euler project 3 ruby> why does this solution work? - ruby

def large_prime(n)
return [] if n==1
factor = (2..n).find {|x| n % x == 0}
[factor] + large_prime(n/factor)
end
I got this solution from somewhere else. I don't understand the 4th line of code where large_prime is called recursively and appended onto factor.
When I change the first line "return []" and leave out the '[]' after the return, I get an error message for on line 4, that says '+':no implicit conversion of nil into Array.
So why does this code work? Thanks
P.S. I'm obviously a noob and everything is very new to me.

The 3rd line finds the first divisor of n between 2 and n. This line itself does not involve recursion.
I don't really get the code you modified, but it seems to return nil in some case, while the original method always return an Array.

You must return an empty array when passed 1 to terminate the recursion. Any positive argument other than one will result in another call to large_prime, but an argument of 1 results in large_prime simply returning an empty array.
At each level of recursion, the program adds an array with the single factor it found to an array consisting of all factors found for the value n/factor. When the last factor (other than 1) is found, the final call to large_prime is made with an argument of 1, large_prime returns an empty array which is then added to the array containing the last factor, giving an array containing just the last factor. This array is then returned and you have
[next-to-last-factor] + [last-factor], giving a return array of [next-to-last-factor, last-factor] which is added to [next-to-next-to-last-factor] giving [next-to-next-to-last-factor, next-to-last-factor, last-factor]. This is then added to an array [next-to-next-to-next-to-last-factor], giving... lather, rinse, repeat until we reach the largest factor and add it in.
You must return an empty array because you can't add nil to an array in Ruby.

Related

Why does my function outputting expected and unexpected values in ruby?

I have a method called fibs_rec that results in an unexpected output:
def fibs_rec(n)
if n == 1 || n == 0
return 1
else
a = fibs_rec(n-1) + fibs_rec(n-2)
puts a
return a
end
end
fibs_rec(5)
The call fibs_rec(5) should return 1,1,2,3,5 but here is the actual output:
2
3
2
5
2
3
8
Not only is the output incorrect, it lacks a number from the beginning.
Can someone explain why is this happening?
This is correct since your recursion is splitting into two sub-problems every time it recurses. If you want the series to appear properly then you should try doing this via dynamic programming for O(n) time complexity. As is, the first and second position won’t be printed because of the base case in the recursion.
As for the incorrect answer, it seems you have not accounted for the sequence starting with 0 index. Either find 4 index in the function which will give the fifth element or modify your function to work with position instead of index.

Beginner array iteration & error code interpretation

I kept getting the following error. After some research I assumed this is because my array access was throwing the error due to (mistakenly) having a NIL value.
my_solution.rb:24:in `count_between': undefined method `>=' for nil:NilClass
(NoMethodError) from my_solution.rb:35:in `<main>'
I'm new to reading error codes, so perhaps that's where I went wrong. But it got tunnel vision on line 24, as the error suggested. However I couldn't fix it, so out of desperation I wound up randomly changing the (<=) on line 23 to just (<). This fixed it.
Why did this fix it? My only guess is that originally using (<=) made it iterate "too far" and thus somehow returned NIL?
Why did the error code say it was the element on line 24 causing the issue, when it was actually the element on line 23? I'm new and am trying to be less intimated by error codes, so this was a curious experience.
Thanks for any guidance.
# count_between is a method with three arguments:
# 1. An array of integers
# 2. An integer lower bound
# 3. An integer upper bound
#
# It returns the number of integers in the array between the lower and upper
# bounds,
# including (potentially) those bounds.
#
# If +array+ is empty the method should return 0
# Your Solution Below:
def count_between(list_of_integers, lower_bound, upper_bound)
if list_of_integers.empty?
return 0
else
count = 0
index = 0
##line 23##
while index <= list_of_integers.length
##line24##
if list_of_integers[index] >= lower_bound &&
list_of_integers[index] <= upper_bound
count += 1
index += 1
else
index += 1
end
end
return count
end
end
puts count_between([1,2,3], 0, 100)
The last index that's <= list_of_integers.length is outside of the array, since the first index of an array is 0 and the last is array.length - 1.
The reason your error says line 24 is that line 23 works fine --- it just computes that the value of index is less than or equal to the the length of the array. Once you try and reference the element at that index in the array, however, it's assigned nil - and you can't perform a >= operation on nil.
One thing that might be helpful here is firing up an irb. If you try to reference an element that's out of bounds, you'll just get nil. If you try and perform an operation (that's not listed in nil.methods) on that same reference, it'll throw the error you're seeing.

