Counting Unique Paths in an Array with Special Rules

Question

Description of the Problem: I have an array of two-digit numbers going from 00 to 99. I must choose a number at random anywhere in the array; let's call this result r. I may now take up to n steps within the array to "travel" to another number in the array, according to the following rules:

1. Adding or subtracting 1 from r takes one (1) step; I cannot add 1 if there is a 9 in the ones place (ex: 09, 19, 29, ...) and I cannot subtract 1 if there is a 0 in the ones place (ex: 00, 10, 20, ...)

2. Adding or subtracting 10 from r takes one (1) step; I cannot bring the result to lower than 00 or higher than 99.

3. By taking two (2) steps, I can swap the digits in the ones and tens place (ex: 13 -> 31, 72 -> 27); however, I can't perform the swap if the digits are the same (ex: can't swap 00, 11, 22, ...)

For a given number x (00 <= x <= 99) I want to count the set of unique values of r from which I can travel to x, given that I can take between 0 and n steps. I call this count how "accessible" x is. I'd like to express this as a formula, A(x, n), rather than just brute-forcing the results for each combination of x and n.

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What I Have Tried: A(x, 0) is easy enough to calculate: A(x, 0) = 1 for all values in the array, because the only way to reach x from r is for r = x; I take zero (0) steps to reach it. A(x, 1) is trickier, but still simple: you just take into account the new paths available if I spend my one step on either Rule #1 or Rule #2, and add them to A(x, 0). A(x, 2) is where I have to start including Rule #3, but also includes the problem of backtracking. For instance, if I want to reach x and x = r, and I have two (2) steps available, I could perform the following operation: Step 1, r -> r' = r+1 (Rule #1); Step 2, r' -> r'' = r'-1 (Rule #1); r'' = x AND r'' = r. This does not add to my count of unique values from which I can travel to x from.

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Where I am Stuck: I cannot figure out how to count the number of backtracking paths in order to remove them from the otherwise simple calculations of A(x, n), so my values of accessibility are coming out too high.

Answer 1

You can use helper attributes

To remove all fields label you can set form_show_labels to False in the init() method. By default it is set to True.

from crispy_forms.helper import FormHelper

class ExampleForm(forms.Form):
    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.helper = FormHelper(self)
        self.helper.form_show_labels = False

To remove field label for certain specific field you can use

self.fields['your_field_name'].label = False