Add next_k_array! and k_array_rank.

[shizejin]

Add next_k_array! and k_array_rank utilities, mimicking the counterpart Python version implemented by @oyamad. It is mainly copying and pasting, and modifying a little part (let index start from 1 rather than 0).

[oyamad]

Thanks @shizejin

k_array_rank is not type stable (the return type changes according to the input value). Run it with @code_warntype.

One possibility is:

function k_array_rank(T::Type{<:Integer}, a::Vector{<:Integer})
    k = length(a)
    idx = one(T)
    for i = 1:k
        idx += binomial(T(a[i])-one(T), T(i))
    end
    return idx
end

k_array_rank(a::Vector{<:Integer}) = k_array_rank(Int, a)

n, k = 100, 50
a = collect((n-k+1):n)
k_array_rank(BigInt, a)

100891344545564193334812497256

k_array_rank(a)

InexactError()

I don't know if this is "Julian": @sglyon ?

[sglyon]

That proposal is quite Julian. It would be great if there was a way to make it "just work" without throwing an error, but unfortunately I don't think there is.

As long as you don't expect the InexactError to arise often in practice, the proposal by @oyamad has my vote.

[oyamad]

@sglyon Thanks.

@shizejin We may add a note about the possibility of an error as well as a sufficient condition for it not to occur, as in the Python version.

[shizejin]

@oyamad Sure, I will modify this.

In this case, in the tournament game, should we set a threshold of the pair of n and k to determine whether use k_array_rank(Int, a) or k_array_rank(BigInt, a)? Or do we just use k_array_rank(Int, a) as the InexactError case happens almost impossibly?

[oyamad]

@shizejin See this.

The size of NumPy arrays is limited by the range of np.intp. Maybe Julia arrays are limited by the range of Csize_t (= UInt)?

[shizejin]

@oyamad It seems that the InexactError of binomial happens when the function tries to convert the calculated result back to the type T of the arguments n and k. Therefore, follow the style of Python code, I think we can add these to Julia version of tournament game generator.

if binomial(BigInt(n), BigInt(k)) > typemax(typeof(n))
    error("Overflow! Maximum allowed size of $(typeof(n)) exceeded")
end

What do you think?

[oyamad]

Are we talking about this PR, or the tournament game? About the latter let's discuss at Games.jl.

[codecov-io]

Codecov Report

Merging #199 into master will increase coverage by 0.09%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #199      +/-   ##
==========================================
+ Coverage   91.02%   91.12%   +0.09%     
==========================================
  Files          24       24              
  Lines        1693     1712      +19     
==========================================
+ Hits         1541     1560      +19     
  Misses        152      152

Impacted Files	Coverage Δ
src/util.jl	96.59% <100%> (+0.93%)	⬆️

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[oyamad]

Looks good to me.