how can I get the location for the maximum value in fortran?

I have a 250*2001 matrix. I want to find the location for the maximum value for a(:,i) where i takes 5 different values: i = i + 256
a(:,256)
a(:,512)
a(:,768)
a(:,1024)
a(:,1280)
I tried using MAXLOC, but since I'm new to fortran, I couldn't get it right.
Try this
maxloc(a(:,256:1280:256))
but be warned, this call will return a value in the range 1..5 for the second dimension. The call will return the index of the maxloc in the 2001*5 array section that you pass to it. So to get the column index of the location in the original array you'll have to do some multiplication. And note that since the argument in the call to maxloc is a rank-2 array section the call will return a 2-element vector.
Your question is a little unclear: it could be either of two things you want.
One value for the maximum over the entire 250-by-5 subarray;
One value for the maximum in each of the 5 250-by-1 subarrays.
Your comments suggest you want the latter, and there is already an answer for the former.
So, in case it is the latter:
b(1:5) = MAXLOC(a(:,256:1280:256), DIM=1)

How to populate an array with incrementally increasing values Ruby

I'm attempting to solve http://projecteuler.net/problem=1.
I want to create a method which takes in an integer and then creates an array of all the integers preceding it and the integer itself as values within the array.
Below is what I have so far. Code doesn't work.
def make_array(num)
numbers = Array.new num
count = 1
numbers.each do |number|
numbers << number = count
count = count + 1
end
return numbers
end
make_array(10)
(1..num).to_a is all you need to do in Ruby.
1..num will create a Range object with start at 1 and end at whatever value num is. Range objects have to_a method to blow them up into real Arrays by enumerating each element within the range.
For most purposes, you won't actually need the Array - Range will work fine. That includes iteration (which is what I assume you want, given the problem you're working on).
That said, knowing how to create such an Array "by hand" is valuable learning experience, so you might want to keep working on it a bit. Hint: you want to start with an empty array ([]) instead with Array.new num, then iterate something num.times, and add numbers into the Array. If you already start with an Array of size num, and then push num elements into it, you'll end up with twice num elements. If, as is your case, you're adding elements while you're iterating the array, the loop never exits, because for each element you process, you add another one. It's like chasing a metal ball with the repulsing side of a magnet.
To answer the Euler Question:
(1 ... 1000).to_a.select{|x| x%3==0 || x%5==0}.reduce(:+) # => 233168
Sometimes a one-liner is more readable than more detailed code i think.
Assuming you are learning Ruby by examples on ProjectEuler, i'll explain what the line does:
(1 ... 1000).to_a
will create an array with the numbers one to 999. Euler-Question wants numbers below 1000. Using three dots in a Range will create it without the boundary-value itself.
.select{|x| x%3==0 || x%5==0}
chooses only elements which are divideable by 3 or 5, and therefore multiples of 3 or 5. The other values are discarded. The result of this operation is a new Array with only multiples of 3 or 5.
.reduce(:+)
Finally this operation will sum up all the numbers in the array (or reduce it to) a single number: The sum you need for the solution.
What i want to illustrate: many methods you would write by hand everyday are already integrated in ruby, since it is a language from programmers for programmers. be pragmatic ;)

What is the pythonic way to detect the last element in a 'for' loop?

