#Robert Dougherty-Bliss, hw3
# OK to post.

read "C3.txt":

# 1.

NewUCG := proc(n)
    local w, res:
    w := [0$n]:
    res := []:
    while w <> FAIL do
        res := [op(res), w]:
        w := NEXG(w):
    od:

    res:
end:

# 2.

BoxG := proc(L)
    local prev:
    local res:
    if nops(L) = 0 then
        return [[]]:
    fi:

    # `prev` is a walk along the first n - 1 dimensions.
    prev := BoxG(L[2..]):

    # Walk through normally with the last component 0, then reversed with the
    # last component 1, then normally with the last component 2, and so on
    # until you've used all components.

    res := []:

    for k from 0 to L[1] do
        newSegment := [seq([k, op(p)], p in prev)]:
        if k mod 2 = 1 then
            newSegment := ListTools[Reverse](newSegment):
        fi:
        res := [op(res), op(newSegment)]:
    od:

    res:
end:

# 3.

# I would write this, but I would rather go outside and play in the snow!

# 4.

# My objection to this problem is similar to the last one...

# Here's how we could start to work this out.

#       1. Just go read what Wilf et al. say about this.
#       2. Using empirical data, guess the index that changes at step n.
#       3. Unroll the recursion in NEXG to find a nice description of what it's
#          doing.

# Doing any of these suggests that you can't *literally* write a non-recursive
# NEXG(w) in a way that is independent of w. That is, any non-recursive NEXG(w)
# must change itself every time it is called to remember, at a minimum, the
# parity of the index it was on.

# Anyway, I'll just leave us with the following fun snippet.

# Return the sequence of indices which change from step to step in the
# n-dimensional Gray code. (Must read-in C3.txt)
DeltaSeq := proc(n)
    local code, current, future, res:
    code := UCG(n):
    res := []:

    for k from 1 to nops(code) - 1 do
        current := code[k]:
        future := code[k + 1]:
        for j from 1 to n do
            if current[j] <> future[j] then
                res := [op(res), j]:
                break:
            fi:
        od:
    od:

    res:
end: