72 lines
3.0 KiB
Markdown
72 lines
3.0 KiB
Markdown
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# Luhn
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Write a program that can take a number and determine whether or not it is valid per the Luhn formula.
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The Luhn formula is a simple checksum formula used to validate a variety
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of identification numbers, such as credit card numbers and Canadian
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Social Insurance Numbers.
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The formula verifies a number against its included check digit, which is
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usually appended to a partial number to generate the full number. This
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number must pass the following test:
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- Counting from rightmost digit (which is the check digit) and moving
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left, double the value of every second digit.
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- For any digits that thus become 10 or more, subtract 9 from the
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result.
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- 1111 becomes 2121.
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- 8763 becomes 7733 (from 2×6=12 → 12-9=3 and 2×8=16 → 16-9=7).
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- Add all these digits together.
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- 1111 becomes 2121 sums as 2+1+2+1 to give a check digit of 6.
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- 8763 becomes 7733, and 7+7+3+3 is 20.
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If the total ends in 0 (put another way, if the total modulus 10 is
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congruent to 0), then the number is valid according to the Luhn formula;
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else it is not valid. So, 1111 is not valid (as shown above, it comes
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out to 6), while 8763 is valid (as shown above, it comes out to 20).
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Write a program that, given a number
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- Can check if it is valid per the Luhn formula. This should treat, for
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example, "2323 2005 7766 3554" as valid.
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- Can return the checksum, or the remainder from using the Luhn method.
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- Can add a check digit to make the number valid per the Luhn formula and
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return the original number plus that digit. This should give "2323 2005 7766
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3554" in response to "2323 2005 7766 355".
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## About Checksums
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A checksum has to do with error-detection. There are a number of different
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ways in which a checksum could be calculated.
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When transmitting data, you might also send along a checksum that says how
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many bytes of data are being sent. That means that when the data arrives on
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the other side, you can count the bytes and compare it to the checksum. If
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these are different, then the data has been garbled in transmission.
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In the Luhn problem the final digit acts as a sanity check for all the prior
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digits. Running those prior digits through a particular algorithm should give
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you that final digit.
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It doesn't actually tell you if it's a real credit card number, only that it's
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a plausible one. It's the same thing with the bytes that get transmitted --
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you could have the right number of bytes and still have a garbled message. So
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checksums are a simple sanity-check, not a real in-depth verification of the
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authenticity of some data. It's often a cheap first pass, and can be used to
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quickly discard obviously invalid things.
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To run the tests simply run the command `go test` in the exercise directory.
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If the test suite contains benchmarks, you can run these with the `-bench`
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flag:
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go test -bench .
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For more detailed info about the Go track see the [help
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page](http://help.exercism.io/getting-started-with-go.html).
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## Source
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The Luhn Algorithm on Wikipedia [view source](http://en.wikipedia.org/wiki/Luhn_algorithm)
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