How can I treat the last element of the input specially, when iterating with a for loop? In particular, if there is code that should only occur "between" elements (and not "after" the last one), how can I structure the code?
Currently, I write code like so:
for i, data in enumerate(data_list):
code_that_is_done_for_every_element
if i != len(data_list) - 1:
code_that_is_done_between_elements
How can I simplify or improve this?
Most of the times it is easier (and cheaper) to make the first iteration the special case instead of the last one:
first = True
for data in data_list:
if first:
first = False
else:
between_items()
item()
This will work for any iterable, even for those that have no len():
file = open('/path/to/file')
for line in file:
process_line(line)
# No way of telling if this is the last line!
Apart from that, I don't think there is a generally superior solution as it depends on what you are trying to do. For example, if you are building a string from a list, it's naturally better to use str.join() than using a for loop “with special case”.
Using the same principle but more compact:
for i, line in enumerate(data_list):
if i > 0:
between_items()
item()
Looks familiar, doesn't it? :)
For #ofko, and others who really need to find out if the current value of an iterable without len() is the last one, you will need to look ahead:
def lookahead(iterable):
"""Pass through all values from the given iterable, augmented by the
information if there are more values to come after the current one
(True), or if it is the last value (False).
"""
# Get an iterator and pull the first value.
it = iter(iterable)
last = next(it)
# Run the iterator to exhaustion (starting from the second value).
for val in it:
# Report the *previous* value (more to come).
yield last, True
last = val
# Report the last value.
yield last, False
Then you can use it like this:
>>> for i, has_more in lookahead(range(3)):
... print(i, has_more)
0 True
1 True
2 False
Although that question is pretty old, I came here via google and I found a quite simple way: List slicing. Let's say you want to put an '&' between all list entries.
s = ""
l = [1, 2, 3]
for i in l[:-1]:
s = s + str(i) + ' & '
s = s + str(l[-1])
This returns '1 & 2 & 3'.
if the items are unique:
for x in list:
#code
if x == list[-1]:
#code
other options:
pos = -1
for x in list:
pos += 1
#code
if pos == len(list) - 1:
#code
for x in list:
#code
#code - e.g. print x
if len(list) > 0:
for x in list[:-1]:
#process everything except the last element
for x in list[-1:]:
#process only last element
The 'code between' is an example of the Head-Tail pattern.
You have an item, which is followed by a sequence of ( between, item ) pairs. You can also view this as a sequence of (item, between) pairs followed by an item. It's generally simpler to take the first element as special and all the others as the "standard" case.
Further, to avoid repeating code, you have to provide a function or other object to contain the code you don't want to repeat. Embedding an if statement in a loop which is always false except one time is kind of silly.
def item_processing( item ):
# *the common processing*
head_tail_iter = iter( someSequence )
head = next(head_tail_iter)
item_processing( head )
for item in head_tail_iter:
# *the between processing*
item_processing( item )
This is more reliable because it's slightly easier to prove, It doesn't create an extra data structure (i.e., a copy of a list) and doesn't require a lot of wasted execution of an if condition which is always false except once.
If you're simply looking to modify the last element in data_list then you can simply use the notation:
L[-1]
However, it looks like you're doing more than that. There is nothing really wrong with your way. I even took a quick glance at some Django code for their template tags and they do basically what you're doing.
you can determine the last element with this code :
for i,element in enumerate(list):
if (i==len(list)-1):
print("last element is" + element)
This is similar to Ants Aasma's approach but without using the itertools module. It's also a lagging iterator which looks-ahead a single element in the iterator stream:
def last_iter(it):
# Ensure it's an iterator and get the first field
it = iter(it)
prev = next(it)
for item in it:
