98 lines
No EOL
5.6 KiB
Markdown
98 lines
No EOL
5.6 KiB
Markdown
https://adventofcode.com/2021/day/3
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---
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## --- Day 3: Binary Diagnostic ---
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The submarine has been making some odd creaking noises, so you ask it to
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produce a diagnostic report just in case.
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The diagnostic report (your puzzle input) consists of a list of binary numbers
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which, when decoded properly, can tell you many useful things about the
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conditions of the submarine. The first parameter to check is the power
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consumption.
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You need to use the binary numbers in the diagnostic report to generate two new
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binary numbers (called the gamma rate and the epsilon rate). The power
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consumption can then be found by multiplying the gamma rate by the epsilon rate.
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Each bit in the gamma rate can be determined by finding the most common bit in
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the corresponding position of all numbers in the diagnostic report. For example,
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given the following diagnostic report:
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```
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00100
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11110
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10110
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10111
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10101
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01111
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00111
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11100
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10000
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11001
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00010
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01010
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```
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Considering only the first bit of each number, there are five `0` bits and
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seven `1` bits. Since the most common bit is `1`, the first bit of the gamma
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rate is `1`.
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The most common second bit of the numbers in the diagnostic report is `0`, so
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the second bit of the gamma rate is `0`.
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The most common value of the third, fourth, and fifth bits are `1`, `1`, and `0`,
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respectively, and so the final three bits of the gamma rate are `110`.
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So, the gamma rate is the binary number `10110`, or `22` in decimal.
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The epsilon rate is calculated in a similar way; rather than use the most common
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bit, the least common bit from each position is used. So, the epsilon rate is
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`01001`, or `9` in decimal. Multiplying the gamma rate (`22`) by the epsilon
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rate (`9`) produces the power consumption, `198`.
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Use the binary numbers in your diagnostic report to calculate the gamma rate
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and epsilon rate, then multiply them together. What is the power consumption of
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the submarine? (Be sure to represent your answer in decimal, not binary.)
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## --- Part Two ---
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Next, you should verify the life support rating, which can be determined by
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multiplying the oxygen generator rating by the CO2 scrubber rating.
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Both the oxygen generator rating and the CO2 scrubber rating are values that
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can be found in your diagnostic report - finding them is the tricky part. Both
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values are located using a similar process that involves filtering out values
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until only one remains. Before searching for either rating value, start with
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the full list of binary numbers from your diagnostic report and consider just
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the first bit of those numbers. Then:
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- Keep only numbers selected by the bit criteria for the type of rating value for which you are searching. Discard numbers which do not match the bit criteria.
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- If you only have one number left, stop; this is the rating value for which you are searching.
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- Otherwise, repeat the process, considering the next bit to the right.
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The bit criteria depends on which type of rating value you want to find:
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- To find oxygen generator rating, determine the most common value (0 or 1) in the current bit position, and keep only numbers with that bit in that position. If 0 and 1 are equally common, keep values with a 1 in the position being considered.
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- To find CO2 scrubber rating, determine the least common value (0 or 1) in the current bit position, and keep only numbers with that bit in that position. If 0 and 1 are equally common, keep values with a 0 in the position being considered.
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For example, to determine the oxygen generator rating value using the same example diagnostic report from above:
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- Start with all 12 numbers and consider only the first bit of each number. There are more `1` bits (7) than `0` bits (5), so keep only the 7 numbers with a `1` in the first position: `11110`, `10110`, `10111`, `10101`, `11100`, `10000`, and `11001`.
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- Then, consider the second bit of the 7 remaining numbers: there are more `0` bits (4) than `1` bits (3), so keep only the 4 numbers with a `0` in the second position: `10110`, `10111`, `10101`, and `10000`.
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- In the third position, three of the four numbers have a `1`, so keep those three: `10110`, `10111`, and `10101`.
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- In the fourth position, two of the three numbers have a `1`, so keep those two: `10110` and `10111`.
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- In the fifth position, there are an equal number of `0` bits and `1` bits (one each). So, to find the oxygen generator rating, keep the number with a 1 in that position: `10111`.
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- As there is only one number left, stop; the oxygen generator rating is `10111`, or `23` in decimal.
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Then, to determine the CO2 scrubber rating value from the same example above:
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- Start again with all 12 numbers and consider only the first bit of each number. There are fewer `0` bits (5) than `1` bits (7), so keep only the 5 numbers with a `0` in the first position: `00100`, `01111`, `00111`, `00010`, and `01010`.
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- Then, consider the second bit of the 5 remaining numbers: there are fewer `1` bits (2) than `0` bits (3), so keep only the 2 numbers with a `1` in the second position: `01111` and `01010`.
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- In the third position, there are an equal number of `0` bits and `1` bits (one each). So, to find the CO2 scrubber rating, keep the number with a `0` in that position: `01010`.
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- As there is only one number left, stop; the CO2 scrubber rating is `01010`, or `10` in decimal.
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Finally, to find the life support rating, multiply the oxygen generator rating
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(`23`) by the CO2 scrubber rating (`10`) to get `230`.
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Use the binary numbers in your diagnostic report to calculate the oxygen
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generator rating and CO2 scrubber rating, then multiply them together. What is
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the life support rating of the submarine? (Be sure to represent your answer in
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decimal, not binary.) |