I have a simple method that finds prime numbers, puts them in an array and then sums them up. What are some possible steps to speed it up?
def prime?(number, array)
array.each do |x|
if number % x == 0
return false
end
end
true
end
def sum_prime(number)
i = 0
prime = 1
output = [2]
while prime < number
if prime?(prime, output)
i += 1
output << prime if prime != 1
p prime
end
prime += 2
end
output.inject(:+)
end
sum_prime(200000)
is array#each ok? Can I concatinate differently for faster results?
This should work. It uses others' suggestions:
require 'prime'
def sum_prime(limit)
Prime.each(limit).inject(0) {|sum, num| sum + num}
end
puts sum_prime(200000)
Related
I have solved a Codewars kata, but I can not submit it because my code takes too long. A lot of people had this problem, but we can not see the solution. The problem is, that generating the prime numbers takes too long (more than 12s) (I generate the primes with a method).
In my computer, I can require the class Prime, and this solves the problem. But in Codewar one can not require the class Prime, therefore, my method of generating prime numbers is too slow.
Any help?
require "pry"
def primeFactors(n)
start_time = Time.now
puts start_time
# find prime numbers smaller than n
nums = (2..(n-1)).to_a
odd_nums = nums.select { |num| num.odd? }
primes = odd_nums.select do |num|
is_prime(num)
end
end_time = Time.now
duration = end_time - start_time
puts end_time
# divide until mod is 1
dividend = n
res_primes = []
while dividend > 1
primes.each do |prime| # prime divisor
new_dividend = dividend.to_f / prime
remainder = dividend % prime
if remainder.zero?
dividend = new_dividend
res_primes << prime
break
end
end
end
freqs = {}
res_primes.each do |res_prime|
freqs[res_prime] = res_primes.count(res_prime)
end
res_string = []
freqs.keys.each do |key|
if freqs[key] == 1
res_string << "(#{key})"
else
res_string << "(#{key}**#{freqs[key]})"
end
end
res_string.join
end
def is_prime(n)
(2..n/2).none?{|i| n % i == 0}
end
Well for starters you really only need to test to Math.sqrt(n).to_i + 1 that should help for larger n values.
This is because if a factor exists where n = a * b then either
If a == b == sqrt(n) # Basically the defn of sqrt
or
If a != b; a < sqrt(n); b > sqrt(n)
If both a and b are less than sqrt(n) then a * b < n
and
If both a and b are greater than sqrt(n) the a * b > n
Secondly, and this is more complex, you only need to test prime numbers to that limit. I could envision a scheme where primes are cached.
Hope this helps.
The more advanced option might look like this:
# Is this number a prime?
module PrimeChecker
#prime_cache = [2,3]
def self.prime?(n)
search_limit = Math.sqrt(n).to_i + 1
last_cache = #prime_cache[-1]
while last_cache < search_limit do
last_cache += 2
#prime_cache << last_cache if PrimeChecker.prime?(last_cache)
end
#prime_cache.each do |pn|
return true if pn > search_limit
return false if (n % pn) == 0
end
true
end
end
# Sample run
#
# 31 mysh>%=PrimeChecker.prime?(1_000_000_000_000)
# false
# Elapsed execution time = 1.592 seconds.
#
This running on an elderly machine with a slow CORE 2 Duo processor.
i am trying to find if array has 2 digits number and if i find one i want to add the two digit and make it single. then add all the numbers in array to come up with a a sum. here is my code so far. and also i am a noob and learning
class Imei
attr_accessor :Imei, :split_total1, :split_total2
def initialize(imei)
#imei = imei.to_i
#split_total1 = []
#split_total2 = []
end
def check_two_digit(num)
if num.to_s.length == 2
num = num.to_s.split(//).partition.with_index{|_,i| i.odd?}
num.each do |a, b|
a.to_i + b.to_i
end
else
num.to_i
end
end
def check_imei
if #imei.to_s.length == 15
split1, split2 = #imei.to_s.split(//).partition.with_index{|_, i| i.odd?}
split1.each do |a|
#split_total1 << check_two_digit(a.to_i * 2)
end
split2.pop
split2.each do |a|
#split_total2 << a.to_i
end
else
puts "IMEI NUMBER INVALID"
end
end
end
imei = Imei.new(123456789102222)
imei.check_imei
puts imei.split_total1.inspect
puts imei.split_total2.inspect
Find below the Luhn Algorithm I wrote in ruby
def luhn_10_valid? imei
digits = imei.reverse.chars.map(&:to_i)
digits.each_with_index.inject(0) do |sum, (digit, i)|
digit *= 2 if i.odd?
