The function to calculate A(n,i) for the video https://www.youtube.com/watch?v=sjcle2vIueU

A.py

def A(n,i):
    # calculate using a simulation approach.
    i = i-1 # convert to 0-based index.
    urinals = np.zeros(n)
    urinals[i] = 1 # the ith is occupied.
    while True:
        # find the furtherest urinal that is away from any occupied urinal.
        candidates = {} # key: the index of the urinal, value: the distance to the nearest occupied urinal.
        for j in range(n):
            if urinals[j] == 1:
                continue
            else:
                left_distance = 0 if j != 0 else np.inf
                right_distance = 0 if j != n-1 else np.inf
                for k in range(j-1,-1,-1):
                    if urinals[k] == 1:
                        break
                    elif k == 0:
                        left_distance = np.inf
                    else:
                        left_distance += 1
                for k in range(j+1,n):
                    if urinals[k] == 1:
                        break
                    elif k == n-1:
                        right_distance = np.inf
                    else:
                        right_distance += 1
                candidates[j] = min(left_distance,right_distance) 
        # keep only non-zero distance urinals
        candidates = {key:value for key,value in candidates.items() if value != 0}
        if len(candidates) == 0:
            break
        else:
            max_distance = max(candidates.values())
            # randomize the choice if there are multiple urinals with the same distance.
            max_keys = [key for key,value in candidates.items() if value == max_distance]
            # print(max_keys)
            idx = np.random.choice(max_keys)
            urinals[idx] = 1
    return urinals.sum()