algorithm – reducing temporal complexity

Here is the link of the problem
and here is my code,

int main ()
int i, j, k, t, n, c = 0;
int num[105]= {0};
num[0]= 0;
scanf ("% d", & t);
for (j = 1; j <= 45360; j ++)
c = 0;
for (k = 1; k <= j; k ++)
if (j% k == 0)
c ++;
if (num[c]== 0)
num[c]= j;
for (i = 0; i <t; i ++)
scanf ("% d", & n);
printf ("% d  n", num[n])
returns 0;

The code gives me TLE (time limit exceeded). Is there a better algorithm or procedure to solve this problem? Or, is there a theory of numbers that I can apply to solve it? I think my procedure is not correct, although it gives me a TLE.

python – Is the complexity of this code temporal?

Explanation of the algorithm: based on an unsorted list, I want to find the indexes of values ​​in another sorted list. Note that all values ​​are unique and both lists have the same values, but in a different order, for example:

# O (log n)
def binary_search (data, value):
n = len (data)
left = 0
right = n - 1
keeping left <= right:
middle = (left + right) / 2
if value < data[middle]:
            right = middle - 1
        elif value > The data[middle]:
left = middle + 1
back in the middle
raise ValueError ('The value is not in the list & # 39;)

# O (n log n)
def find_indexes (data1, data2):
return [binary_search(data2, value) for value in data1]

if __name__ == __ hand __:
data1 = [9, 1, 8, 2]
    data2 = [1, 2, 8, 9]
    print (find_indexes (data1, data2))
# >> [3, 0, 2, 1]

Can any one please confirm that the function find_indexes has quasi-linear temporal complexity?

Note that this is not a real problem and that I am not trying to improve this algorithm. I'm just trying to illustrate the simple operation of a quasi-linear algorithm.

asymptotic – What is the (large) temporal complexity of this specific implementation of the web robot?

I've built a simple "web crawler" and I wanted to know what was the temporal complexity of the central "processing" logic.

Here is a diagram of the architecture:

Specifically, the part of the algorithm that interests me is the Caterpillar which:

  1. sets the size of the work pool
  2. inserts tasks into a channel
  3. processes tasks simultaneously within the pool

In the robot code, we:

  • accept a list of N elements
  • each item in the list has a nested list of N items
  • we look at each element and decide whether to treat it or not

Note the analyzer and Cartographer parts of the code all have the same underlying design but How the & # 39; task & # 39; is treated is slightly different and so although I can imagine the time complexity of those who might be different depending on the procedure to follow, the principle is always the same: we continue to go through all the elements and decide on something to do .

What is this temporal complexity BigO?

At first, it might seem like it's just O (1) because we visit each item in the list as well as each item in the nested list.

Is that it? or am I missing something altogether obvious?

I do not think it's O (n Log n) because this does not reduce the number of loopback operations in nested lists. The same applies to O (n * n) as the nested loop does not necessarily have the same length as the parent list. I do not think it's either O (2 n) as nested lists do not grow exponentially (they are just an unknown number of elements).

temporal complexity – Relative efficiency of n tasks in 1 loop versus 1 task each in n loops?

Let's say I have 3 simple tasks, find the min, the max and the average of an array of numbers.

A modular approach would be to write a function for each, thus iterating the table three times. However, this seems unnecessary if all information can be collected in a single iteration.

I understand that both approaches take 3n but I wonder if one approach is better than the other in the general case and why.

Decidability of temporal complexity

Let $ t: mathbb {N} rightarrow mathbb {N} $ to be a building function in time with $ t (n) geq n + 100 $. Show that there is no MT $ T $ this being given the gödel number of another TM $ M $, decides if M is limited in time by $ t $. Can someone help me with that? I have no idea

Understand the dynamic deformation of the frequency (not the dynamic temporal strain)

I am developing a paper that requires dynamic frequency distortion as a component. They wrote very briefly about this algorithm and quote
this article: Transformation of the voice using the PSOLA technique (page 9/13 of the PDF document, section 3.3). I read it but I can not understand its mechanics. I've also done some research on Google, but I have almost no improvement. As I understand it, DFW takes an input of 2 spectrums (A and B) and then calculates a deformation matrix converting A-> B. Can someone give me a clearer intuition?

Thanks in advance.

Turing Machines – Spatial and Temporal Complexity of $ L = {a ^ nb ^ {n ^ 2} mid n≥1 } $

Consider the following language:
$$ L = {a ^ nb ^ {n ^ 2} mid n≥1 } , $$

When it comes to determining the time and space complexity of a multi-band TM, we can use two memory bands, the first one to count $ n $and the second to repeat $ n $ times the number of $ n $. So, because of the way we use the second band, it should have a $ Theta (n ^ 2) $ complexity of space, and I would say the same thing about time. I thought it was ok, but the solution is $ TM (x) = | x | + n + 2 $, or, $ x $ is, supposedly, the length of the string, from where $ Theta (| x |) $. That sounds right to me, so is my reasoning completely wrong or is it just a different way to express it?

Could we have reasoned differently, and say, for example, for every $ a $ we write a symbol on the first tape and then count the $ b $, swiping the symbols back and forth $ n $ time? This time, the complexity of the space should just be $ Theta (n) $, while the temporal complexity should remain unchanged. What would change if we had an MT on a single tape?

algorithms – Rank of points in the temporal complexity of the 2D plane?

I read about the search algorithm ranks all points in a 2D plane, I do not understand the corresponding time complexity formula. It has four steps:

  1. Calculate the median of the x coordinates of any point and divide the plane into two left and right halves.
  2. Recursively do 1. then when there is only 1 point, rank (this point) = 0.
  3. Sort the points by y coordinate separately, left and right.
  4. Update right.

I understand the idea of ​​these steps and 3. has a complexity $ O (n log n) $but the formula of temporal complexity in my book is

$$ T (n) = 2T (n / 2) + Theta (n), $$

why the last term is not $ Theta (n lg n) $? This is my current idea is that the $ T (n) = Theta (n lg ^ 2n) $, applying the theorem of the master.

Theory of complexity – Without using the temporal hierarchy theorem, is there another way to prove P / = EXP?

Some of your past responses have not been well received and you may be stuck.

Please pay close attention to the following tips:

  • Please make sure to respond to the question. Provide details and share your research!

But to avoid

  • Ask for help, clarification, or answer other answers.
  • Make statements based on opinions; save them with references or personal experience.

To learn more, read our tips for writing good answers.

Resources more complicated than temporal and spatial complexity

The wikipedia page on computing resources indicates that there are many different resources that have been defined:

In computer complexity theory, an IT resource is a resource used by some computer models in solving computer problems.

The simplest calculation resources are the calculation time, the number of steps needed to solve a problem, the memory space, the amount of memory needed to solve the problem, but many more complex resources have been defined.[citation needed]

Unfortunately, this claim does not have a quote.

What are these more complex resources that have been defined?

  • Can I imagine something like the complexity of parallel processing?