# OK to post homework
# RDB, 2022-03-27, HW16

# 1.

# 2.

read "C16.txt":

IsCondorcet := proc(P)
    local v, n:
    v := nops(P):
    n := nops(P[1]):
    not member(n - 1, SV(Tour(P))):
end:

# 3.

ExactCond := proc(n, v)
    option remember:
    local count:
    count := coeff(add(IsCondorcet(p), p in RP(n, v)), true):

    count / n!^v
end:

# 4.

EstCond := proc(n, v, K)
    local count:
    count := coeff(add(IsCondorcet(RandP(n, v)), k=1..K), true):

    evalf(count / K):
end:

# 5.

Borda := proc(P)
    local n, points, ballot, i:
    n := nops(P[1]):
    points := [0 $ n]:

    for ballot in P do
        for i from 1 to n do
            points[ballot[i]] += n - i:
        od:
    od:

    points:
end:

# 6 / 7.

with(ListTools):

Ranks := proc(P, f)
    local ranking, vals, classes, i, v:
    ranking := f(P):

    # I'm going to use the fact that sets are sorted by default in my Maple. I
    # don't love this.
    vals := {op(ranking)}:

    classes := table():

    for i from 1 to nops(ranking) do
        v := ranking[i]:
        if not assigned(classes[v]) then
            classes[v] := {}
        fi:

        classes[v] := classes[v] union {i}:
    od:

    Reverse([entries(classes, 'nolist')]):
end:

CondorcetRank := proc(P)
    Ranks(P, x -> SV(Tour(x))):
end:

BordaRank := proc(P)
    Ranks(P, x -> Borda(x)):
end: