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# Instructions | ||
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Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find all prime numbers less than or equal to a given number. | ||
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A prime number is a number larger than 1 that is only divisible by 1 and itself. | ||
For example, 2, 3, 5, 7, 11, and 13 are prime numbers. | ||
By contrast, 6 is _not_ a prime number as it not only divisible by 1 and itself, but also by 2 and 3. | ||
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To use the Sieve of Eratosthenes, you first create a list of all the numbers between 2 and your given number. | ||
Then you repeat the following steps: | ||
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1. Find the next unmarked number in your list (skipping over marked numbers). | ||
This is a prime number. | ||
2. Mark all the multiples of that prime number as **not** prime. | ||
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You keep repeating these steps until you've gone through every number in your list. | ||
At the end, all the unmarked numbers are prime. | ||
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~~~~exercism/note | ||
The tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes. | ||
To check you are implementing the Sieve correctly, a good first test is to check that you do not use division or remainder operations. | ||
~~~~ | ||
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## Example | ||
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Let's say you're finding the primes less than or equal to 10. | ||
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- List out 2, 3, 4, 5, 6, 7, 8, 9, 10, leaving them all unmarked. | ||
- 2 is unmarked and is therefore a prime. | ||
Mark 4, 6, 8 and 10 as "not prime". | ||
- 3 is unmarked and is therefore a prime. | ||
Mark 6 and 9 as not prime _(marking 6 is optional - as it's already been marked)_. | ||
- 4 is marked as "not prime", so we skip over it. | ||
- 5 is unmarked and is therefore a prime. | ||
Mark 10 as not prime _(optional - as it's already been marked)_. | ||
- 6 is marked as "not prime", so we skip over it. | ||
- 7 is unmarked and is therefore a prime. | ||
- 8 is marked as "not prime", so we skip over it. | ||
- 9 is marked as "not prime", so we skip over it. | ||
- 10 is marked as "not prime", so we stop as there are no more numbers to check. | ||
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You've examined all numbers and found 2, 3, 5, and 7 are still unmarked, which means they're the primes less than or equal to 10. |
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@echo off | ||
setlocal enabledelayedexpansion | ||
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set bitmap= | ||
set n=Y | ||
set "limit=%~1" | ||
set "result=" | ||
set /a test=3,npri=3 | ||
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if %limit% geq 2 set "result=%result% 2" | ||
if %limit% geq 3 set "result=%result% 3" | ||
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:nextpri | ||
set /a test+=2,index=0,div=3 | ||
if %test% LSS 8000 set bitmap=%bitmap%%n% | ||
if %test% gtr 64000000 exit /b | ||
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:nextest | ||
if "!bitmap:~%index%,1!"=="N" goto nextdiv | ||
set /a resi=!test!%%!div! | ||
if %resi% equ 0 set n=N& goto nextpri | ||
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:nextdiv | ||
set /a index+=1, div+=2 | ||
set /a div2=div*div | ||
if %test% gtr %limit% goto :end | ||
if %div2% gtr %test% ( | ||
set n=Y | ||
set "result=%result% %test%" | ||
set /a npri+=1 | ||
goto nextpri) | ||
goto nextest | ||
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:end | ||
if defined result ( | ||
set result=%result:~1% | ||
echo !result! | ||
) |
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{ | ||
"authors": ["GroophyLifefor", "Antoni Gual"], | ||
"files": { | ||
"solution": [ | ||
"Sieve.bat" | ||
], | ||
"test": [ | ||
"SieveTest.bat" | ||
], | ||
"example": [ | ||
".meta/Example.bat" | ||
] | ||
}, | ||
"blurb": "Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.", | ||
"source": "Sieve of Eratosthenes at Wikipedia" | ||
} |
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# This is an auto-generated file. | ||
# | ||
# Regenerating this file via `configlet sync` will: | ||
# - Recreate every `description` key/value pair | ||
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications | ||
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) | ||
