I'm a beginner in Ruby and I don't understand what this code is doing, could you explain it to me, please?
def a(n)
s = 0
for i in 0..n-1
s += i
end
s
end
def defines a method. Methods can be used to run the same code on different values. For example, lets say you wanted to get the square of a number:
def square(n)
n * n
end
Now I can do that with different values and I don't have to repeat n * n:
square(1) # => 1
square(2) # => 4
square(3) # => 9
= is an assignment.
s = 0 basically says, behind the name s, there is now a zero.
0..n-1 - constructs a range that holds all numbers between 0 and n - 1. For example:
puts (0..3).to_a
# 0
# 1
# 2
# 3
for assigns i each consecutive value of the range. It loops through all values. So first i is 0, then 1, then ... n - 1.
s += i is a shorthand for s = s + i. In other words, increments the existing value of s by i on each iteration.
The s at the end just says that the method (remember the thing we opened with def) will give you back the value of s. In other words - the sum we accumulated so far.
There is your programming lesson in 5 minutes.
This example isn't idiomatic Ruby code even if it is syntactically valid. Ruby hardly ever uses the for construct, iterators are more flexible. This might seem strange if you come from another language background where for is the backbone of many programs.
In any case, the program breaks down to this:
# Define a method called a which takes an argument n
def a(n)
# Assign 0 to the local variable s
s = 0
# For each value i in the range 0 through n minus one...
for i in 0..n-1
# ...add that value to s.
s += i
end
# The result of this method is s, the sum of those values.
s
end
The more Ruby way of expressing this is to use times:
def a(n)
s = 0
# Repeat this block n times, and in each iteration i will represent
# a value in the range 0 to n-1 in order.
n.times do |i|
s += i
end
s
end
That's just addressing the for issue. Already the code is more readable, mind you, where it's n.times do something. The do ... end block represents a chunk of code that's used for each iteration. Ruby blocks might be a little bewildering at first but understanding them is absolutely essential to being effective in Ruby.
Taking this one step further:
def a(n)
# For each element i in the range 0 to n-1...
(0..n-1).reduce |sum, i|
# ...add i to the sum and use that as the sum in the next round.
sum + i
end
end
The reduce method is one of the simple tools in Ruby that's quite potent if used effectively. It allows you to quickly spin through lists of things and compact them down to a single value, hence the name. It's also known as inject which is just an alias for the same thing.
You can also use short-hand for this:
def a(n)
# For each element in the range 0 to n-1, combine them with +
# and return that as the result of this method.
(0..n-1).reduce(&:+)
end
Where here &:+ is shorthand for { |a,b| a + b }, just as &:x would be short for { |a,b| a.x(b) }.
As you are a beginner in Ruby, let's start from the small slices.
0..n-1 => [0, n-1]. E.g. 0..3 => 0, 1, 2, 3 => [0, 3]
for i in 0.. n-1 => this is a for loop. i traverses [0, n-1].
s += i is same as s = s + i
So. Method a(n) initializes s = 0 then in the for loop i traverse [0, n - 1] and s = s + i
At the end of this method there is an s. Ruby omits key words return. so you can see it as return s
def a(n)
s = 0
for i in 0..n-1
s += i
end
s
end
is same as
def a(n)
s = 0
for i in 0..n-1
s = s + i
end
return s
end
a(4) = 0 + 1 + 2 + 3 = 6
Hope this is helpful.
The method a(n) calculates the sums of the first n natural numbers.
Example:
when n=4, then s = 0+1+2+3 = 6
Let's go symbol by symbol!
def a(n)
This is the start of a function definition, and you're defining the function a that takes a single parameter, n - all typical software stuff. Notably, you can define a function on other things, too:
foo = "foo"
def foo.bar
"bar"
end
foo.bar() # "bar"
"foo".bar # NoMethodError
Next line:
s = 0
In this line, you're both declaring the variable s, and setting it's initial value to 0. Also typical programming stuff.
Notably, the value of the entire expression; s = 0, is the value of s after the assignment:
s = 0
r = t = s += 1 # You can think: r = (t = (s += 1) )
# r and t are now 1
Next line:
for i in 0..n-1
This is starting a loop; specifically a for ... in ... loop. This one a little harder to unpack, but the entire statement is basically: "for each integer between 0 and n-1, assign that number to i and then do something". In fact, in Ruby, another way to write this line is:
(0..n-1).each do |i|
This line and your line are exactly the same.
For single line loops, you can use { and } instead of do and end:
(0..n-1).each{|i| s += i }
This line and your for loop are exactly the same.
(0..n-1) is a range. Ranges are super fun! You can use a lot of things to make up a range, particularly, time:
(Time.now..Time.new(2017, 1, 1)) # Now, until Jan 1st in 2017
You can also change the "step size", so that instead of every integer, it's, say, every 1/10:
(0..5).step(0.1).to_a # [0.0, 0.1, 0.2, ...]
Also, you can make the range exclude the last value:
(0..5).to_a # [0, 1, 2, 3, 4, 5]
(0...5).to_a # [0, 1, 2, 3, 4]
Next line!
s += i
Usually read aloud a "plus-equals". It's literally the same as: s = s + 1. AFAIK, almost every operator in Ruby can be paired up this way:
s = 5
s -= 2 # 3
s *= 4 # 12
s /= 2 # 6
s %= 4 # 2
# etc
Final lines (we'll take these as a group):
end
s
end
The "blocks" (groups of code) that are started by def and for need to be ended, that's what you're doing here.
But also!
Everything in Ruby has a value. Every expression has a value (including assignment, as you saw with line 2), and every block of code. The default value of a block is the value of the last expression in that block.
For your function, the last expression is simply s, and so the value of the expression is the value of s, after all is said and done. This is literally the same as:
return s
end
For the loop, it's weirder - it ends up being the evaluated range.
This example may make it clearer:
n = 5
s = 0
x = for i in (0..n-1)
s += i
end
# x is (0..4)
To recap, another way to write you function is:
def a(n)
s = 0
(0..n-1).each{ |i| s = s + i }
return s
end
Questions?
Related
I was attempting to solve Project Euler #58 in a functional manner with ruby.
Briefly, I created an enumerator to return the corner number of each ring. I was then chaining functional operators on the enumerator. When I get my result, I find that it has a different class depending on how I use it.
spiral = Enumerator.new do |yielder|
n = 3
step = 2
loop do
vals = n.step(nil, step).take(4)
yielder.yield vals
step += 2
n = vals.last + step
end
end
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113]
levels = spiral
.lazy
.map { |ring| ring.count { |n| primes.include? n } }
.with_object({:total=>1.0, :primes=>0})
.take_while do |ring_primes, counts|
counts[:total] += 4
counts[:primes] += ring_primes
(counts[:primes] / counts[:total]) > 0.5
end
The class of levels is a lazy enumerator. I would expect it to contain the number of primes in each ring [3, 2, 3, etc.] - see the project euler reference.
If I just print from the enumerator, I get what I expect:
levels.each do |level|
puts "#{level}"
end
Returns:
3
2
3
1
But if I loop .with_index I get an array result back where the expected value is the first member and the second is my .with_object parameter
levels.each.with_index do |level, ix|
puts "#{ix}: #{level}"
end
Returns:
0: [3, {:total=>5.0, :primes=>3}]
1: [2, {:total=>9.0, :primes=>5}]
2: [3, {:total=>13.0, :primes=>8}]
3: [1, {:total=>17.0, :primes=>9}]
Why does the lazy enumerator work this way and how could I predict for it in the future?
Update
I asked around on the IRC ruby channel and no one there had any idea about it. They said they had discussed it a day or two ago and hadn't come to any conclusions.
In general, it seems one must just deal with it and move on.
What's happening here is you're conveniently ignoring the structure that's returned and plucking out the first item to display. In this case the first item is the counts structure you produce.
Have a look at this:
levels.each do |*level|
puts level.inspect
end
That shows you what's actually in the levels results. When Ruby calls a lambda it will discard any additional data that doesn't fit with the number of arguments the block accepts.
If you don't need that metadata, strip it out:
levels = spiral
.lazy
.map { |ring| ring.count { |n| primes.include? n } }
.with_object({:total=>1.0, :primes=>0})
.take_while do |ring_primes, counts|
counts[:total] += 4
counts[:primes] += ring_primes
(counts[:primes] / counts[:total]) > 0.5
end
.map { |r,_| r }
That removes the extraneous element in the results.
