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GeneralizedColorings.py
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""" | |
Counts the number of colorings possible if n walls are colored with n colors. Also partitions the set of all colors by the number of colors used. | |
Uses itertools product function to comtrol the number of nested for loops. The itertools library | |
contains functions for creating iterators for efficient looping. | |
See: | |
https://docs.python.org/3/library/itertools.html#itertools.product | |
for detailed documentation. | |
""" | |
colors = ['a' ,'b','c','d', 'e', 'f', 'g', 'i', 'j', 'k', 'l'] | |
n = 7 | |
colorlist = [] | |
colorcount = [] | |
colorstring = '' | |
import itertools as it | |
for i in range(n): | |
colorlist.append([]) # liss of colorings | |
colorcount.append([]) # list of cardinality of colorings | |
colorstring += colors[i] # String of the n colors | |
tuples = it.product(colorstring, repeat=n) | |
all = [] | |
for i in tuples: | |
newlist = list(i) | |
all.append(newlist) | |
for k in range(n): | |
if len(set(newlist)) == k+1: | |
colorlist[k].append(newlist) | |
""" | |
if len(set(i)) == 5: | |
quadlist.append(i) | |
if len(set(i)) == 6: | |
quadlist.append(i) | |
""" | |
# Compute the number of colorings by finding the length of each list. | |
for i in range(n): | |
colorcount[i] = len(colorlist[i]) | |
for i in range(n): | |
print('\n********************************') | |
print(f"The number of colorings using {i+1} color(s) is: {colorcount[i]}") | |
print('**********************************') | |
print(f"\nTotal number of colorings: {len(all)}") | |
sum = 0 | |
for i in range(n): | |
sum +=colorcount[i] | |
print(f"Sum is {sum}") | |
""" | |
print('\n**********') | |
print('Monos') | |
print('**********') | |
print(colorlist[0]) | |
print('\n**********') | |
print('Duos') | |
print('**********') | |
print(colorlist[1]) | |
print('\n**********') | |
print('Trios') | |
print('**********') | |
print(colorlist[2]) | |
print('\n**********') | |
print('Quads') | |
print('**********') | |
print(colorlist[3]) | |
""" |
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