# Lag by one item so I know I'm not at the end
yield 0, prev
prev = item
# Last item
yield 1, prev
def test(data):
result = list(last_iter(data))
if not result:
return
if len(result) > 1:
assert set(x[0] for x in result[:-1]) == set([0]), result
assert result[-1][0] == 1
test([])
test([1])
test([1, 2])
test(range(5))
test(xrange(4))
for is_last, item in last_iter("Hi!"):
print is_last, item
We can achieve that using for-else
cities = [
'Jakarta',
'Surabaya',
'Semarang'
]
for city in cities[:-1]:
print(city)
else:
print(' '.join(cities[-1].upper()))
output:
Jakarta
Surabaya
S E M A R A N G
The idea is we only using for-else loops until n-1 index, then after the for is exhausted, we access directly the last index using [-1].
You can use a sliding window over the input data to get a peek at the next value and use a sentinel to detect the last value. This works on any iterable, so you don't need to know the length beforehand. The pairwise implementation is from itertools recipes.
from itertools import tee, izip, chain
def pairwise(seq):
a,b = tee(seq)
next(b, None)
return izip(a,b)
def annotated_last(seq):
"""Returns an iterable of pairs of input item and a boolean that show if
the current item is the last item in the sequence."""
MISSING = object()
for current_item, next_item in pairwise(chain(seq, [MISSING])):
yield current_item, next_item is MISSING:
for item, is_last_item in annotated_last(data_list):
if is_last_item:
# current item is the last item
Is there no possibility to iterate over all-but the last element, and treat the last one outside of the loop? After all, a loop is created to do something similar to all elements you loop over; if one element needs something special, it shouldn't be in the loop.
(see also this question: does-the-last-element-in-a-loop-deserve-a-separate-treatment)
EDIT: since the question is more about the "in between", either the first element is the special one in that it has no predecessor, or the last element is special in that it has no successor.
I like the approach of #ethan-t, but while True is dangerous from my point of view.
data_list = [1, 2, 3, 2, 1] # sample data
L = list(data_list) # destroy L instead of data_list
while L:
e = L.pop(0)
if L:
print(f'process element {e}')
else:
print(f'process last element {e}')
del L
Here, data_list is so that last element is equal by value to the first one of the list. L can be exchanged with data_list but in this case it results empty after the loop. while True is also possible to use if you check that list is not empty before the processing or the check is not needed (ouch!).
data_list = [1, 2, 3, 2, 1]
if data_list:
while True:
e = data_list.pop(0)
if data_list:
print(f'process element {e}')
else:
print(f'process last element {e}')
break
else:
print('list is empty')
The good part is that it is fast. The bad - it is destructible (data_list becomes empty).
Most intuitive solution:
data_list = [1, 2, 3, 2, 1] # sample data
for i, e in enumerate(data_list):
if i != len(data_list) - 1:
print(f'process element {e}')
else:
print(f'process last element {e}')
Oh yes, you have already proposed it!
There is nothing wrong with your way, unless you will have 100 000 loops and wants save 100 000 "if" statements. In that case, you can go that way :
iterable = [1,2,3] # Your date
iterator = iter(iterable) # get the data iterator
try : # wrap all in a try / except
while 1 :
item = iterator.next()
print item # put the "for loop" code here
except StopIteration, e : # make the process on the last element here
print item
Outputs :
1
2
3
3
But really, in your case I feel like it's overkill.
In any case, you will probably be luckier with slicing :
for item in iterable[:-1] :
print item
print "last :", iterable[-1]
#outputs
1
2
last : 3
or just :
for item in iterable :
print item
print iterable[-1]
#outputs
1
2
3
last : 3
Eventually, a KISS way to do you stuff, and that would work with any iterable, including the ones without __len__ :
item = ''
for item in iterable :
print item
print item
Ouputs:
1
2
3
3
If feel like I would do it that way, seems simple to me.
Use slicing and is to check for the last element:
for data in data_list:
<code_that_is_done_for_every_element>
if not data is data_list[-1]:
<code_that_is_done_between_elements>
