Time complexity – number of product factors of subarrays

The problem

With an array of N elements (not necessarily different), we have multiple queries. For each query we have to get the number of factors of the numerical product from (L, R) (2 indices of the array), where 1 <= L <= R <= N. We have to answer each of these questions.
Each element of the array <= 10 ^ 6
Number of queries Q <= 10 ^ 5
Number of elements N <= 10 ^ 5

An approach to a solution

Since the queries are offline, we could use Mo's algorithm to find a solution.
I used the Sieve method to get the prime factorization of each number in the array (precalculated) in O time (N log N). Then I kept an array F of 10 ^ 6 elements to store the frequency of the prime factors of each element in an array. Since a number A can have at most a number of prime factors log A and we come across a new element or remove an element in the sorted queries (moving the start or end pointer), we can change our array F to O (log) accordingly A ) ~ O (log N) time.

But I'm stuck here. To get the total number of factors, we have to go through array F each time and find the sum by finding (a1 + 1) (a2 + 1) … (an + 1), n ​​with ai> 0 and ai execute a prime number. This increases the complexity considerably. Please let me know a way out.

Windows 7 – How do I see how much delay / CPU time a Google Chrome extension adds when a page loads?

How can I see how much delay / CPU time a Google Chrome extension adds when a page loads?

For example, I want to know how much delay / CPU time the Google Chrome extension Dark Reader adds when the website loads. How do pseudo-random and really random numbers differ and why is that important?

If the solution depends on the operating system, I use Windows 7 SP1 x64 Ultimate.


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Is SEO Really Helpful? Is the money and time invested worth it? | Proxies-free

Hey there,
I created my new website and now I want to make it popular. I want to reach a good audience and have been thinking about doing search engine optimization. I have spoken to an SEO company but they charge too much and the time they ask us is at least 6 months. Will it be worth it or if there is another way to reach the audience, please guide me.

Complexity Theory – Isn't Every Polynomial Time Problem an NP Problem?

Look here. Backpack problem – NP-complete despite dynamic programming solution?

The only reason why the backpack problem is NP-complete is because the input is made as binary numbers, so n is actually 2 ^ n. Because the weight is an axis of the DP array.

Then for every single problem, for example one that requires an O (n) loop through an O (n) sized array, if we actually consider the array to be 2 ^ n bits long or something in the direction of this effect that actually Doesn't it make sense, aren't all of these problems actually NP-complete?

It seems to me that the original "feeling / intuition" of relatively mediocre test cases for NP problems that don't even work is rejected, because then almost every algorithm will ever be NP.

Email server – Postfix whitelist in real time

I use Postfix & # 39; s postscreen Filter and I've whitelisted a couple of static CIDRs with that postscreen_access_list Feature. However, when I tested this feature, I found that sending emails to my servers with a large email host did so after the first try and the expected …

NOQUEUE: reject: RCPT from (###.###.###.###):#####: 450 4.3.2 Service currently unavailable;
PASS NEW (###.###.###.###):#####

… when the next attempt is made (the one that should come through because it was automatically whitelisted), it usually comes from a completely different IP address, since the outgoing servers are part of a farm. As a result, some emails are delayed by more than an hour, if not more.

I understand that this is by design, but in our scenario MANY client servers will have this delay, and I wonder if there is a way to create a centralized whitelist that all of our client servers will update and validate against instead of theirs to maintain your own?