum.