Practical numbers: Difference between revisions

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=={{header|Sidef}}==

Built-in:

<lang ruby>say is_practical(2**128 + 1) #=> false

say is_practical(2**128 + 4) #=> true</lang>

Slow implementation (as the task requires):

<lang ruby>func is_practical(n) {

var set = Set()

n.divisors.grep { _ < n }.subsets {|*a|

set << a.sum

}

1..n-1 -> all { set.has(_) }

}

var from = 1

var upto = 333

var list = (from..upto).grep { is_practical(_) }

say "There are #{list.len} practical numbers in the range #{from}..#{upto}."

say "#{list.first(10).join(', ')} ... #{list.last(10).join(', ')}\n"

for n in ([666, 6666, 66666]) {

say "#{'%5s' % n } is practical? #{is_practical(n)}"

}</lang>

Efficient algorithm:

<lang ruby>func is_practical(n) {

n.is_odd && return (n == 1)

n.is_pos || return false

var p = 1

var f = n.factor_exp

f.each_cons(2, {|a,b|

p *= sigma(a.head**a.tail)

b.head > (1 + p) && return false

})

return true

}</lang>

{{out}}

<pre>

There are 77 practical numbers in the range 1..333.

1, 2, 4, 6, 8, 12, 16, 18, 20, 24 ... 288, 294, 300, 304, 306, 308, 312, 320, 324, 330

666 is practical? true

6666 is practical? true

66666 is practical? false