I don't quite understand how to "initialize a multidimensional array to equal 1" as the initial for loops seem to suggest here. I haven't learned to properly read pseudocode, and I don't fully understand how this program works.
function countRoutes(m,n)
grid ← array[m + 1][n + 1]
for i = 0 to m do
grid[i][0] ← 1
end for
for j = 0 to n do
grid[0][j] ← 1
end for
for i = 1 to m do
for j = 1 to n do
grid[i][j] ← grid[i − 1][j] + grid[i][j − 1]
end for
end for
return grid[m][n]
end function
Thanks for your help!
This isn't hard to translate.. Ruby uses = instead of left arrow for assignment, and def instead of function to define a subroutine (which it calls a method instead of a function), but that's about it. Let's go through it.
function countRoutes(m,n)
That's beginning a function definition. In Ruby we use a method instead, and the keyword to define such a thing is def. It's also convention in Ruby to use snake_case for multiword names instead of camelCase:
def count_routes(m, n)
Now to create the grid:
grid ← array[m + 1][n + 1]
Ruby arrays are dynamic, so you don't normally need to specify the size at creation time. But that also means you don't get initialization or two-dimensionality for free. So what we have to do here is create an array of m+1 arrays, each of which can be empty (we don't need to specify that the sub-arrays need to hold n+1 items). Ruby's Array constructor has a way to do just that:
grid = Array.new(m+1) do [] end
Now the initialization. Ruby technically has for loops, but nobody uses them. Instead, we use iterator methods. For counting loops, there's a method on integers called times. But the pseudocode counts from 0 through m inclusive; times also starts at 0, but only counts up to one less than the invocant (so that way when you call 3.times, the loop really does execute "three times", not four). In this case, that means to get the behavior of the pseudocode, we need to call times on m+1 instead of m:
(m+1).times do |i|
grid[i][0] = 1
end
As an aside, we could also have done that part of the initialization inside the original array creation:
grid = Array.new(m+1) do [1] end
Anyway, the second loop, which would be more awkward to incorporate into the original creation, works the same as the first. Ruby will happily extend an array to assign to not-yet-existent elements, so the fact that we didn't initialize the subarrays is not a problem:
(n+1).times do |j|
grid[0][j] = 1
end
For the nested loops, the pseudocode is no longer counting from 0, but from 1. Counting from 1 through m is the same number of loop iterations as counting from 0 through m-1, so the simplest approach is to let times use its natural values, but adjust the indexes in the assignment statement inside the loop. That is, where the pseudocode starts counting i from 1 and references i-1 and i, the Ruby code starts counting i from 0 and references i and i+1 instead.
m.times do |i|
n.times do |j|
grid[i+1][j+1] = grid[i][j+1] + grid[i+1][j]
end
end
And the return statement works the same, although in Ruby you can leave it off:
return grid[m][n]
end
Putting it all together, you get this:
def count_routes(m, n)
grid = Array.new(m+1) do [1] end
(n+1).times do |j|
grid[0][j] = 1
end
m.times do |i|
n.times do |j|
grid[i+1][j+1] = grid[i][j+1] + grid[i+1][j]
end
end
return grid[m][n]
end
The notation grid[i][j] ← something means assigning something to the element of grid taking place on i-th line in j-th position. So the first two loops here suggest setting all values of the first column and the first row of the grid (correspondingly, the first and the second loops) to 1.
Related
I need to DRY this code but I don't know how.
I tried to dry the if condition but I don't know how to put the while in this.
def sum_with_while(min, max)
# CONSTRAINT: you should use a while..end structure
array = (min..max).to_a
sum = 0
count = 0
if min > max
return -1
else
while count < array.length
sum += array[count]
count += 1
end
end
return sum
end
Welcome to stack overflow!
Firstly, I should point out that "DRY" stands for "Don't Repeat Yourself". Since there's no repetition here, that's not really the problem with this code.
The biggest issue here is it's unrubyish. The ruby community has certain things it approves of, and certain things it avoids. That said, while loops are themselves considered bad ruby, so if you've been told to write it with a while loop, I'm guessing you're trying to get us to do your homework for you.
