# Challenge 090

## Table of Contents

## Task 2 - Ethiopian Multiplication

You are given two positive numbers $A and $B.

Write a script to demonstrate Ethiopian Multiplication using the given numbers.

### Raku

- Program: raku/ch-2.raku

Start by taking `$A`

& `$B`

which are defined to be `Int`

& positive.

sub MAIN ( #= positive numbers Int $A is copy where * > 0, Int $B is copy where * > 0 ) { ... }

Here's relevant part from the link that was given above:

Start with the two numbers on top. Halve one, ignoring any remainders or fractions, and double the other, stopping when you get to 1.

14 & 12 7 & 24 3 & 48 [See how I ignored the fact that halving 7 leaves 1 left over?] 1 & 96 <— Stop here.

Now look at the numbers on the right. Some are across from an even number: in this case, 12 is across from the original 14. Ignore those, and add the rest. So we’ll add 24, 48, and 96, which were across from odd numbers, and get 168. And that’s the product! Isn’t that cool?

We do the same thing & also print the instructions.

my %sets; say "Ethopian Multiplication.\n"; say "Start with $A, $B."; say "Divide $A by 2 & multiple $B by 2 at each step."; say "Continue until $A equals 1. Drop the remainder, both should be Integer.\n"; say "$A, $B"; while True { %sets{$A} = $B.Int; $A = ($A / 2).Int; $B = ($B * 2).Int; last if $A < 1; say "$A, $B"; } say "\nNow to find the product, simply add all the numbers on right side of ','."; say "But skip those numbers which have an even number on the left side.\n"; my Int $product = 0; for %sets.sort({.key.Int}).reverse -> $pair { if $pair.key % 2 != 0 { $product += $pair.value; say "- Adding ", $pair.value, " to product."; } else { say "- Skipping ", $pair.value, " because ", $pair.key, " is even."; } } say "\nProduct: $product";