# Creating the table of 4-element permutations and all the inversion related vectors in
# https://en.wikiversity.org/wiki/Inversion_(discrete_mathematics)#Example:_All_permutations_of_four_elements

from itertools import permutations


def based_0_or_1(perm):
    # returns 0 if the permutation is 0-based and 1 if it is 1-based
    length = len(perm)
    if sorted(perm) == list(range(length)):
        return 0
    elif sorted(perm) == list(range(1, length+1)):
        return 1
    else:
        print('Input is no 0-based or 1-based permutation.')


def zeroify(perm):
    # returns a 0-based permutation
    base = based_0_or_1(perm)
    if base == 0:
        return perm
    if base == 1:
        return [i-1 for i in perm]


def l_inv_count(perm):
    length = len(perm)
    result = [0] * length
    for i in range(length):
        count = 0
        for k in range(i):
            if perm[k] > perm[i]:
                count += 1
        result[i] = count
    return result


def r_inv_count(perm):
    length = len(perm)
    result = [0] * length
    for i in range(length):
        count = 0
        for k in range(i+1, length):
            if perm[k] < perm[i]:
                count += 1
        result[i] = count
    return result


def inv_vect(perm_in):
    perm = zeroify(perm_in)
    length = len(perm)
    result = [0] * length
    for i in range(length):
        count = 0
        for k in range(i):
            if perm[k] > perm[i]:
                count += 1
        result[perm[i]] = count
    return result


def l2s(l):
    # turns [1, 2, 3] to '123'
    s = ''
    for e in l:
        s += str(e)
    return s


inv = [0, 1, 2, 4, 3, 5, 6, 7, 12, 18, 13, 19, 8, 10, 14, 20, 16, 22, 9, 11, 15, 21, 17, 23]


perms_iter = permutations([1, 2, 3, 4])
perms_dict = {}

for i, perm in enumerate(perms_iter):
    perms_dict[23-i] = perm[::-1]  # create reverse colexicographic order


def c(abbrs):
    # turns c('rs') to ' ||style="color:red;font-size:50%;"| '
    abbr_to_code = {
        'b': 'font-weight:bold;',
        'x': 'font-size:40%;',
        's': 'font-size:50%;',
        'l': 'font-size:110%;',
        't': 'border-left:3px solid darkgray;',
        'r': 'color:red;'
    }
    res = ' ||style="'
    for abbr in abbrs:
        res += abbr_to_code[abbr]
    res += '"| '
    return res


table = ''
for i in range(24):
    perm = perms_dict[i]
    p = l2s(perm)
    l = l2s(l_inv_count(perm)[1:])
    r = l2s(r_inv_count(perm)[:-1])
    v = l2s(inv_vect(perm)[:-1])
    invnum = str(sum(inv_vect(perm)))

    if i in [1, 2, 5, 6, 14, 21]:
        numcolor = '33eb2a'  # green
    elif i in [9, 10, 13, 17, 18, 22]:
        numcolor = 'ffbb00'  # orange
    else:
        numcolor = 'ffffff'  # white

    if i in [0, 7, 16, 23]:
        numweight = 'font-weight:bold;'
    else:
        numweight = ''

    start = '\n|- style="height:38px"\n|style="font-size:110%;background-color:#' + numcolor + ';' + numweight \
            + 'letter-spacing:0;"| ' + str(i) \
            + ' || [[File:4-el perm matrix ' + str(i).zfill(2) + '.svg|30px]]'

    z = '<span style="opacity: .3;">0</span>'

    row = start \
          + c('b') + p + c('bx') + p[::-1] \
          + c('t') + '[[File:4-el perm invset ' + str(inv[i]).zfill(2) + '.svg|55px]]' \
          + c('tr') + v+z + c('rs') + z+v[::-1] \
          + c('trs') + l[::-1]+z + c('r') + z+l \
          + c('t') + '[[File:4-el perm invset ' + str(i).zfill(2) + '.svg|55px]]' \
          + c('tr') + r+z + c('rs') + z+r[::-1] \
          + c('trl') + invnum

    table += row

print(table)