So I'm going to give you a couple of things to do a web search for that will help start you off:
ruby guard clauses - this will reduce your if-else-end into a simple if
ruby array pop - you can do while item = array.pop - since pop returns nil once the array is empty, you don't need a count. Again, bad ruby to do this... but maybe consider while array.any?
ruby implicit method return - generally we avoid commands we don't need
It's worth noting that using the techniques above, you can get the content of the method down to 7 reasonably readable lines. If you're allowed to use .inject or .sum instead of while, this whole method becomes 2 lines.
(as HP_hovercraft points out, the ternary operator reduces this down to 1 line. On production code, I'd be tempted to leave it as 2 lines for readability - but that's just personal preference)
You can put the whole thing in one line with a ternary:
def sum_with_while(min, max)
min > max ? -1 : [*(min..max)].inject(0){|sum,x| sum + x }
end
This is one option, cleaning up your code, see comments:
def sum_with_while(range) # pass a range
array = range.to_a
sum, count = 0, 0 # parallel assignment
while count < array.length
sum += array[count]
count += 1
end
sum # no need to return
end
sum_with_while(10..20)
#=> 165
More Rubyish:
(min..max).sum
Rule 1: Choose the right algorithm.
You wish to compute an arithmetic series.1
def sum_with_while(min, max)
max >= min ? (max-min+1)*(min+max)/2 : -1
end
sum_with_while(4, 4)
#=> 4
sum_with_while(4, 6)
#=> 15
sum_with_while(101, 9999999999999)
#=> 49999999999994999999994950
1. An arithmetic series is the sum of the elements of an arithmetic sequence. Each term of the latter is computed from the previous one by adding a fixed constant n (possibly negative). Heremax-min+1 is the number of terms in the sequence and (min+max)/2, if (min+max) is even, is the average of the values in the sequence. As (max-min+1)*(min+max) is even, this works when (min+max) is odd as well.
This is a program that came from a textbook:
# Initialize our counter
i = 1
# i: [0, 100]
while (i <= 100)
# Initialize prime flag
prime_flag = true
j = 2
# Test divisibility of i from [0, i/2]
while (j <= i / 2)
# puts " i ==> " to i.to_s + " j ==> " + j.to_s
if (i % j == 0)
prime_flag = false
# break
end
j = j + 1
end
# We found a prime!
if prime_flag
puts "Prime ==> " + i.to_s
end
# Increment the counter
i += 1
end
The while (j <= i / 2) introduces a new loop. What if we are trying to find prime numbers. Why is this written? Prime numbers don't have square roots. What is the purpose of j being <= i / 2? I do not understand why j is introduced.
You are correct that you should be only checking numbers <= floor(sqrt(i)). The above code is unnecessarily checking numbers from ceil(sqrt(i)) through i/2. It would give the correct answer, however.
In addition, this is not very Ruby-like code. It's terrible and the author should feel terrible (unless they intended to show you something bad in order for you to be amazed when you see how you can write it better!).
Here's the same code done in a more Ruby-like manner. Note that prime? can definitely be a one-liner, but I split things on to more lines readability in the context of the question:
def prime?(i) # Define a function that takes 1 parameter `i`
MAX_NUM_TO_CHECK = Math.sqrt(i) # No need to check numbers greater than sqrt(i)
(2..MAX_NUM_TO_CHECK).all? do |j| # Return `true` if the following line is true for
# all numbers [2,MAX_NUM_TO_CHECK]
i % j != 0 # true if `i` is evenly not divisible by `j`. Any
# input that evaluates to false here is not prime.
end
end
# Test primality of numbers [1,100]
(1..100).each {|n| puts "Prime ==> #{n}" if prime? n}
I think the biggest differences between your book and this code are:
The algorithm is different in that we do not check all values, but rather limit the checks to <= sqrt(i). We also stop checking once we know a number is not prime.
We iterate over Ranges rather than keeping counters. This is slightly higher level and easier to read once you get the syntax.
I split the code into two parts, a function that calculates whether a parameter is prime or not, and then we iterate over a Range of inputs (1..100). This seems like a good division of functionality to me, helping readability.
Some language features used here not in your example:
If statements can go after expressions, and the expression is only evaluated if the predicate (the thing after the if) evaluates to true. This can make some statements more readable.
A range is written (x..y) and allows you to quickly describe a series of values that you can iterate over without keeping counters.
