# Extract of Combinatorics.jl
#
# You may (or may not!) want to call the function `permutations(a, t)` in your
# solution. If you would like to use it, include this file with
# `include("permutations.jl")`.
#
# License:
#
#    Copyright (c) 2013-2015: Alessandro Andrioni, Jiahao Chen and other
#    contributors.
#
#    Permission is hereby granted, free of charge, to any person obtaining a
#    copy of this software and associated documentation files (the "Software"),
#    to deal in the Software without restriction, including without limitation
#    the rights to use, copy, modify, merge, publish, distribute, sublicense,
#    and/or sell copies of the Software, and to permit persons to whom the
#    Software is furnished to do so, subject to the following conditions:
#
#    The above copyright notice and this permission notice shall be included in
#    all copies or substantial portions of the Software.
#
#    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
#    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
#    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
#    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
#    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
#    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
#    DEALINGS IN THE SOFTWARE.

struct Permutations{T}
    a::T
    t::Int
end

Base.eltype(::Type{Permutations{T}}) where {T} = Vector{eltype(T)}

Base.length(p::Permutations) = (0 <= p.t <= length(p.a)) ? factorial(length(p.a), length(p.a)-p.t) : 0

"""
    permutations(a)

Generate all permutations of an indexable object `a` in lexicographic order. Because the number of permutations
can be very large, this function returns an iterator object.
Use `collect(permutations(a))` to get an array of all permutations.
"""
permutations(a) = Permutations(a, length(a))

"""
    permutations(a, t)

Generate all size `t` permutations of an indexable object `a`.
"""
function permutations(a, t::Integer)
    if t < 0
        t = length(a) + 1
    end
    Permutations(a, t)
end

function Base.iterate(p::Permutations, s = collect(1:length(p.a)))
    (!isempty(s) && max(s[1], p.t) > length(p.a) || (isempty(s) && p.t > 0)) && return
    nextpermutation(p.a, p.t ,s)
end

function nextpermutation(m, t, state)
    perm = [m[state[i]] for i in 1:t]
    n = length(state)
    if t <= 0
        return(perm, [n+1])
    end
    s = copy(state)
    if t < n
        j = t + 1
        while j <= n &&  s[t] >= s[j]; j+=1; end
    end
    if t < n && j <= n
        s[t], s[j] = s[j], s[t]
    else
        if t < n
            reverse!(s, t+1)
        end
        i = t - 1
        while i>=1 && s[i] >= s[i+1]; i -= 1; end
        if i > 0
            j = n
            while j>i && s[i] >= s[j]; j -= 1; end
            s[i], s[j] = s[j], s[i]
            reverse!(s, i+1)
        else
            s[1] = n+1
        end
    end
    return (perm, s)
end
