How to resolve the algorithm Sum multiples of 3 and 5 step by step in the J programming language

Published on 12 May 2024 09:40 PM
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How to resolve the algorithm Sum multiples of 3 and 5 step by step in the J programming language

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Problem Statement

The objective is to write a function that finds the sum of all positive multiples of 3 or 5 below n. Show output for n = 1000. This is is the same as Project Euler problem 1. Extra credit: do this efficiently for n = 1e20 or higher.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Sum multiples of 3 and 5 step by step in the J programming language

Source code in the j programming language

NB. Naive method
NB. joins two lists of the multiples of 3 and 5, then uses the ~. operator to remove duplicates.
echo 'The sum of the multiples of 3 or 5 < 1000 is ', ": +/ ~. (3*i.334), (5*i.200)

NB. slightly less naive: select the numbers which have no remainder when divided by 3 or 5:
echo 'The sum of the multiples of 3 or 5 < 1000 is still ', ": +/I.+./0=3 5|/i.1000



NB. inclusion/exclusion

triangular =: -:@:(*: + 1&*)
sumdiv =: dyad define
    (triangular <. x % y) * y
)

echo 'For 10^20 - 1, the sum is ', ": +/ (".(20#'9'),'x') sumdiv 3 5 _15

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