surprising-challenge-generating-comprehensive-python-list.py

from itertools import permutations, combinations_with_replacement

_profiling = True  # profiling toggle

if _profiling:
    from cProfile import Profile
    from pstats import Stats
    prof = Profile()
    prof.disable()

def join_adjacent_repeated_materials(potential_structure):
    """
    Self-explanitory...
    """
    #print potential_structure

    new_layers = [] # List to hold re-cast structure
    for layer in potential_structure:
        if len(new_layers) > 0: # if not the first item in the list of layers
            last_layer=new_layers[-1] # last element of existing layer list
            if layer[0] == last_layer[0]: # true is the two layers are the same material
                combined_layer = (layer[0], layer[1] + last_layer[1])
                new_layers[len(new_layers)-1] = combined_layer
            else: # adjcent layers are different material so no comibantion is possible
                new_layers.append(layer)
        else: # for the first layer
            new_layers.append(layer)

    return tuple(new_layers)

def calculate_unique_structure_lengths(thicknesses, materials, maximum_number_of_layers,\
                                       maximum_individual_layer_thicknesses, \
                                       maximum_total_material_thicknesses):
    """
    Create a set on all possible multilayer combinations.

    thicknesses : if this contains '0' the total number of layers will vary
                  from 0 to maximum_number_of_layers, otherwise, the
                  number total number layers will always be maximum_number_of_layers
                  e.g. arange(0 , 100, 5)

    materials : list of materials used
                e.g. ['Metal', 'Dielectric']

    maximum_number_of_layers : pretty self-explanitory...
                               e.g. 5

    maximum_individual_layer_thicknesses : filters the created the multilayer structures
                                           preventing the inclusion layers that are too thick
                                           - this is important after the joining of
                                           adjacent materials
                                           e.g. (('Metal',30),('Dielectric',20))

    maximum_total_material_thicknesses : similar to the above but filters structures where the total
                                         amount of a particular material is exceeded
                                         e.g. (('Metal',50),('Dielectric',100))


    """
    # generate all possible thickness combinations and material combinations
    all_possible_thickness_sets = set(permutations(combinations_with_replacement(thicknesses, maximum_number_of_layers)))
    all_possible_layer_material_orders = set(permutations(combinations_with_replacement(materials, maximum_number_of_layers)))


    first_set = set() # Create set object (list of unique elements, no repeats)
    for layer_material_order in all_possible_layer_material_orders:
        for layer_thickness_set in all_possible_thickness_sets:
            potential_structure = [] # list to hold this structure
            for layer, thickness in zip(layer_material_order[0], layer_thickness_set[0]): # combine the layer thickness with its material
                if thickness != 0: # layers of zero thickness are not added to potential_structure
                    potential_structure.append((layer, thickness))
            first_set.add(tuple(potential_structure)) # add this potential_structure to the first_set set

    #print('first_set')
    #for struct in first_set:
    #    print struct

    ## join adjacent repeated materials
    second_set = set() # create new set
    for potential_structure in first_set:
        second_set.add(join_adjacent_repeated_materials(potential_structure))

    ## remove structures where a layer is too thick
    third_set = set()
    for potential_structure in second_set: # check all the structures in the set
        conditions_satisfied=True # default
        for max_condition in maximum_individual_layer_thicknesses: # check this structure using each condition
            for layer in potential_structure: # examine each layer
                if layer[0] == max_condition[0]: # match condition with material
                    if layer[1] > max_condition[1]: # test thickness condition
                        conditions_satisfied=False
        if conditions_satisfied:
            third_set.add(potential_structure)

    ##remove structures that contain too much of a certain material
    fourth_set = set()
    for potential_structure in second_set: # check all the structures in the set
        conditions_satisfied=True # default
        for max_condition in maximum_total_material_thicknesses: # check this structure using each condition
            amount_of_material_in_this_structure = 0 # initialise a counter
            for layer in potential_structure: # examine each layer
                if layer[0] == max_condition[0]: # match condition with material
                    amount_of_material_in_this_structure += layer[1]
                    if amount_of_material_in_this_structure > max_condition[1]: # test thickness condition
                        conditions_satisfied=False
        if conditions_satisfied:
            fourth_set.add(potential_structure)

    return fourth_set

thicknesses = [0,1,2]
materials = ('A', 'B') # Tuple cannot be accidentally appended to later
maximum_number_of_layers = 3
maximum_individual_layer_thicknesses=(('A',30),('B',20))
maximum_total_material_thicknesses=(('A',20),('B',15))

if _profiling:
    prof.enable()

calculate_unique_structure_lengths(thicknesses, materials, maximum_number_of_layers,\
                                   maximum_individual_layer_thicknesses = maximum_individual_layer_thicknesses, \
                                   maximum_total_material_thicknesses = maximum_total_material_thicknesses)

if _profiling:
    prof.disable()
    prof.dump_stats('unique.stats')
    with open('unique_stats.txt', 'wt') as output:
        stats = Stats('unique.stats', stream=output)
        stats.strip_dirs().sort_stats('cumulative', 'time')
        stats.sort_stats('cumulative', 'time')
        stats.print_stats()