Code inside
do |param1, ..., paramN| <CODE>; end
or
{|param1, ..., paramN| <CODE>}
is called a block. It's an anonymous function (a function passed in as a parameter to another function/method). We use this with all? and each here.
each is used to run a block of code on each element of a collection, ignoring the return value
all? can be used to determine whether a block returns true for every item in a collection.
If you're not familiar with passing code into functions, this is probably a little confusing. It allows you to execute different code based on your needs. For example, each runs the yielded block for every item in the collection.You could do anything in that block without changing the definition of each... you just yield it a block and it runs that block with the proper parameters. Here is a good blog post to get you started on how this works and what else you can use it for.
I'm trying to implement merge sort on my own using recursion.
def merge_sort(a,i,j)
if i < j
merge_sort(a,i,j/2)
merge_sort(a,j/2+1,j)
merge(a,i,j/2,j/2+1,j)
end
end
def merge(a,i,j,k,l)
# No implementation yet
end
The problem is my implementation results in the stack going too deep. I shouldn't be getting this error message for such a small array. The array I'm trying to sort is just five elements.
b = [5,4,3,2,1]
p merge_sort(b,0,b.size - 1) # => results in 'stack to deep' message
Here's a step in the right direction that's made a bit more Ruby-like in how it's more forgiving, plus as a bonus has actual names instead of mathematical shorthand:
def merge_sort(arr,from = nil,to = nil)
from ||= 0
to ||= arr.length
if (from < to)
part = from + (to - from) / 2
merge_sort(arr, from, part)
merge_sort(arr, part + 1, to)
merge(arr, from,part, part+1, to)
end
end
def merge(a,from,j,k,l)
# No implementation yet
end
b = [5,4,3,2,1]
merge_sort(b)
The mistake came about from not properly defining the partition point. In the original code for an array of length 5 the cut point would be 2, and when that's further divided, the cut point is 2/1 or 1, not 2+(5-3)/2 or 3 as it should be. From there it all went crazy because it was doing the math wrong and kept calling itself for no reason.
My problem was my mid-point formula was off throwing the recursion into an infinite loop recursing until the stack overflowed. Instead of
j / 2 + 1
It should have been
(i+j) / 2 + 1
tadman got the formula right in his re-versioning
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?
def random_select(array, n)
result = []
n.times do
# I do not fully understand how this line below works or why. Thank you
result.push array[rand(array.length)]
end
result
end
You are probably confused by this part:
n.times do
result.push(array[rand(array.length)])
end
n.times says it should loop n times.
result.push says to basically "push" or "put" something in the array. For example:
a = []
a.push(1)
p a #=> [1]
In array[rand(array.length)] , rand(array.length) will produce a random number as an index for the array. Why? rand(n) produces a number from 0 to n-1. rand(5) will produce either 0,1,2,3 or 4, for example.
Arrays use 0-based indexing, so if you have an array, say a = ['x', 'y', 'z'], to access 'x' you do a[0], to access y you do a[1] and so on. If you want to access a random element from a, you do a[rand(array.length)], because a.length in this case is 3, and rand(3) will produce a number that is either 0, 1 or 2. 0 is the smallest index and 2 is the largest index of our example array.
So suppose we call this method:
random_select([6,3,1,4], 2)
Try to see this code from the inside out. When the code reaches this part:
result.push(array[rand(array.length)])
it will first execute array.length which will produce 4. It will then execute rand(array.length) or rand(4) which will get a number between 0 and 3. Then, it will execute array[rand(array.length)] or array(some_random_number_between_0_and_3) which will get you a random element from the array. Finally, result.push(all_of_that_code_inside_that_got_us_a_random_array_element) will put the random element from the array in the method (in our example, it will be either 6, 3, 1 or 4) in the results array. Then it will repeat this same process once again (remember, we told it to go 2 times through the iteration).
The code can be rewritten to be much simpler, using the block-form Array constructor:
def random_select(array, n)
Array.new(n) {array.sample}
end
This creates a new array of size n and fills it with random samples from the array.
Note that the above solution, like your sample code, selects from the entire array each time which allows duplicate selections. If you don't want any duplicate selections, it's even simpler, since it is the default behavior of Array#sample:
def random_select(array, n)
array.sample(n)
end