Highest safe rung problem?

Highest Safe rung problem : There are many rungs on a ladder in increasing order of height. A bottle is thrown from a rung, and depending on the height of the rung, the bottle may break or may not (bottle breaks for higher height rungs, and doesn’t for lower rungs). We need to find the maximum height safe rung for which the bottle doesn’t break given that:

(1) We have only 1 bottle with us.

(2) We have infinite bottles with us.

(3) We have exactly 2 bottles with us.

(4) We have k bottles with us. ($ 1 \leq k$ ).

Design algorithms for solving (1) – (4) in best possible time complexity. (Also note that (3) and (4) should be an asymptotic improvement over (1).]

My method: (1) is just a linear search and (2) is a divide and conquer approach to solving the problem. I cannot find an asymptotically improved algorithm for (3) – the only methods which I kept thinking of provide some constant factor improvements in time complexity over (1), I am absolutely clueless on how to solve for (3) and (4).

P.S: This is a problem from Chapter 1 of Kleinberg and Tardos. I couldn’t find it’s solution online.

is no system really safe?

It may seem like a very general question but I couldn’t find any detailed debates over it. This is a purely theoretical question as of 2019.

Suppose we are to create our own product and safety design would be our priority. According to what we can see on the media (movies, games, whatever) hackers mention, that “no system is safe” and it got me wondering: is it true, that absolutely no system is safe from the hackers? I was browsing some basics online on what it means to be a hacker (as far as I know it often involves exploiting a security vulnerability). I am aware, that hackers can utilize a range of tools to hack a system (brute force, injections, hijacking, back doors…).

Would it be possible to design a system to be unhackable or are we limited to have a system, that is virtually unhackable? Because for most problems there exists a solution (like temp-banning a certain IP address when DDOS or brute force attacks happen) and this theoretical question takes exactly that into consideration. I am also aware, that security varies greatly by technologies such as HTTPS web servers/FTP, bluetooth, network, operating systems, authentication forms, databases, smart devices, software, bio-metric scanners…

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Are Snap and Flatpack apps safe to install? Are they “official”, approved or tested for a particular distro version?

I don’t like installing apps outside my distro’s official repositories.

Linux security relies a lot on having a repository meticulosly curated and tested for library compatibility with current distro version, stability and security.

Once I installed, from outside repos, a fancy terminal emulator that mimicked retro green/amber phosphor monitors. This app wreaked havoc in my system and I had to reinstall Ubuntu.

I hesitate a lot about using ppas as well.

I only trust very few external sources, ppas or packages downloaded from websites.

But now Snap and Flatpack seems to be all the rage in Ubuntu-specialized sites.

  • Is it safe to install Snap apps or Flatpack apps?
  • Are there official repos for such?
  • Am I missing something here?
  • How is safety and stability taken cared of with this non apt stuff.

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