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125 lines
5.4 KiB
Markdown
125 lines
5.4 KiB
Markdown
https://adventofcode.com/2021/day/8
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## \--- Day 8: Seven Segment Search ---
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You barely reach the safety of the cave when the whale smashes into the cave
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mouth, collapsing it. Sensors indicate another exit to this cave at a much
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greater depth, so you have no choice but to press on.
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As your submarine slowly makes its way through the cave system, you notice
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that the four-digit [seven-segment
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displays](https://en.wikipedia.org/wiki/Seven-segment_display) in your
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submarine are malfunctioning; they must have been damaged during the escape.
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You'll be in a lot of trouble without them, so you'd better figure out what's
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wrong.
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Each digit of a seven-segment display is rendered by turning on or off any of
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seven segments named `a` through `g`:
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[code]
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0: 1: 2: 3: 4:
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_aaaa_ .... _aaaa aaaa_ ....
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_b c_ . _c_ . _c_ . _c b c_
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_b c_ . _c_ . _c_ . _c b c_
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.... .... _dddd dddd dddd_
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_e f_ . _f e_ . . _f_ . _f_
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_e f_ . _f e_ . . _f_ . _f_
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_gggg_ .... _gggg gggg_ ....
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5: 6: 7: 8: 9:
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_aaaa aaaa aaaa aaaa aaaa_
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_b_ . _b_ . . _c b c b c_
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_b_ . _b_ . . _c b c b c_
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_dddd dddd_ .... _dddd dddd_
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. _f e f_ . _f e f_ . _f_
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. _f e f_ . _f e f_ . _f_
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_gggg gggg_ .... _gggg gggg_
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[/code]
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So, to render a `1`, only segments `c` and `f` would be turned on; the rest
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would be off. To render a `7`, only segments `a`, `c`, and `f` would be turned
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on.
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The problem is that the signals which control the segments have been mixed up
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on each display. The submarine is still trying to display numbers by producing
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output on signal wires `a` through `g`, but those wires are connected to
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segments _randomly_. Worse, the wire/segment connections are mixed up
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separately for each four-digit display! (All of the digits _within_ a display
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use the same connections, though.)
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So, you might know that only signal wires `b` and `g` are turned on, but that
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doesn't mean _segments_ `b` and `g` are turned on: the only digit that uses
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two segments is `1`, so it must mean segments `c` and `f` are meant to be on.
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With just that information, you still can't tell which wire (`b`/`g`) goes to
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which segment (`c`/`f`). For that, you'll need to collect more information.
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For each display, you watch the changing signals for a while, make a note of
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_all ten unique signal patterns_ you see, and then write down a single _four
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digit output value_ (your puzzle input). Using the signal patterns, you should
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be able to work out which pattern corresponds to which digit.
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For example, here is what you might see in a single entry in your notes:
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[code]
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acedgfb cdfbe gcdfa fbcad dab cefabd cdfgeb eafb cagedb ab |
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cdfeb fcadb cdfeb cdbaf
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[/code]
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(The entry is wrapped here to two lines so it fits; in your notes, it will all
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be on a single line.)
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Each entry consists of ten _unique signal patterns_ , a `|` delimiter, and
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finally the _four digit output value_. Within an entry, the same wire/segment
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connections are used (but you don't know what the connections actually are).
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The unique signal patterns correspond to the ten different ways the submarine
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tries to render a digit using the current wire/segment connections. Because
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`7` is the only digit that uses three segments, `dab` in the above example
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means that to render a `7`, signal lines `d`, `a`, and `b` are on. Because `4`
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is the only digit that uses four segments, `eafb` means that to render a `4`,
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signal lines `e`, `a`, `f`, and `b` are on.
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Using this information, you should be able to work out which combination of
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signal wires corresponds to each of the ten digits. Then, you can decode the
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four digit output value. Unfortunately, in the above example, all of the
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digits in the output value (`cdfeb fcadb cdfeb cdbaf`) use five segments and
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are more difficult to deduce.
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For now, _focus on the easy digits_. Consider this larger example:
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[code]
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be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb |
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_fdgacbe_ cefdb cefbgd _gcbe_
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edbfga begcd cbg gc gcadebf fbgde acbgfd abcde gfcbed gfec |
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fcgedb _cgb_ _dgebacf_ _gc_
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fgaebd cg bdaec gdafb agbcfd gdcbef bgcad gfac gcb cdgabef |
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_cg_ _cg_ fdcagb _cbg_
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fbegcd cbd adcefb dageb afcb bc aefdc ecdab fgdeca fcdbega |
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efabcd cedba gadfec _cb_
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aecbfdg fbg gf bafeg dbefa fcge gcbea fcaegb dgceab fcbdga |
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_gecf_ _egdcabf_ _bgf_ bfgea
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fgeab ca afcebg bdacfeg cfaedg gcfdb baec bfadeg bafgc acf |
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_gebdcfa_ _ecba_ _ca_ _fadegcb_
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dbcfg fgd bdegcaf fgec aegbdf ecdfab fbedc dacgb gdcebf gf |
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_cefg_ dcbef _fcge_ _gbcadfe_
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bdfegc cbegaf gecbf dfcage bdacg ed bedf ced adcbefg gebcd |
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_ed_ bcgafe cdgba cbgef
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egadfb cdbfeg cegd fecab cgb gbdefca cg fgcdab egfdb bfceg |
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_gbdfcae_ _bgc_ _cg_ _cgb_
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gcafb gcf dcaebfg ecagb gf abcdeg gaef cafbge fdbac fegbdc |
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_fgae_ cfgab _fg_ bagce
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[/code]
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Because the digits `1`, `4`, `7`, and `8` each use a unique number of
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segments, you should be able to tell which combinations of signals correspond
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to those digits. Counting _only digits in the output values_ (the part after
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`|` on each line), in the above example, there are `_26_` instances of digits
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that use a unique number of segments (highlighted above).
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_In the output values, how many times do digits`1`, `4`, `7`, or `8` appear?_
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