# - Preserve any other key/value pair | ||
# | ||
# As user-added comments (using the # character) will be removed when this file | ||
# is regenerated, comments can be added via a `comment` key. | ||
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[af9ffe10-dc13-42d8-a742-e7bdafac449d] | ||
description = "Say Hi!" |
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@echo off | ||
setlocal enabledelayedexpansion | ||
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set "limit=%~1" | ||
set "result=" | ||
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REM Your code goes here | ||
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echo %result% |
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@echo off | ||
REM --------------------------------------------------- | ||
REM Sieve Unit Testing | ||
REM --------------------------------------------------- | ||
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:Main | ||
REM Initalize result variable | ||
set "slug=Sieve" | ||
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CALL :Initialize | ||
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REM -------------------- | ||
REM Test Case Start \/\/ | ||
REM Resource: https://github.com/exercism/problem-specifications/blob/main/exercises/grains/canonical-data.json | ||
REM -------------------- | ||
set "expected=" | ||
set "if_success=Test passed" | ||
set "if_failed=Test failed: no primes under two" | ||
CALL :Assert "1" | ||
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set "expected=2" | ||
set "if_success=Test passed" | ||
set "if_failed=Test failed: find first prime" | ||
CALL :Assert "2" | ||
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set "expected=2 3 5 7" | ||
set "if_success=Test passed" | ||
set "if_failed=Test failed: find primes up to 10" | ||
CALL :Assert "10" | ||
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set "expected=2 3 5 7 11 13" | ||
set "if_success=Test passed" | ||
set "if_failed=Test failed: limit is prime" | ||
CALL :Assert "13" | ||
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set "expected=2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997" | ||
set "if_success=Test passed" | ||
set "if_failed=Test failed: find primes up to 1000" | ||
CALL :Assert "1000" | ||
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REM -------------------- | ||
REM Test Case End /\/\/\ | ||
REM -------------------- | ||
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CALL :ResolveStatus | ||
exit /b %errorlevel% | ||
REM End of Main | ||
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REM --------------------------------------------------- | ||
REM Assert [..Parameters(up to 9)] | ||
REM --------------------------------------------------- | ||
GOTO :End REM Prevents the code below from being executed | ||
:Assert | ||
set "stdout=" | ||
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REM Run the program and capture the output then delete the file | ||
CALL %slug%.bat %~1 %~2 %~3 %~4 %~5 %~6 %~7 %~8 %~9 > stdout.bin 2>&1 | ||
set /p stdout=<stdout.bin | ||
del stdout.bin | ||
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REM Check if the result is correct | ||
if "%stdout%" == "%expected%" ( | ||
if defined if_success ( | ||
echo %if_success% | ||
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REM Reset the variable to avoid duplicating the message. | ||
set "if_success=" | ||
set "if_failed=" | ||
) | ||
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REM If the result is correct, exit with code 0 | ||
set /a successCount+=1 | ||
exit /b 0 | ||
) else ( | ||
if defined if_failed ( | ||
echo %if_failed% | ||
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REM Reset the variable to avoid duplicating the message. | ||
set "if_success=" | ||
set "if_failed=" | ||
) | ||
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REM If the result is incorrect, exit with code 1 | ||
set /a failCount+=1 | ||
exit /b 1 | ||
) | ||
GOTO :EOF REM Go back to the line after the call to :Assert | ||
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:Initialize | ||
REM It's for initialize, not about checking empty file | ||
set "successCount=0" | ||
set "failCount=0" | ||
GOTO :EOF REM Go back to the line after the call to :CheckEmptyFile | ||
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:ResolveStatus | ||
set "status=" | ||
if %failCount% gtr 0 ( | ||
REM status: Fail | ||
REM message: The test failed. | ||
exit /b 1 | ||
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) else ( | ||
REM status: Pass | ||
exit /b 0 | ||
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) | ||
GOTO :EOF REM Go back to the line after the call to :ExportResultAsJson | ||
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:End |