adventofcode/2024/day05/problem

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[15]Cloudsmith - Code shapes reality; now solve your next puzzle: global
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--- Day 5: Print Queue ---
Satisfied with their search on Ceres, the squadron of scholars suggests
subsequently scanning the stationery stacks of sub-basement 17.
The North Pole printing department is busier than ever this close to
Christmas, and while The Historians continue their search of this
historically significant facility, an Elf operating a [16]very familiar
printer beckons you over.
The Elf must recognize you, because they waste no time explaining that the
new sleigh launch safety manual updates won't print correctly. Failure to
update the safety manuals would be dire indeed, so you offer your
services.
Safety protocols clearly indicate that new pages for the safety manuals
must be printed in a very specific order. The notation X|Y means that if
both page number X and page number Y are to be produced as part of an
update, page number X must be printed at some point before page number Y.
The Elf has for you both the page ordering rules and the pages to produce
in each update (your puzzle input), but can't figure out whether each
update has the pages in the right order.
For example:
47|53
97|13
97|61
97|47
75|29
61|13
75|53
29|13
97|29
53|29
61|53
97|53
61|29
47|13
75|47
97|75
47|61
75|61
47|29
75|13
53|13
75,47,61,53,29
97,61,53,29,13
75,29,13
75,97,47,61,53
61,13,29
97,13,75,29,47
The first section specifies the page ordering rules, one per line. The
first rule, 47|53, means that if an update includes both page number 47
and page number 53, then page number 47 must be printed at some point
before page number 53. (47 doesn't necessarily need to be immediately
before 53; other pages are allowed to be between them.)
The second section specifies the page numbers of each update. Because most
safety manuals are different, the pages needed in the updates are
different too. The first update, 75,47,61,53,29, means that the update
consists of page numbers 75, 47, 61, 53, and 29.
To get the printers going as soon as possible, start by identifying which
updates are already in the right order.
In the above example, the first update (75,47,61,53,29) is in the right
order:
 75 is correctly first because there are rules that put each other page
after it: 75|47, 75|61, 75|53, and 75|29.
 47 is correctly second because 75 must be before it (75|47) and every
other page must be after it according to 47|61, 47|53, and 47|29.
 61 is correctly in the middle because 75 and 47 are before it (75|61
and 47|61) and 53 and 29 are after it (61|53 and 61|29).
 53 is correctly fourth because it is before page number 29 (53|29).
 29 is the only page left and so is correctly last.
Because the first update does not include some page numbers, the ordering
rules involving those missing page numbers are ignored.
The second and third updates are also in the correct order according to
the rules. Like the first update, they also do not include every page
number, and so only some of the ordering rules apply - within each update,
the ordering rules that involve missing page numbers are not used.
The fourth update, 75,97,47,61,53, is not in the correct order: it would
print 75 before 97, which violates the rule 97|75.
The fifth update, 61,13,29, is also not in the correct order, since it
breaks the rule 29|13.
The last update, 97,13,75,29,47, is not in the correct order due to
breaking several rules.
For some reason, the Elves also need to know the middle page number of
each update being printed. Because you are currently only printing the
correctly-ordered updates, you will need to find the middle page number of
each correctly-ordered update. In the above example, the correctly-ordered
updates are:
75,47,61,53,29
97,61,53,29,13
75,29,13
These have middle page numbers of 61, 53, and 29 respectively. Adding
these page numbers together gives 143.
Of course, you'll need to be careful: the actual list of page ordering
rules is bigger and more complicated than the above example.
Determine which updates are already in the correct order. What do you get
if you add up the middle page number from those correctly-ordered updates?
To begin, [17]get your puzzle input.
Answer: [18]_____________________ [19][ [Submit] ]
You can also [Shareon [20]Bluesky [21]Twitter [22]Mastodon] this puzzle.
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