"""
Schreibe einen genetischen Algorithmus, der die Parameter
(a,b,c,d) der Funktion f (x ) = ax 3 + bx 2 + cx + d so optimiert,
dass damit die Funktion g(x ) = e x im Bereich [-1..1] möglichst
gut angenähert wird. Nutze dazu den quadratischen Fehler (oder
alternativ die Fläche zwischen der e-Funktion und dem Polynom).
Zeichne die Lösung und vergleiche die Koeffizienten mit denen der
Taylor-Reihe um 0.
"""

import numpy as np
import random
import time
import utils

POPULATION_SIZE = 10
SELECTION_SIZE = (POPULATION_SIZE * 7) // 10  # 70% of population, rounded down for selection
XOVER_PAIR_SIZE = (POPULATION_SIZE - SELECTION_SIZE)
XOVER_POINT = 3 # 4th position
MUTATION_BITS = POPULATION_SIZE // 2

fitness = 2
fitness_arr = [0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1]
gray_pop = [] # 32 Bit-Binary as String 
bin_pop = [] # 32 Bit-Binary as String
bin_pop_params = [] # Arrays with 4 Binary values of 8s
new_pop = [] # 32 Bit Gray-Code as String

def generate_random_population(num=POPULATION_SIZE):
    """ Puts random 32 Bit binary strings into 4 * 8 Bit long params. """
        
    # Generate new population
    for _ in range(num):
        gray = format(random.getrandbits(32), '032b')
        gray_pop.append(gray)
        
        bin_str = utils.gray_to_bin(gray)
        bin_pop.append(bin_str)
        
        params = [bin_str[i:i+7] for i in range(0, 31, 8)]
        bin_pop_params.append(params)

    return bin_pop_params

def quadratic_error(original_fn, approx_fn, n):
    error = 0.0
    
    for i in range(-(n // 2), (n // 2) + 1):
        error += (original_fn(i) - approx_fn(i))**2
        
    return error

def eval_fitness(bin_pop_values):
    """ Returns an array with fitness value of every individual in a population. """
    fitness_arr = []
    for params in bin_pop_values:
        # Convert binary string to parameters for bin_values
        a, b, c, d = [utils.bin_to_param(param) for param in params] # assign params to batch of population
        
        # Create polynomial function with current parameters
        approx = lambda x: a*x**3 + b*x**2 + c*x + d
        e_func = lambda x: np.e**x
        quad_error = quadratic_error(e_func, approx, 3) # the bigger the error, the worse the fitness
        
        inverse_fitness = 1 / quad_error # using inverse to find small errors easier
        inverse_fitness = round(inverse_fitness, 2)
        print("Fitness: " + str(inverse_fitness)) # debugging
        fitness_arr.append(inverse_fitness) # save fitness
        
    return fitness_arr

def select(fitness_arr):
    gray_pop_copy = gray_pop.copy() # copy of population
    fitness_arr_copy = fitness_arr.copy() # copy of fitness array
    selected_pop = []
    
    while len(selected_pop) < SELECTION_SIZE:
        sum_of_fitness = sum(fitness_arr_copy)
        if sum_of_fitness == 0:
            break
            
        # Roulette logic
        roulette_num = random.random()
        cumulative_p = 0
        
        for i, fitness in enumerate(fitness_arr_copy):
            cumulative_p += fitness / sum_of_fitness
            if roulette_num < cumulative_p:
                # Add the selected individual
                selected_pop.append(gray_pop_copy[i])
                
                # Remove selected individual and their fitness
                gray_pop_copy.pop(i)
                fitness_arr_copy.pop(i)
                break
    return selected_pop
     
def xover(population):
    """Performs crossover on pairs of individuals from population."""
    offspring = []
    
    # Randomly shuffle the population to avoid bias
    population_copy = population.copy()
    random.shuffle(population_copy)
    
    # Process pairs
    i = 0
    while i < XOVER_PAIR_SIZE:
            
        parent_a = population_copy[i]
        parent_b = population_copy[i + 1]
        
        # Create two new offspring by swapping parts at random xover point
        offspring_a = parent_a[:XOVER_POINT] + parent_b[XOVER_POINT:]
        offspring_b = parent_b[:XOVER_POINT] + parent_a[XOVER_POINT:]
        
        offspring.extend([offspring_a, offspring_b])
        i += 2  # Move to next pair
        
    if len(offspring) > XOVER_PAIR_SIZE:
        offspring = offspring[:XOVER_PAIR_SIZE]
        
    return offspring

def mutate(population, mutation_rate):
    """Mutate random bits in the population with given mutation rate"""
    for _ in range(mutation_rate):
        # Select random individual and convert to list for efficient modification
        random_num = random.randrange(POPULATION_SIZE)
        bits = list(population[random_num])
        
        # Flip random bit
        bit_pos = random.randrange(32)
        bits[bit_pos] = '1' if bits[bit_pos] == '0' else '0'
        
        # Convert back to string and update population
        population[random_num] = ''.join(bits) # will work because lists are passed by reference

bin_pop_values = generate_random_population(POPULATION_SIZE)

print("Working...")
iteration = 0 # debugging
while not np.any((np.array(fitness_arr)) > 200):  # Continue while any fitness value is > 1
    print("\nIteration: " + str(iteration)) # debugging
    
    # Evaluate fitness
    fitness_arr = eval_fitness(bin_pop_values)
            
    # Selection        
    new_pop = select(fitness_arr) # assigns
            
    # Crossover        
    offspring = xover(gray_pop)
    new_pop.extend(offspring)  # Add offspring to population
    
    # Mutation
    mutate(new_pop, MUTATION_BITS)
    
    # Update populations for next generation
    gray_pop = new_pop.copy()
    bin_pop_values = []
    for gray_bin_string in gray_pop:
        bin_str = utils.gray_to_bin(gray_bin_string)
        params = [bin_str[i:i+7] for i in range(0, 31, 8)]
        bin_pop_values.append(params)
    
    # time.sleep(0.5) # debugging
    iteration += 1 # debugging

max_fitness_index = np.argmax(np.array(fitness_arr))
a, b, c, d = [utils.bin_to_param(param) for param in bin_pop_values[max_fitness_index]]

print("Chosen value: " + str(fitness_arr[max_fitness_index])) # debugging
print("at index: " + str(max_fitness_index)) # debugging
print("a: " + str(a) + "; b: " + str(b) + "; c: " + str(c) + "; d: " + str(d) )

utils.plot_graph(a, b, c, d)