manvillej

>>>transitionMatrix = np.matrix([
...     [0, 1, 1, 0],
...     [2, 0, 0, 0],
...     [2, 0, 0, 1],
...     [0, 0, 2, 0]], dtype=object)

manvillej

def getMatrix(matrix, turns):
    """
    returns a matrix represents the number of unique paths starting in one position and ending in another in N turns
    """

    # get an array of the binary powers we need to calculate
    baseTwoArray = getArrayOfPowersOfTwos(turns)

    # start with an identity matrix
    resultMatrix = np.identity(matrix.shape[0], dtype=object)

manvillej

def getArrayOfPowersOfTwos(number):
    """
    breaks an integer into an array of numbers that represent the number as a series of 2 to a power in order from lowest to highest.
    for example: 9 = 2**0 + 2**3. 
    >>> getArrayOfPowerssOfTwos(9)
    [0, 3]

    """
    array = list()

manvillej

import numpy as np
import math
from functools import lru_cache

@lru_cache(maxsize=None) # for memoization
def getMatrix(turns):
    """
    returns a matrix represents the number of unique paths starting in one position and ending in another in N turns
    """

manvillej

startingVector0 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
startingVector1 = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
startingVector2 = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
startingVector3 = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
startingVector4 = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
startingVector5 = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
startingVector6 = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
startingVector7 = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
startingVector8 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
startingVector9 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]

manvillej

import numpy as np

def getPossibilities(startingPosition, turns):
    """
    Calculates the total number of uniques paths from the starting position in N turns for the transition matrix
    """
    
    # edgecase: 0 turns, return 1
    if turns == 0:
        return 1

manvillej

def getArrayOfMultiplesOfTwos(number):
    """
    breaks an integer into an array of numbers that represent the number as a series of 2 to a power in order from lowest to highest.
    for example: 9 = 2**0 + 2**3. 
    >>> getArrayOfMultiplesOfTwos(9)
    [0, 3]

    """
    array = list()

manvillej

def getMatrix(matrix, turns):
    """
    returns a matrix equal to the original matrix multiplied by itself a number of times equal to the number of turns minus one
    """

    if turns==1:
        return matrix

    else:
        turnsBaseTwo = math.log(turns, 2)

manvillej

def getBaseTwoTurnsMatrix(matrix, baseTwoTurns):
    """
    use this function to calculate the resulting matrix from raising matrix to the 2^baseTwoTurns power.
    """

    for _ in range(baseTwoTurns):
        matrix = matrix*matrix
    return matrix

manvillej

def getMatrix(matrix, turns):
    """
    returns a matrix equal to the original matrix multiplied by itself a number of times euqal to the number of turns minus one
    """
    if turns==1:
        return matrix

    else:
        turnsBaseTwo = math.log(turns, 2)