Caveat emptor: This only works if all elements in the list are actually different (have different locations in memory). Under the hood, Python may detect equal elements and reuse the same objects for them. For instance, for strings of the same value and common integers.
Google brought me to this old question and I think I could add a different approach to this problem.
Most of the answers here would deal with a proper treatment of a for loop control as it was asked, but if the data_list is destructible, I would suggest that you pop the items from the list until you end up with an empty list:
while True:
element = element_list.pop(0)
do_this_for_all_elements()
if not element:
do_this_only_for_last_element()
break
do_this_for_all_elements_but_last()
you could even use while len(element_list) if you don't need to do anything with the last element. I find this solution more elegant then dealing with next().
For me the most simple and pythonic way to handle a special case at the end of a list is:
for data in data_list[:-1]:
handle_element(data)
handle_special_element(data_list[-1])
Of course this can also be used to treat the first element in a special way .
Better late than never. Your original code used enumerate(), but you only used the i index to check if it's the last item in a list. Here's an simpler alternative (if you don't need enumerate()) using negative indexing:
for data in data_list:
code_that_is_done_for_every_element
if data != data_list[-1]:
code_that_is_done_between_elements
if data != data_list[-1] checks if the current item in the iteration is NOT the last item in the list.
Hope this helps, even nearly 11 years later.
if you are going through the list, for me this worked too:
for j in range(0, len(Array)):
if len(Array) - j > 1:
notLast()
Instead of counting up, you can also count down:
nrToProcess = len(list)
for s in list:
s.doStuff()
nrToProcess -= 1
if nrToProcess==0: # this is the last one
s.doSpecialStuff()
I will provide with a more elegant and robust way as follows, using unpacking:
def mark_last(iterable):
try:
*init, last = iterable
except ValueError: # if iterable is empty
return
for e in init:
yield e, True
yield last, False
Test:
for a, b in mark_last([1, 2, 3]):
print(a, b)
The result is:
1 True
2 True
3 False
If you are looping the List,
Using enumerate function is one of the best try.
for index, element in enumerate(ListObj):
# print(index, ListObj[index], len(ListObj) )
if (index != len(ListObj)-1 ):
# Do things to the element which is not the last one
else:
# Do things to the element which is the last one
Delay the special handling of the last item until after the loop.
>>> for i in (1, 2, 3):
... pass
...
>>> i
3
There can be multiple ways. slicing will be fastest. Adding one more which uses .index() method:
>>> l1 = [1,5,2,3,5,1,7,43]
>>> [i for i in l1 if l1.index(i)+1==len(l1)]
[43]
If you are happy to be destructive with the list, then there's the following.
We are going to reverse the list in order to speed up the process from O(n^2) to O(n), because pop(0) moves the list each iteration - cf. Nicholas Pipitone's comment below
data_list.reverse()
while data_list:
value = data_list.pop()
code_that_is_done_for_every_element(value)
if data_list:
code_that_is_done_between_elements(value)
else:
code_that_is_done_for_last_element(value)
This works well with empty lists, and lists of non-unique items.
Since it's often the case that lists are transitory, this works pretty well ... at the cost of destructing the list.
Assuming input as an iterator, here's a way using tee and izip from itertools:
from itertools import tee, izip
items, between = tee(input_iterator, 2) # Input must be an iterator.
first = items.next()
do_to_every_item(first) # All "do to every" operations done to first item go here.
for i, b in izip(items, between):
do_between_items(b) # All "between" operations go here.
do_to_every_item(i) # All "do to every" operations go here.
Demo:
>>> def do_every(x): print "E", x
...
>>> def do_between(x): print "B", x
...
>>> test_input = iter(range(5))
>>>
>>> from itertools import tee, izip
>>>
>>> items, between = tee(test_input, 2)
>>> first = items.next()
>>> do_every(first)
E 0
>>> for i,b in izip(items, between):
... do_between(b)
... do_every(i)
...
B 0
E 1
B 1
E 2
B 2
E 3
B 3
E 4
>>>
The most simple solution coming to my mind is:
for item in data_list:
try:
print(new)
