Number of ways getting sum K with a pair of 6sided dices. - sum

Given a of 6sided pair of dices, in how many ways can I get sum K.
Can someone give a detailed explanation to me how to use dynamic programming to solve this problem.
I have done reading on it but still hard to understand link

Related

Average Number of Comparisons

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In this question, for the element which is not the part of the list, what is the average number of comparisons? I thought that it should be n+1 but my friends suggests that it should be n+3 but I didn’t understand his solution. How should I approach in this kind of questions?

Number of divisors for very large number

Is there any fast way to find total divisors of a very large number supposedly 10^18.
I have tried a method which is of o(n^(1/3))
Forgive me asking direct question without providing any background or something else.
The fastest algorithm for that would be General number field sieve, probably fits your question.
On this question there is some discussion ongoing about how to efficiently find all divisors. GNFS is used for factorization, so only accounts prime numbers. You'll have to derive all divisors from that, if you need to. How to I find all divisors from prime factorization?
Further reading: A beginner's guide to the Number Field Sieve; Factoring Integers with the Number Field Sieve

Greedy Vertex Cover on Bipartite Graphs

I have the following problem. All suggestions appreciated.
Given a set of questions Q and subjects S, select q questions such that all subjects S are covered. A question might cover multiple subjects.
I built a greedy algorithm over SQL Server. I pick the first question associated with the subject s1 and remove all other subjects that are covered by it. I continue and see if there is a solution.
Here's the catch. Now I want to improve my algorithm and create question sets that are still covering the subjects but are not similar to each other more than 50%.
Any advice on the formal name of this problem. Any algorithms. Should this problem be solved for all sets together, or can it be solved one set at a time.

Example for an algorithm with greater than n splits

I was doing the derivation for masters theorem using the tree method and I noticed something.
So we have:
$T(n)=a*T(n/b) + n^c$
From this: we notice, the last level of the tree will have $a^(log_b_n)$ splits, which equals $n^(log_b_a)$
Now, if $a=b$, I get n splits in the last level, which is I've seen used in quick sort and merge sort, and if a
Is there a practical example for greater than n splits?
Where we actually repeat operations for elements?
*Also, math overflow formatting doesn't seem to work. Would appreciate if anyone helps.
The classical matrix multiplication by divide and conquer would be such an example. The recurrence relation is: T(n)=8T(n/2)+ Theta(n^2). Another would be Straussen algorithm.
Math notation is (sadly) limited to only a few stackexchange sites.

Fourier Transformation -

I've been doing a lot of research on this topic and I'm finally getting somewhere. Below is two complex numbers from the java code I'm using:
-9771.0 - j2125.0
-16184.09634718744 - j53968.71008512241
I know the amplitude/magnitude can be computed by doing the sqrt(a^2 + b^2) and this as far as I've gotten with this. I've read about sample rate but I'll need a better explanation of this alone and would like to be pointed in the right direction to obtain the knowledge. I've done the powerspectum graph but I need to do this on paper so I'll know how to obtain the frequency.
Applying Fourier Transformation to two values is pretty meaningless. You apply it to series of values (signal), then frequency starts to make sense. You can't speak about frequency in series of two values.