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Comment by vonmoltke | Hacker News Reader

> algorithms are implemented with data structures

Eh, for a certain definition of "algorithm". Plenty of signal processing algorithms, for instance, have nothing to do with data structures.

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Yes, I would say the relationship is the opposite. Data structures imply a set of algorithms based on the promises of the data structure implementation. Algorithms themselves are free-floating things that can be reasoned about just as well in a C program as an instruction flow diagram as a Turing machine program. Take for instance an algorithm to divide two 32-bit integers. Or an algorithm that computes the max in a sequence (which is an abstraction) of numbers. There is no data structure, unless the argument is that a memory cell is itself a data structure.

As the title of Wirth's book goes:

Algorithms + Data Structures = Programs

I would consider the signal's value over time to be a sequence.

Algorithms that work over multiple samples are not tied to a data structure, except in an overly broad and useless sense of "data structure". A time or frequency series is not a data structure. It can be stored in any of several data structures, with various pros and cons depending on other circumstances, but the choice of data structure has nothing to do with the algorithm.

> It can be stored in any of several data structures, with various pros and cons depending on other circumstances, but the choice of data structure has nothing to do with the algorithm.

It has nothing to do with the theory of the algorithm. But everything to do with the implementation. So I think the original statement is true.

> algorithms are implemented with data structures

Where are the data structures? [0]

    MIN := X[N]; k := N;
    for j := N-1 step -1 until 1 do
      if X[j] < MIN then
        begin MIN := X[j]; k := j;
        end;

[0] https://assets.cs.ncl.ac.uk/seminars/139.pdf

X is data. There is no defined structure to it apart from the fact that there are N elements and you can select them. Is it a linked list, is it a random access array? It is not yet defined to be structured in any way. Furthermore you can analyze (and implement) this algorithm independent of the assumptions you make about how the access operation is performed, and then add those assumptions back in if you want to do another analysis.

You seem to be disputing a bunch of statements nobody made; all was said was "algorithms are implemented with data structures", and that example fits - you need a data structure to implement that algorithm. That's all that was claimed.

> X is data. There is no defined structure to it apart from the fact that there are N elements and you can select them. Is it a linked list, is it a random access array? It is not yet defined to be structured in any way.

Sure, but then that's not the entire implementation, error: X is undefined. If you want to actually run that code, it needs to be one of those (or many other) things.

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