digit -= 9 if digit > 9
sum += digit
end % 10 == 0
end
For Luhn algorithm I really like the divmod method, which simplifies things
array.reverse.each_slice(2).map { |x, y|
y ||= 0
[x, (y * 2).divmod(10)]
}.flatten.inject(:+) % 10 == 0
If a contains only non-negative integers, this is one Ruby-like way to compute the sum:
a.reduce(0) {|t,i| t + (((10..99).cover? i) ? i.divmod(10).reduce(:+) : i )}
Explanation:
If i => 46, (10..99).cover?(46) => true, 46.divmod(10) => [4,6], [4,6].reduce(:+) => 10. Recall that reduce is aka inject. [4,6]reduce(:+) has the same result as (but,technically, is not 'equivalent to'):
[4,6].reduce { |u,j| u+j }
The zero initial value is needed for the first reduce, as
a[46].reduce {|t,i| t+(((10..99).cover? i) ? i.divmod(10).reduce(:+):i)}
#=> 46
which is incorrect.
If a instead contains string representations of integers and/or the integers may be negative, let me know and I'll change my answer accordingly.
Write a function that prints out all the factors for each of the numbers 1 through 100.
Really amateur coder but here's my attempt so far.
def factors_numbers(n1,n2)
(n1..n2).each do |n|
factors = []
factors << 1 ##every number has a factor of 1
factors << n ##every number is a factor of itself
i = 1
while i < n
new_number = n % (n-i)
if new_number == 0 #if 0, divisible and that means two numbers are factors
factors << new_number
factors << (n-i)
end
i += 1
end
return factors
end
end
Here is an improved version of your code:
def factors_numbers(n1,n2)
all_factors = {}
(n1..n2).each do |n|
factors = []
(1..Math.sqrt(n).floor).each do |i|
remainder = n % i
if remainder == 0 #if 0, divisible and that means two numbers are factors
factors << i
factors << n/i
end
end
factors = factors.sort.uniq
puts "Factors of #{n}: #{factors.join(',')}"
all_factors[n]=[factors]
end
return all_factors
end
Do you want unique factors? That is, in the range 1-100, should I get the number 1 a hundred times, or only once?
The easiest way to do this is by leveraging the "inject" Enumerable method.
def find_all_factors_between(n1,n2)
(n1..n2).inject([]) do |factors, num|
factors + (1..num).inject([]) { |arry, test| num % test == 0 ? arry + [test] : arry }
end
end
One final thing to note is that Ruby has implicit returns; that is, as long as the output of the last line of your method is your factors variable, you don't have to say return factors.
And my entry would be:
def find_all_factors_between(n1, n2)
factors = -> (n) { (1..n).select {|i| n % i == 0} }
(n1..n2).each { |n| puts "Factors of #{n}: #{factors.(n).join(', ')}" }
end
find_all_factors_between(1,100)
Well, if you wanted to do it with enumerables, there's always
def factor_numbers(rng)
factors = rng.map do |n|
(1..Math.sqrt(n).floor) # search numbers <= square root
.select { |d| n % d == 0 } # find factors <= square root
.flat_map { |x| [x, n / x] } # combine with factors >= square root
.sort # order from least to greatest
.uniq # remove dupes (basically the square root)
end
Hash[rng.zip(factors)] # rng = keys, factors = values
end
puts factor_numbers(1..100)
It's not the most efficient, but my point is just that many of the for/while constructs you'd see in languages like C or JavaScript can be expressed in other ways in Ruby.