Here's a way of cleaning up your Enumerator a bit:
class Spiral
include Enumerable
def each
Enumerator.new do |yielder|
n = 3
step = 2
loop do
vals = n.step(nil, step).take(4)
yielder.yield vals
step += 2
n = vals.last + step
end
end
end
end
Then you can create one with:
Spiral.new.each ...
If I randomly put in two numbers (first number is smaller), how do I use a for-loop to add all the numbers between and itself?
ex:
first number: 3
second number: 5
the computer should give an answer of '12'.
How do I do that using a for-loop?
In Ruby we seldom use a for loop because it leaves litter behind. Instead, you can very simply do what you want using inject:
(3..5).inject(:+) # => 12
This is using some of the deeper Ruby magic (:+), which is a symbol for the + method and is passed into inject. How it works is a different question and is something you'll need to learn later.
Don't insist on doing something in a language using a particular construct you learned in another language. That will often force non-idiomatic code and will keep you from learning how to do it as other programmers in that language would do it. That creates maintenance issues and makes you less desirable in the workplace.
Simple for loop across the range you defined:
puts "Enter first number: "
first = gets.to_i
puts "Enter second number: "
second = gets.to_i
total = 0
for i in (first..second) do
total += i
end
puts total
Note that if you don't enter a valid number, it will converted to 0. Also this assumes the second number is larger than the first.
In Rails, or in plain-vanilla Ruby with ActiveSupport, you can do something even simpler than a for loop, or than what other people wrote.
(first_num..second_num).sum
This is shorthand for sum in Ruby:
sum = 0
(first_num..second_num).each { |num| sum += num }
first, second = [3,5]
for x in (0..0) do
p (first + second)*(second - first + 1) / 2
end
I know you said for loop, but why not use what Ruby gives you?
> a = 3
> b = 5
> a.upto(b).inject(0) {|m,o| m += o}
=> 12
If you insist on a for loop...
> m = 0
=> 0
> for i in 3..5
* m += i
* end
=> 3..5
> m
=> 12
Since Ruby 2.4 you directly call sum on an Enumerable.
For Example [1, 2, 3].sum #=> 6
In Ruby it's very rare to see a for loop. In this instance a more idiomatic method would be upto:
x = 3
y = 5
total = 0
x.upto(y) do |n|
total += n
end
puts total
# => 12
Another method would be to use reduce:
total = x.upto(y).reduce do |sum, n|
sum += n
end
...which can be shortened to this:
total = x.upto(y).reduce(&:+)
Working on Problem 12 of Project Euler:
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?
Here's what I've got:
require 'reusable'
# The idea here is that 2^n is the smallest number with n factors,
# according to their definition, so it's a good place to start.
# It also happens to be a HUGE number, so I'm worried I'm thinking
# about this wrong. Did 4999 instead of 5000, just to make sure
# I didn't overshoot.
start = 2 * 4999
# The faster way to calculate the nth Triangle number
def nthTriangle(n)
n * (n + 1) / 2
end
def answer(num)
i = startingTriangle(num)
while true
triangle = i*(i+1)/2
puts triangle
factors = numFactors(triangle)
return "#{triangle} is triangle number #{i}, with #{factors} factors." if factors > num
i += 1
end
end
# Basic reversal of the nthTriangle thing to figure
# out which n to start with in the answer function.
def startingTriangle(n)
power = n - 2
sqrt(power * 2).to_i - 1
end
puts answer(5000)
And that required file (where I'm trying to put methods I'll reuse in a bunch of Euler problems):
def primesUpTo(n)
nums = [0, 0] + (2..n).to_a
(2..sqrt(n).to_i+1).each do |i|
if nums[i].nonzero?
