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Theory of book recommendations in computer science

I am looking for a computer theory book containing the following topics: data structures, algorithms, discrete mathematics, automata …
I would like the book to contain exercises.

Classification of Programming Exercises – Computer Science Stack Exchange

I wondered what attempts had been made to classify student programming exercises (just like the "taxonomy" in biology) into their learning path.
For example :

  • A criterion of "concept (s) covered (s)" (generic to specific):

    • At level 1, we have "general" concepts: Iteration, Recursion, ADT, Conditionnals, etc.
    • At level 2, we have "less general" concepts: for loop, tail recursion, list, ternary operator
  • A criterion of "difficulty" (easy, intermediate, difficult)

According to my research (on many search engines like https://dblp.uni-trier.de/), there is only one very mentioned: Bloom's taxonomy. What other classifications exist, except this one?

Thank you in advance for your help

operating system – Computer Science Stack Exchange

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combinatorics – 8 puzzle problem – Computer Science Stack Exchange

Problem 8-puzzle: The puzzle consists of an area divided into a grid of 3 out of 3. On each box of the grid is a tile, with the exception of a box that remains empty . A tile next to the empty square of the grid can be moved into the empty space, leaving its previous position empty in its turn.

Whatever the initial state of the puzzle, there is exactly $ 9 / $ 2 accessible states. How can I prove it? And how should I generalize the proof to $ (n ^ 2-1) $derived nozzle problem using $ n $ by $ n $ Grid?

Python Libraries for Algorithms – Computer Science Stack Exchange

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Simple NP-hard proof question – Computer Science Stack Exchange

$ 3SATplus $

  • Entry: 2 CNF formulas $ F_1 $, $ F_2 $ where all clauses have exactly $ 3 $ literals.

  • Question: Does every truth assignment satisfy at least as much? $ F_2 $ clauses like $ F_1 $is?

assume $ 3SATPLUS in NP $

Prove $ 3SAT leq_p $ $ 3SATplus $

The reduction is as follows

$ F_1 = (x lor bar {x} lor x) land dots land (x lor bar {x} lor x) $

For $ n $ clauses. That means that he will always accept $ n $ clauses.

$ F_2 = F $

It's polytime because its $ 2n $ clauses only $ n $ more than $ F $

if $ F in 3SAT $then $ F_1 = F_2 $ since they both satisfy $ n $ clauses so $ F_1, F_2 in 3SATplus $

I will prove the contrapositive

Yes $ F notin 3SAT $then $ F_1 $ satisfied $ n $ clauses and $ F_2 $ can satisfy that up to $ n-1 $ so $ F_1> F_2 $ always. Therefore, $ F_1, F_2 notin 3SATplus $

Is there anything else to be said or does it confirm its $ NP-hard $?

Formal Languages ​​of Automata – Computer Science Stack Exchange

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Stopping the problem in C ++ – Computer Science Stack Exchange

The stopping problem is based on the fluidity of the Turing machines. That is, a string can represent a machine.

Can you do the same for C ++ on a modern computer?

Let's see my first attempt. Let bool h (string x, string y) the supposed function that decides to stop and always stops. You can easily make a complete program.

Now let's define a contradictory function F:

bool f (string x) {
if (h (x, x))
for (;;);
return true;
}

int main () {
cost << h (f, f) << endl;
}

The problem is that I can not feed the code of F in h in main ().

My second attempt: prepare 4 files: h.cpp, h.exe, f.cpp, f.exe. And suppose that the call formats are

h.exe filename1 filename2
f.exe file name

My problem is that in f.cpp I need to call h.exewhich in turn must be part of f.cpp.

What is your work plan?