N Puzzle Solvability

n_puzzle_solvability

first_prob_arr =[
    [6,1,10,2],
    [7,11,4,14],
    [5,None,9,15],
    [8,12,13,3]
]

ex_prob_1 =[
    [7,1,2],
    [5,None,4],
    [8,3,6]
]

ex_prob_2 =[
    [6,1,10,2],
    [7,11,4,14],
    [5,None,9,15],
    [8,12,13,3]
]

ex_prob_3 =[
    [13,10,11,6],
    [5,7,4,8],
    [1,12,14,9],
    [3,15,2,None]
]

# random.sample(range(1,16),15)

def flatten_list(list):
    flat_list = []

    for sublist in list:
        for item in sublist:
            if item is not None:
                flat_list.append(item)
    return flat_list

def count_inversion(item,flat_list,index):
    inversion = 0
    for i in range(index,len(flat_list)):
        if( flat_list[i] < item ):
            inversion += 1

    return inversion

def get_blank_tile_row(prob_arr):
    for row,sublist in enumerate(prob_arr):
        for item in sublist:
            if item is None:
                return (len(prob_arr) - row)

def is_odd(num):
    return num%2 != 0

def is_even(num):
    return num%2 == 0

def is_solvable(prob_arr):
    dim_x = len(prob_arr[0])
    dim_y = len(prob_arr)
    dim = dim_x
    blank_tile_row = get_blank_tile_row(prob_arr)
    
    flat_list = flatten_list(prob_arr)

    inversion_map = {}
    total_inversion = 0

    for index, item in enumerate(flat_list):
        inversion = count_inversion(item,flat_list,index)
        total_inversion += inversion
        inversion_map[item] = inversion

    print("Blank tile row:",blank_tile_row);
    print("Total Inversion:",total_inversion)

    if( is_odd(dim) ):
        if( is_even(dim) ):
            print("Solvable: dimension odd, inversion even")
        else:
            print("Not Solvable: dimension odd, inversion odd")
    else:
        if is_odd(blank_tile_row) and is_even(total_inversion):
            print("Solvable: dimension even, row odd inversion even")
        elif is_even(blank_tile_row) and is_odd(total_inversion):
            print("Solvable: dimension even, row even inversion odd")
        else:
            print("Not Solvable")
    print()

import random
def get_random_prob(dim):
    up = dim*dim
    rnd = random.sample(range(0,up),up)

    new_prob = []
    row_num = 0
    for i,item in enumerate(rnd):
        row_num = i % dim
        
        if(len(new_prob) - 1 < row_num):
            new_prob.append([])

        if item is 0:
             new_prob[row_num].append(None)
        else:
             new_prob[row_num].append(item)
       
        

    return new_prob
            
        

is_solvable(first_prob_arr)
is_solvable(ex_prob_1)
is_solvable(ex_prob_2)
is_solvable(ex_prob_3)
print()

is_solvable(get_random_prob(4))

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if item is 0:

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if item == 0: