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126 lines
5.3 KiB
126 lines
5.3 KiB
import sys
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import argparse
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parser = argparse.ArgumentParser()
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parser.add_argument("-l", "--length", help="length of the initial string", type=int, default=5)
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parser.add_argument("output", help="file to output to", type=argparse.FileType('w'), nargs="?", default=sys.stdout)
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args = parser.parse_args()
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node_marker = 'O'
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class TreeNode:
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"""A binary tree node for the purpose of doing tree manipulations and generating tamari lattices. Not very pretty code."""
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def __init__(self,l,v,r):
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"""Arguments are: left node, payload, right node."""
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self.l = l
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self.v = v
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self.r = r
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def __str__(self):
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"""Return the string which would be parsed into this object."""
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if self.l is None or self.r is None: return str(self.v)
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return node_marker + str(self.l) + str(self.r)
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def pretty_string(self):
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"""Return a string suitable for a label."""
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if self.l is None or self.r is None: return str(self.v)
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return "(" + self.l.pretty_string() + "," + self.r.pretty_string() + ")"
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def rotate_left(self):
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if not leaf(self) and not leaf(self.r):
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self.l = TreeNode(self.l, None, self.r.l)
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self.r = self.r.r
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def rotate_right(self):
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if not leaf(self) and not leaf(self.l):
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self.r = TreeNode(self.l.r, None, self.r)
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self.l = self.l.l
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def clone(self):
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if leaf(self): return TreeNode(None, self.v, None)
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else: return TreeNode(self.l.clone(), self.v, self.r.clone())
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def count_nodes(self):
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if leaf(self): return 0
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else: return self.l.count_nodes() + self.r.count_nodes() + 1
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def do_on_nth_node(self, n, f):
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"""Call the second argument on the nth node in the tree, going depth first from left to right."""
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if leaf(self): return n
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remaining = self.l.do_on_nth_node(n,f)
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if remaining is 0: return 0
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if remaining is 1:
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f(self)
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return 0
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return self.r.do_on_nth_node(remaining-1,f)
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def __eq__(self, other):
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"""Comparison for sets. Just checks if the string representation is the same."""
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return str(self) == str(other)
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def __hash__(self):
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"""Much like __eq__, this is needed for using this in sets. This just hashes the string representation."""
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return hash(str(self))
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def nth_node_helper(root, n, f):
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"""This is so ugly. I just want to do something on the nth node and return the transformed tree! ... But it works. Note: don't extend this script ever. It should stay in its little awful box."""
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root.do_on_nth_node(n, f)
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return root
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def leaf(node):
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return node.l is None or node.r is None
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def generate_children(root):
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"""Return a set of all the trees produced by rotating left at one point in the tree that is passed in."""
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# If there are n nodes in the tree, then there are at most n places to do a rotation.
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# I didn't feel like figuring out a more direct method to generate all rotations, so I just did this:
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# Try rotating at each child node. Remove all the ones that weren't changed (that is, where it failed).
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children = set(nth_node_helper(root.clone(), i, TreeNode.rotate_left) for i in range(root.count_nodes()))
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return children - {root} # Return the children, except without the root. We don't care about the root.
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def _parse(s):
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"""Parse one token of the string passed in, and return a tuple: (the tree we parsed, the remainer that wasn't parsed).
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This function recursively calls itself, to parse the whole string. """
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if s[0] is node_marker:
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first, remainder = _parse(s[1:])
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second, secondRemainder = _parse(remainder)
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return (TreeNode(first, None, second), secondRemainder)
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return (TreeNode(None, s[0], None), s[1:])
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def parse(string):
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"""Parses a string, assuming the node marker in node_marker, and returns a TreeNode.
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This is a wrapper around _parse."""
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return _parse(string)[0]
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# The string we start with is just a slice of the alphabet, with length specified by the command line argument -l.
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root_string = "abcdefghijklmnopqrstuvwxyz"[:args.length]
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root_string = "".join( "O" + char for char in root_string )
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root_string = "".join( root_string.rsplit("O", 1) )
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# helper function for generating node labels
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label_from_node = lambda x: "{name} [label=\"{label}\"];".format(name=str(x), label=x.pretty_string())
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# Here's the root we start with!
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RootOfAllEvil = parse(root_string)
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#print(RootOfAllEvil)
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current_generation = set()
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next_generation = {RootOfAllEvil}
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edges = set()
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labels = set()
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while len(current_generation ^ next_generation): # So long as we haven't reached stability...
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# Move to look at the next generation.
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#print("current_generation: {}, next_generation: {}".format(current_generation, next_generation))
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current_generation = next_generation
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# Clear out the next generation so that we can fill it with the children of the now-current generation.
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next_generation = set()
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#print("current_generation: {}, next_generation: {}".format(current_generation, next_generation))
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labels = labels | set(label_from_node(parent) for parent in current_generation)
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for parent in current_generation:
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children = generate_children(parent)
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#print("children of {parent}: {children}".format(parent=parent, children=children))
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labels = labels | set(label_from_node(child) for child in children)
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edges = edges | set(str(parent) + " -> " + str(child) + ";" for child in children)
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next_generation = next_generation | children
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args.output.write(u"digraph tamari {\n")
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args.output.write(u"\n".join(labels) + "\n")
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args.output.write(u"\n".join(edges))
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args.output.write(u"\n}\n")
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