(i**2..n).step(i) {|m| nums[m] = 0}
end
end
nums.find_all {|m| m.nonzero?}
end
def prime?(n)
test = primesUpTo(sqrt(n).to_i)
test.each do |i|
if n % i == 0
return false
end
end
true
end
# Just for faster, more intuitive (to me) array summing
def sum(array)
array.inject(0) {|s, n| s + n }
end
# Ditto
def product(array)
array.inject(1) {|p, n| p * n}
end
# I don't like typing the 'Math.'
def sqrt(n)
Math.sqrt(n)
end
# Returns an array of arrays of the prime factors of num
# Form [[factor1, power1],[factor2, power2]]
# Ex: primeFactors(12) == [[2,2],[3,1]]
def primeFactors(n)
array = []
# 2 3
primesUpTo((n/2).to_i+1).select{ |i| n % i == 0 }.each do |p|
pcount = 1
n = n / p
while n % p == 0
pcount += 1
n = n / p
end
array << [p, pcount]
end
array
end
# Returns the number of factors a number has
# INCLUDING both the number itself and 1
# ex: numFactors(28) = 6
def numFactors(n)
return 2 if prime?(n)
product = 1
primeFactors(n).each do |i|
product *= i[1] + 1
end
product
end
My problem is that my code is really super slow. If I start at 1 instead of my start number, it takes a minute + before it gets to like 200000 (nowhere near 2^4999). But apart from scrapping the library prime-number solution and adding all primes to an array I keep referring to -- which I feel would only make it a small amount faster -- I can't think of how to make this much faster. And it needs to be WAY faster.
Am I thinking about this all wrong? Any suggestions?
Also useful would be any suggestions for how to improve the efficiency of any of my library methods, which I'll probably be using again and again. I wanted to make them from scratch so I understood them, but I'm afraid they're very inefficient.
From your code:
The idea here is that 2^n is the smallest number with n factors
From the stated Project Euler task:
We can see that 28 is the first triangle number to have over five divisors.
I'm not sure why you think 2^n is the smallest number with n factors, but the example given in the question clearly proves your assumption wrong, as 2^5 = 32, which is greater than 28.
My solution starts the search at 1 and is reasonably efficient. I don't use primes at all.
Addendum: For the sake of completeness, the other large issue besides starting at a number far too high is searching for greater than 5000 divisors rather than greater than 500, as you noticed and pointed out in the comments.
I'm learning Ruby, and there has been a bit of talk about the upto method in the book from which I am learning. I'm confused. What exactly does it do?
Example:
grades = [88,99,73,56,87,64]
sum = 0
0.upto(grades.length - 1) do |loop_index|
sum += grades[loop_index]
end
average = sum/grades.length
puts average
Let's try an explanation:
You define an array
grades = [88,99,73,56,87,64]
and prepare a variable to store the sum:
sum = 0
grades.length is 6 (there are 6 elements in the array), (grades.length - 1) is 5.
with 0.upto(5) you loop from 0 to 5, loop_index will be 0, then 1...
The first element of the array is grades[0] (the index in the array starts with 0).
That's why you have to subtract 1 from the number of elements.
0.upto(grades.length - 1) do |loop_index|
Add the loop_index's value to sum.
sum += grades[loop_index]
end
Now you looped on each element and have the sum of all elements of the array.
You can calculate the average:
average = sum/grades.length
Now you write the result to stdout:
puts average
This was a non-ruby-like syntax. Ruby-like you would do it like this:
grades = [88,99,73,56,87,64]
sum = 0
grades.each do |value|
sum += value
end
average = sum/grades.length
puts average
Addendum based on Marc-Andrés comment:
You may use also inject to avoid to define the initial sum:
grades = [88,99,73,56,87,64]
sum = grades.inject do |sum, value|
sum + value
end
average = sum / grades.length
puts average
Or even shorter:
grades = [88,99,73,56,87,64]
average = grades.inject(:+) / grades.length
puts average
From http://www.ruby-doc.org/docs/ProgrammingRuby/html/ref_c_integer.html#upto:
upto int.upto( anInteger ) {| i | block }
Iterates block, passing in integer values from int up to and
including anInteger.
5.upto(10) { |i| print i, " " }
produces:
5 6 7 8 9 10
Upto executes the block given once for each number from the original number "upto" the argument passed. For example:
1.upto(10) {|x| puts x}
will print out the numbers 1 through 10.
It is just another way to do a loop/iterator in Ruby. It says do this action n times based on i being the first number the the number in parens as the limit.
