dog_walking.py

n_dogs = 1
n_walkers = 1

dogs = []
# ------


def entrypoint():
    groups = [((float('-inf'), float('inf')), 0) for w in range(n_walkers)]
    valid, r = helper(groups, float('inf'))
    
def is_group_valid(groups):
    for (max_dog, min_dog), cnt in groups:
        if cnt == 0:
            return False
    return True

def helper(groups, best_range):
    v = is_group_valid(groups)
    if len(dogs) == 0:
        return v, best_range
    
    r = 0
    for (max_dog, min_dog), cnt in groups:
        if cnt < 2:
            continue
        r += max_dog - min_dog
        
    if v and r >= best_range:
        return v, best_range
    
    dogs_left = len(dogs)
    for _ in range(0, dogs_left):
        for g_idx in range(n_walkers):
            d = dogs.pop()
            (max_dog, min_dog), count = groups[g_idx]
            groups[g_idx] = (max(max_dog, d), min(min_dog, d)), count+1
            
            _v, _r = helper(groups, best_range)
            if _v:
                v = True
                best_range = max(best_range, _r)
            
            groups[g_idx] = (max_dog, min_dog), count
            dogs.append(d)
            
    return v, best_range