(n1..n2).each{|x| print "#{x}: #{(1..x).select{|y| x % y == 0}}\n"}
That oughta do it :)
edit: Implemented Cary Swoveland's suggestion
def factor_nums(n1,n2)
all_factors = {}
(n1..n2).each do |n|
factors = []
(1..n).each do |i|
remainder = n % i
factors << i if remainder == 0
end
all_factors[n] = factors
end
return all_factors
end
Could someone help me figure this out how to do this in Ruby?
I have an array of integers. For each of those integers, I need to find a divisor that is two digits long (whole numbers as well). Right now, the code is looping to infinity. The answer I'm trying to get is:
int_a = 2, int_b = 11, and x = 22
Here is the code:
[22, 33].each do |x|
x.to_f
int_a = 1
int_b = x.quo(int_a)
until int_a > 15 || int_b%2==0 && sprintf("%g", int_b).to_s.length == 2
puts "#{x}"
puts "#{int_a}"
puts "#{int_b}"
end
int_a += 1
end
I can't understand your code, but by your definition:
For each of those integers, I need to find a divisor that is two digits long(whole numbers as well)
Give this a try:
numbers = [22,33]
numbers.map do |n|
raise "invalid number" if n < 10
div = 10.0
div += 1 while (n%div) != 0
div
end
#result: [11,22]
As #fotanus, I can't understand your code, but answering your question, I used this code a while ago for finding divisors:
require 'prime'
def divisors_for(n)
n.prime_division.map do |n,mp|
(0..mp).map { |i| n**i }
end.inject([1]) do |a, factor_group|
a.product(factor_group)
end.map do |factors|
factors.flatten.reduce(:*)
end - [n]
end
[22, 23].map do |n|
divisors_for(n).select { |d| d.to_s.size == 2 }
end
I am learning Ruby and doing some math stuff. One of the things I want to do is generate prime numbers.
I want to generate the first ten prime numbers and the first ten only. I have no problem testing a number to see if it is a prime number or not, but was wondering what the best way is to do generate these numbers?
I am using the following method to determine if the number is prime:
class Integer < Numeric
def is_prime?
return false if self <= 1
2.upto(Math.sqrt(self).to_i) do |x|
return false if self%x == 0
end
true
end
end
In Ruby 1.9 there is a Prime class you can use to generate prime numbers, or to test if a number is prime:
require 'prime'
Prime.take(10) #=> [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
Prime.take_while {|p| p < 10 } #=> [2, 3, 5, 7]
Prime.prime?(19) #=> true
Prime implements the each method and includes the Enumerable module, so you can do all sorts of fun stuff like filtering, mapping, and so on.
If you'd like to do it yourself, then something like this could work:
class Integer < Numeric
def is_prime?
return false if self <= 1
2.upto(Math.sqrt(self).to_i) do |x|
return false if self%x == 0
end
true
end
def next_prime
n = self+1
n = n + 1 until n.is_prime?
n
end
end
Now to get the first 10 primes:
e = Enumerator.new do |y|
n = 2
loop do
y << n
n = n.next_prime
end
end
primes = e.take 10
require 'prime'
Prime.first(10) # => [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
Check out Sieve of Eratosthenes. This is not Ruby specific but it is an algorithm to generate prime numbers. The idea behind this algorithm is that you have a list/array of numbers say
2..1000
You grab the first number, 2. Go through the list and eliminate everything that is divisible by 2. You will be left with everything that is not divisible by 2 other than 2 itself (e.g. [2,3,5,7,9,11...999]
Go to the next number, 3. And again, eliminate everything that you can divide by 3. Keep going until you reach the last number and you will get an array of prime numbers. Hope that helps.
http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
People already mentioned the Prime class, which definitely would be the way to go. Someone also showed you how to use an Enumerator and I wanted to contribute a version using a Fiber (it uses your Integer#is_prime? method):
primes = Fiber.new do
Fiber.yield 2
value = 3
loop do
Fiber.yield value if value.is_prime?
