def romanCode(i) :
"""
Determine possibilities for a string of 'I's.
Parameters:
i - Number of 'I's.
Returns:
Set of possibilities, where each possibility is a set.
"""
#Nothing left!
if i == 0 :
return([[]])
#Ends in I.
elif i == 1 :
return([[1]])
#Ends in II.
elif i == 2 :
return([[1, 1], [2]])
#Ends in III.
elif i == 3 :
return([[1, 1, 1], [1, 2], [2, 1], [3]])
#RECURSIVE!
#If ending in IIII or more, 1, 2, or 3 could be the next digit before looking at the remaining right numerals.
else :
P = []
#..., 1, ...
for j in romanCode(i-1) :
P.append([1]+j)
#..., 2, ...
for l in romanCode(i-2) :
P.append([2]+l)
#..., 3, ...
for k in romanCode(i-3) :
P.append([3]+k)
return(P)
def romanCodeEC(S) :
"""
Determine possibilities for string of 'I's and 'V's.
Parameters:
i - Number of 'I's.
Returns:
Set of possibilities, where each possibility is a set.
"""
#Nothing left!
if S == '' :
return([[]])
#Ends in I.
elif S == 'I' :
return([[1]])
#Ends in II.
elif S == 'II' :
return([[1, 1],
[2]])
#Ends in III.
elif S == 'III' :
return([[1, 1, 1], [1, 2],
[2, 1],
[3]])
#Ends in IV.
elif S == 'IV' :
return([[1, 5], [4]])
#Ends in V.
elif S == 'V' :
return([[5]])
#Ends in VI.
elif S == 'VI' :
return([[5, 1],
[6]])
#Ends in VII.
elif S == 'VII' :
return([[5, 1, 1], [5, 2],
[6, 1],
[7]])
elif S == 'VIII' :
return([[5, 1, 1, 1], [5, 1, 2], [5, 2, 1], [5, 3],
[6, 1, 1], [6, 2],
[7, 1],
[8]])
#RECURSIVE!
#If ending in IIII or more, 1, 2, or 3 could be the next digit before looking at the remaining right numerals.
else :
P = []
#..., 1, ...
if S[0] == 'I' :
for j in romanCodeEC(S[1:]) :
P.append([1] + j)
#..., 2, ...
if S[0:2] == 'II' :
for j in romanCodeEC(S[2:]) :
P.append([2] + j)
#..., 3, ...
if S[0:3] == 'III' :
for j in romanCodeEC(S[3:]) :
P.append([3] + j)
#..., 4, ...
if S[0:2] == 'IV' :
for j in romanCodeEC(S[2:]) :
P.append([4] + j)
#..., 5, ...
if S[0] == 'V' :
for j in romanCodeEC(S[1:]) :
P.append([5] + j)
#..., 6, ...
if S[0:2] == 'VI' :
for j in romanCodeEC(S[2:]) :
P.append([6] + j)
#..., 7, ...
if S[0:3] == 'VII' :
for j in romanCodeEC(S[3:]) :
P.append([7] + j)
#..., 8, ...
if S[0:4] == 'VIII' :
for j in romanCodeEC(S[4:]) :
P.append([8] + j)
return(P)
def createDist(L) :
"""
Create distribution frequency
Parameters:
L - List of lists.
Returns:
Dictionary with keys that are length, frequency is values.
"""
dist = {}
for l in L :
n = len(l)
if n in dist.keys() :
dist[n] += 1
else :
dist[n] = 1
return(dist)
createDist(romanCode(10))
{10: 1, 9: 9, 8: 36, 7: 77, 6: 90, 5: 51, 4: 10}
len(romanCode(10))
274
createDist(romanCodeEC('IIIVIIIVIIIVIII'))
{15: 1,
14: 14,
13: 85,
12: 295,
11: 650,
10: 955,
9: 955,
8: 650,
7: 295,
6: 85,
5: 14,
4: 1}
len(romanCodeEC('IIIVIIIVIIIVIII'))
4000
for code in ['IVI', 'IVIVI', 'IVIVIVI', 'IVIVIVIVI',
'IVVI', 'IVVIVVI', 'IVVIVVIVVI', 'IVVIVVIVVIVVI',
'IIVII', 'IIVIIVII', 'IIVIIVIIVII', 'IIVIIVIIVIIVII',
'IIVVII', 'IIVVIIVVII', 'IIVVIIVVIIVVII', 'IIVVIIVVIIVVIIVVII',
'IIIVIII', 'IIIVIIIVIII', 'IIIVIIIVIIIVIII', 'IIIVIIIVIIIVIIIVIII'] :
print('<b>' + code + '</b> has ' + str(len(romanCodeEC(code))) + ' combinations.')
<b>IVI</b> has 3 combinations. <b>IVIVI</b> has 8 combinations. <b>IVIVIVI</b> has 21 combinations. <b>IVIVIVIVI</b> has 55 combinations. <b>IVVI</b> has 4 combinations. <b>IVVIVVI</b> has 12 combinations. <b>IVVIVVIVVI</b> has 36 combinations. <b>IVVIVVIVVIVVI</b> has 108 combinations. <b>IIVII</b> has 10 combinations. <b>IIVIIVII</b> has 50 combinations. <b>IIVIIVIIVII</b> has 250 combinations. <b>IIVIIVIIVIIVII</b> has 1250 combinations. <b>IIVVII</b> has 12 combinations. <b>IIVVIIVVII</b> has 72 combinations. <b>IIVVIIVVIIVVII</b> has 432 combinations. <b>IIVVIIVVIIVVIIVVII</b> has 2592 combinations. <b>IIIVIII</b> has 40 combinations. <b>IIIVIIIVIII</b> has 400 combinations. <b>IIIVIIIVIIIVIII</b> has 4000 combinations. <b>IIIVIIIVIIIVIIIVIII</b> has 40000 combinations.