I wrote the code to check perfect number and semipefrect number in Ruby. Semiperfect number is also called pseudoperfect number.
Perfect Number
A positive integer that is equal to the sum of its proper positive divisors.
Semiperfect Number
A natural number n that is equal to the sum of all or some of its proper divisors.
Perfect number is also semiperfect number.
I created the class called Number. is_perfect? returns whether the number is perfect, is_semiperfect? returns whether the number is semi-perfect.
初期化処理のところで約数を配列に入れてしまっています。 初期化でそれをやるべきかというのは考えるべきことではありますが、今回は目的が特化しているのでこれで。
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class Number
attr_reader : n
def initialize ( n )
@n = n
@factors = [ 1 ]
u = ( @n * * 0.5 ) . to _ i
2.step ( u , 1 ) do | i |
if @n % i == 0
@factors . push ( i )
s = @n / i
if i != s
@factors . push ( s )
end
end
end
@factors . sort !
end
def is_perfect ?
return @factors . sum == @n
end
def is_semiperfect ?
return check_semiperfect ( [ ] , 0 , @factors . length - 1 )
end
private
def check_semiperfect ( element_array , sub_total , upper_index )
if sub_total == @n
return true
end
if upper_index < 0
return false
end
if sub_total > @n || sub_total + @factors [ 0 , upper_index + 1 ] . sum < @n
return false
end
if check_semiperfect ( element_array + [ @factors [ upper_index ] ] , sub_total + @factors [ upper_index ] , upper_index - 1 )
return true
end
if upper_index > 0
if check_semiperfect ( element_array + [ @factors [ upper_index - 1 ] ] , sub_total + @factors [ upper_index - 1 ] , upper_index - 2 )
return true
end
end
return false
end
end
The first argument of check_semiperfect? is array whose member constructs subset sum. In this case, it only show whether perfect/semi-perfect or not, so it’s not used, but in outputting the sequence of elements which compose subset, it can be used.
We can use the above code as follows.
for i in 1..100
n = Number . new ( i )
puts n . n . to_s + " : " + n . is_perfect ? . to_s + " / " + n . is_semiperfect ? . to _ s
end
Its output is the following.
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100
1 : true / true
2 : false / false
3 : false / false
4 : false / false
5 : false / false
6 : true / true
7 : false / false
8 : false / false
9 : false / false
10 : false / false
11 : false / false
12 : false / true
13 : false / false
14 : false / false
15 : false / false
16 : false / false
17 : false / false
18 : false / true
19 : false / false
20 : false / true
21 : false / false
22 : false / false
23 : false / false
24 : false / true
25 : false / false
26 : false / false
27 : false / false
28 : true / true
29 : false / false
30 : false / true
31 : false / false
32 : false / false
33 : false / false
34 : false / false
35 : false / false
36 : false / true
37 : false / false
38 : false / false
39 : false / false
40 : false / true
41 : false / false
42 : false / true
43 : false / false
44 : false / false
45 : false / false
46 : false / false
47 : false / false
48 : false / true
49 : false / false
50 : false / false
51 : false / false
52 : false / false
53 : false / false
54 : false / true
55 : false / false
56 : false / true
57 : false / false
58 : false / false
59 : false / false
60 : false / true
61 : false / false
62 : false / false
63 : false / false
64 : false / false
65 : false / false
66 : false / true
67 : false / false
68 : false / false
69 : false / false
70 : false / false
71 : false / false
72 : false / true
73 : false / false
74 : false / false
75 : false / false
76 : false / false
77 : false / false
78 : false / true
79 : false / false
80 : false / true
81 : false / false
82 : false / false
83 : false / false
84 : false / true
85 : false / false
86 : false / false
87 : false / false
88 : false / true
89 : false / false
90 : false / true
91 : false / false
92 : false / false
93 : false / false
94 : false / false
95 : false / false
96 : false / true
97 : false / false
98 : false / false
99 : false / false
100 : false / true
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