except NameError: pass
new = item
print('The last item: ' + str(new))
So we always look ahead one item by delaying the the processing one iteration. To skip doing something during the first iteration I simply catch the error.
Of course you need to think a bit, in order for the NameError to be raised when you want it.
Also keep the `counstruct
try:
new
except NameError: pass
else:
# continue here if no error was raised
This relies that the name new wasn't previously defined. If you are paranoid you can ensure that new doesn't exist using:
try:
del new
except NameError:
pass
Alternatively you can of course also use an if statement (if notfirst: print(new) else: notfirst = True). But as far as I know the overhead is bigger.
Using `timeit` yields:
...: try: new = 'test'
...: except NameError: pass
...:
100000000 loops, best of 3: 16.2 ns per loop
so I expect the overhead to be unelectable.
Count the items once and keep up with the number of items remaining:
remaining = len(data_list)
for data in data_list:
code_that_is_done_for_every_element
remaining -= 1
if remaining:
code_that_is_done_between_elements
This way you only evaluate the length of the list once. Many of the solutions on this page seem to assume the length is unavailable in advance, but that is not part of your question. If you have the length, use it.
One simple solution that comes to mind would be:
for i in MyList:
# Check if 'i' is the last element in the list
if i == MyList[-1]:
# Do something different for the last
else:
# Do something for all other elements
A second equally simple solution could be achieved by using a counter:
# Count the no. of elements in the list
ListLength = len(MyList)
# Initialize a counter
count = 0
for i in MyList:
# increment counter
count += 1
# Check if 'i' is the last element in the list
# by using the counter
if count == ListLength:
# Do something different for the last
else:
# Do something for all other elements
Just check if data is not the same as the last data in data_list (data_list[-1]).
for data in data_list:
code_that_is_done_for_every_element
if data != data_list[- 1]:
code_that_is_done_between_elements
So, this is definitely not the "shorter" version - and one might digress if "shortest" and "Pythonic" are actually compatible.
But if one needs this pattern often, just put the logic in to a
10-liner generator - and get any meta-data related to an element's
position directly on the for call. Another advantage here is that it will
work wit an arbitrary iterable, not only Sequences.
_sentinel = object()
def iter_check_last(iterable):
iterable = iter(iterable)
current_element = next(iterable, _sentinel)
while current_element is not _sentinel:
next_element = next(iterable, _sentinel)
yield (next_element is _sentinel, current_element)
current_element = next_element
In [107]: for is_last, el in iter_check_last(range(3)):
...: print(is_last, el)
...:
...:
False 0
False 1
True 2
This is an old question, and there's already lots of great responses, but I felt like this was pretty Pythonic:
def rev_enumerate(lst):
"""
Similar to enumerate(), but counts DOWN to the last element being the
zeroth, rather than counting UP from the first element being the zeroth.
Since the length has to be determined up-front, this is not suitable for
open-ended iterators.
Parameters
----------
lst : Iterable
An iterable with a length (list, tuple, dict, set).
Yields
------
tuple
A tuple with the reverse cardinal number of the element, followed by
the element of the iterable.
"""
length = len(lst) - 1
for i, element in enumerate(lst):
yield length - i, element
Used like this:
for num_remaining, item in rev_enumerate(['a', 'b', 'c']):
if not num_remaining:
print(f'This is the last item in the list: {item}')
Or perhaps you'd like to do the opposite:
for num_remaining, item in rev_enumerate(['a', 'b', 'c']):
if num_remaining:
print(f'This is NOT the last item in the list: {item}')
Or, just to know how many remain as you go...
for num_remaining, item in rev_enumerate(['a', 'b', 'c']):
print(f'After {item}, there are {num_remaining} items.')
I think the versatility and familiarity with the existing enumerate makes it most Pythonic.
Caveat, unlike enumerate(), rev_enumerate() requires that the input implement __len__, but this includes lists, tuples, dicts and sets just fine.

Resources