tkmharris

# frozen_string_literal: true

# Lock Problem
#   * We're given a 4-digit combination lock and a known correct unlock code.
#   * The allowed moves are to rotate any dial, or any two, three or four
#     adjacent dials by one place in either direction.
#   * We're looking for an efficient algorithm that returns the least number
#     of "moves" required to get to the unlock code. We'd also like the path.
#   * e.g.
#     - It takes 5 moves to get from [1,2,3,4] to [6,6,6,6].

tkmharris

"""
Script to generate the (integer) vertices of Loday's realisation
of the n-associahedron in (n-1)-dimensional associahedron 
as calculated using planar binary trees in:
https://arxiv.org/abs/math/0212126
(Realisation of the Stasheff Polytope)

Loday construction is as follows:
- each planar binary tree has a canonical "left to right" labelling of its internal nodes
- given a planar binary tree so labelled, Loday prescribes a rule for generating a vector (of integers)

tkmharris

{-- Haskell function for getting the Bell numbers via the Bell triangle --}

{-- Bell number B_n is the number of partitions of {1,...,n} into nonempty subsets.
    
    The Bell triangle A_{i,j}, 0<=j<=i is defined as follows:
    1. A_{0,0} = 1
    2. A_{i+1,0} = A_{i,i}
    3. A_{i+1,j+1} = A_{i+1,j} + A_{i,j}
    The Bell numbers can then be read off as B_n = A_{n,0}
    

tkmharris

"""
Function to calculate terms of the order of the torsion part of the algebraic K-theory of the integers.
"""
from sympy import bernoulli

def a345267(n):
	"""
	Calculate the terms of OEIS entry A345267.
	(Order of the image of the torsion part of the algebraib K-theory of the integers.).
	

tkmharris

"""
Function to calculate terms of the order of the image of the J-homomorphism.
"""
from sympy import bernoulli

def a345262(n):
	"""
    Calculate the terms of OEIS entry A345262.
    (Order of the image of the J-homomorphism in the stable homotopy group π_n^S).
    

tkmharris

"""
Function to calculate terms of OEIS sequence A345225.
"""

def a345225(n):
	"""
    Calculate OEIS entry A345225(n)
    (Orders of 2-primary subgroups of K_n(Z), the algebraic K-theory of the integers.)
    
    n: int, >=0

tkmharris

"""
Function to calculate terms of OEIS sequence A345209.
"""

from sympy import primefactors

def a345209(n):
    """
    Calculate OEIS entry A345209(n)
    (Number of Petrie polygons on regular triangular map corresponding to the principal congruence subgroup Γ(n) of the mmodular group)

tkmharris

# coding: utf8

import random

class OutOfTimeError(Exception):
    """Raised when game passes maximum number of turns"""
    pass

class Player:

tkmharris

"""
Quick implementation of the two trees for partitions discussed here:
https://11011110.github.io/blog/2005/08/07/two-trees-on.html
"""

from treelib import Node, Tree

# partition class

class InvalidPartitionError(Exception):

tkmharris