My example would have been this:
1.upto(5) { |i| puts "Countup: #{i}" }
So what you're actually doing here is saying, I want to count up from 1 to the number 5, that's specifically what this part is saying:
1.upto(5)
The latter part of code (a block) is just outputting the iteration of going through the count from 1 up to 5. This is the output you might expect to see:
Countup: 1
Countup: 2
Countup: 3
Countup: 4
Countup: 5
Note: This can be written is another way if you're using multilines:
1.upto(5) do |i|
puts "Countup: #{i}"
end
Hope this helps.
An alternative that looks more like Ruby to me is
require 'descriptive_statistics'
grades=[88,99,73,56,87,64]
sum = grades.sum
average = grades.mean
sd = grades.standard_deviation
Of course it depends what you're doing.
I am learning ruby and practicing it by solving problems from Project Euler.
This is my solution for problem 12.
# Project Euler problem: 12
# What is the value of the first triangle number to have over five hundred divisors?
require 'prime'
triangle_number = ->(num){ (num *(num + 1)) / 2 }
factor_count = ->(num) do
prime_fac = Prime.prime_division(num)
exponents = prime_fac.collect { |item| item.last + 1 }
fac_count = exponents.inject(:*)
end
n = 2
loop do
tn = triangle_number.(n)
if factor_count.(tn) >= 500
puts tn
break
end
n += 1
end
Any improvements that can be made to this piece of code?
As others have stated, Rubyists will use methods or blocks way more than lambdas.
Ruby's Enumerable is a very powerful mixin, so I feel it pays here to build an enumerable in a similar way as Prime. So:
require 'prime'
class Triangular
class << self
include Enumerable
def each
sum = 0
1.upto(Float::INFINITY) do |i|
yield sum += i
end
end
end
end
This is very versatile. Just checking it works:
Triangular.first(4) # => [1, 3, 7, 10]
Good. Now you can use it to solve your problem:
def factor_count(num)
prime_fac = Prime.prime_division(num)
exponents = prime_fac.collect { |item| item.last + 1 }
exponents.inject(1, :*)
end
Triangular.find{|t| factor_count(t) >= 500} # => 76576500
Notes:
Float::INFINITY is new to 1.9.2. Either use 1.0/0, require 'backports' or do a loop if using an earlier version.
The each could be improved by first checking that a block is passed; you'll often see things like:
def each
return to_enum __method__ unless block_given?
# ...
Rather than solve the problem in one go, looking at the individual parts of the problem might help you understand ruby a bit better.
The first part is finding out what the triangle number would be. Since this uses sequence of natural numbers, you can represent this using a range in ruby. Here's an example:
(1..10).to_a => [1,2,3,4,5,6,7,8,9,10]
An array in ruby is considered an enumerable, and ruby provides lots of ways to enumerate over data. Using this notion you can iterate over this array using the each method and pass a block that sums the numbers.
sum = 0
(1..10).each do |x|
sum += x
end
sum => 55
This can also be done using another enumerable method known as inject that will pass what is returned from the previous element to the current element. Using this, you can get the sum in one line. In this example I use 1.upto(10), which will functionally work the same as (1..10).
1.upto(10).inject(0) {|sum, x| sum + x} => 55
Stepping through this, the first time this is called, sum = 0, x = 1, so (sum + x) = 1. Then it passes this to the next element and so sum = 1, x = 2, (sum + x) = 3. Next sum = 3, x = 3, (sum + x) = 6. sum = 6, x = 4, (sum + x) = 10. Etc etc.
That's just the first step of this problem. If you want to learn the language in this way, you should approach each part of the problem and learn what is appropriate to learn for that part, rather than tackling the entire problem.
REFACTORED SOLUTION (though not efficient at all)
def factors(n)
(1..n).select{|x| n % x == 0}
end
def triangle(n)
(n * (n + 1)) / 2
end
n = 2
until factors(triangle(n)).size >= 500
puts n
n += 1
end
puts triangle(n)
It looks like you are coming from writing Ocaml, or another functional language. In Ruby, you would want to use more def to define your methods. Ruby is about staying clean. But that might also be a personal preference.
And rather than a loop do you could while (faction_count(traingle_number(n)) < 500) do but for some that might be too much for one line.