# Scala algorithm: Compute single-digit sum of digits

Published

## Algorithm goal

$$909$$ sums to $$18$$, which sums to $$9$$.

Find the best way to compute it for any positive $$n$$, efficiently.

## Test cases in Scala

assert(sumOfDigits(0) == 0)
assert(sumOfDigits(2) == 2)
assert(sumOfDigits(8) == 8)
assert(sumOfDigits(10) == 1)
assert(sumOfDigits(16) == 7)
assert(sumOfDigits(32) == 5)
assert(sumOfDigits(64) == 1)
assert(sumOfDigits(101) == 2)
assert(sumOfDigits(109) == 1)
assert(sumOfDigits(128) == 2)
assert(sumOfDigits(256) == 4)
assert(sumOfDigits(512) == 8)
assert(sumOfDigits(999) == 9)
assert(sumOfDigits(1024) == 7)
assert(sumOfDigits(2048) == 5)
assert(sumOfDigits(4096) == 1)


## Algorithm in Scala

4 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

## Explanation

This involves a bit of mathematics to figure out - but we can get an $$O(1)$$ solution here:

The sum of digits of sum of digits... is equal to that digit modulo 9; if we take a number that is composed of digits$$abcd$$, which equals $$10^3 \times a + 10 ^ 2 \times b + 10 \times c + d$$, and then using %/modulo 9 we get:$$a + b + c + d (\mod 9)$$, which is also $$((a + b) (\mod 9) + (c + d) (\mod 9))(\mod 9)$$. Combining with a modulo table, you will notice thatindeed for example $$8 + 7 = 15$$, and applying modulo 9 on $$15$$ gives us $$6$$, which is precisely the sum of digits $$1$$ and $$5$$. (this is © from www.scala-algorithms.com)

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