value += 2
end
end
10.times { p primes.resume }
# First 10 Prime Numbers
number = 2
count = 1
while count < 10
j = 2
while j <= number
break if number%j == 0
j += 1
end
if j == number
puts number
count += 1
end
number += 1
end
Implemented the Sieve of Eratosthene (more or less)
def primes(size)
arr=(0..size).to_a
arr[0]=nil
arr[1]=nil
max=size
(size/2+1).times do |n|
if(arr[n]!=nil) then
cnt=2*n
while cnt <= max do
arr[cnt]=nil
cnt+=n
end
end
end
arr.compact!
end
Moreover here is a one-liner I like a lot
def primes_c a
p=[];(2..a).each{|n| p.any?{|l|n%l==0}?nil:p.push(n)};p
end
Of course those will find the primes in the first n numbers, not the first n primes, but I think an adaptation won't require much effort.
Here is a way to generate the prime numbers up to a "max" argument from scratch, without using Prime or Math. Let me know what you think.
def prime_test max
primes = []
(1..max).each {|num|
if
(2..num-1).all? {|denom| num%denom >0}
then
primes.push(num)
end
}
puts primes
end
prime_test #enter max
I think this may be an expensive solution for very large max numbers but seems to work well otherwise:
def multiples array
target = array.shift
array.map{|item| item if target % item == 0}.compact
end
def prime? number
reversed_range_array = *(2..number).reverse_each
multiples_of_number = multiples(reversed_range_array)
multiples_of_number.size == 0 ? true : false
end
def primes_in_range max_number
range_array = *(2..max_number)
range_array.map{|number| number if prime?(number)}.compact
end
class Numeric
def prime?
return self == 2 if self % 2 == 0
(3..Math.sqrt(self)).step(2) do |x|
return false if self % x == 0
end
true
end
end
With this, now 3.prime? returns true, and 6.prime? returns false.
Without going to the efforts to implement the sieve algorithm, time can still be saved quickly by only verifying divisibility until the square root, and skipping the odd numbers. Then, iterate through the numbers, checking for primeness.
Remember: human time > machine time.
I did this for a coding kata and used the Sieve of Eratosthenes.
puts "Up to which number should I look for prime numbers?"
number = $stdin.gets.chomp
n = number.to_i
array = (1..n).to_a
i = 0
while array[i]**2 < n
i = i + 1
array = array.select do |element|
element % array[i] != 0 || element / array[i] == 1
end
end
puts array.drop(1)
Ruby: Print N prime Numbers
http://mishra-vishal.blogspot.in/2013/07/include-math-def-printnprimenumbernoofp.html
include Math
def print_n_prime_number(no_of_primes=nil)
no_of_primes = 100 if no_of_primes.nil?
puts "1 \n2"
count = 1
number = 3
while count < no_of_primes
sq_rt_of_num = Math.sqrt(number)
number_divisible_by = 2
while number_divisible_by <= sq_rt_of_num
break if(number % number_divisible_by == 0)
number_divisible_by = number_divisible_by + 1
end
if number_divisible_by > sq_rt_of_num
puts number
count = count+1
end
number = number + 2
end
end
print_n_prime_number
Not related at all with the question itself, but FYI:
if someone doesn't want to keep generating prime numbers again and again (a.k.a. greedy resource saver)
or maybe you already know that you must to work with subsequent prime numbers in some way
other unknown and wonderful cases
Try with this snippet:
require 'prime'
for p in Prime::Generator23.new
# `p` brings subsequent prime numbers until the end of the days (or until your computer explodes)
# so here put your fabulous code
break if #.. I don't know, I suppose in some moment it should stop the loop
end
fp
If you need it, you also could use another more complex generators as Prime::TrialDivisionGenerator or Prime::EratosthenesGenerator. More info
Here's a super compact method that generates an array of primes with a single line of code.
def get_prime(up_to)
(2..up_to).select { |num| (2...num).all? { |div| (num % div).positive? } }
end
def get_prime(number)
(2..number).each do |no|
if (2..no-1).all? {|num| no % num > 0}
puts no
end
end
end
get_prime(100)