"Graph the progression towards Kaprekar's constant"
from collections import Counter
class Cache(dict):
'Single variable caching decorator, accessible as a dictionary'
def __init__(self, func):
self.func = func
__call__ = dict.__getitem__
def __missing__(self, key):
result = self[key] = self.func(key)
return result
@Cache
def step(n):
'Do a single step in the Kaprekar process'
# http://en.wikipedia.org/wiki/6174_(number)
s = format(n, '04d') # 1253 --> '1253'
t = ''.join(sorted(s)) # '1253' --> '1235'
u = t[::-1] # '1235' --> '5321'
return int(u) - int(t) # (5321 - 1235) --> 4086
main_template = '''
digraph kaprekar {
rankdir=LR;
%s
%s
}
'''
node_template = ' "%s" [label="%s: %s"];\n'
pair_template = ' "%s" -> "%s";\n'
def make_graph(show_counts=True):
'Generate a dot file'
# python analyze_6174.py | dot -Tpng > a6174.png && open a6174.png
for i in range(10000):
step(i)
outs = Counter(step.values()) # only show destination nodes
nodes = []
if show_counts:
nodes = [node_template % (i, c, i) for i, c in outs.items()]
results = results = [pair_template % (i, step(i)) for i in outs]
return main_template % (''.join(nodes), ''.join(results))
if __name__ == '__main__':
print make_graph(show_counts=True)
