Script for calculating spotify's discover weekly probabilities

spot.py

from __future__ import print_function, division
import itertools, sys, time

# simple factorial function
def fact(n, acc=1):
    return acc if n == 0 else fact(n - 1, n * acc)

# binomial coefficient
def newton(n, k):
    return 0 if k > n else fact(n) / (fact(k) * fact(n - k))

# our function!
def discover_weekly_prob(n, x, y):
    if x * y < n:
        return 0
    sigma_sum = sum([((-1)**(i - 1)) * newton(n, i) * (((newton((n - i), y) 
        * fact(y) * fact(n - y)) / (fact(n)))**x) for i in range(1, n - y + 1)])
    return 1 - sigma_sum

def filter_heads(p, head):
# This function flattens a tuple of tuples into list of gotten heads
# filter_heads(((1,4,2,3), (3,1,2,4)), 2) => [1,4,3,1]
    return [y for x in p for y in x[:head]]

def brute_prob(n, x, y):
    # all possible permutations of our initial set
    permuts = [p for p in itertools.permutations(range(n))]
    # list of every possible outcome of our experiment. Shrinked to y-long heads.
    space = [filter_heads(prdct, y) for prdct in itertools.product(permuts, repeat=x)]
    # the number of outcomes in which we got all elements of our initial set
    good = sum([1 for outcome in space if len(set(outcome)) == n])
    return (good / len(space))

def tests(n=5):
    for x in range(1, n+1):
        for h in range(1, n):
            for t in range(1, 4):
                w = brute_prob(x, t, h)
                # if w>0:
                    # print('for n:{} x:{} y:{} prob is {}'.format(x,t,h,w))
                assert (abs(w - discover_weekly_prob(x,t,h)) < 0.01)
    print('--tests passed--')


def best_ratio(sngtme=5, hours=7, scale=1, prnt=False, tmlimit=False):
    TIME_LIMIT = hours*60/sngtme
    res = []
    data_dict = {'x':[], 'y':[], 'ratio':[]}  # dict used for creating a scatter plot
    for x in range(1,31):
        for y in range(1,31):
            prob = discover_weekly_prob(30, x, y)
            filtered_prob = 0 if prob <= 0.5 else prob
            if tmlimit:
                if prob == 0 or (x*y > TIME_LIMIT):
                    continue
            ratio = (30*scale*filtered_prob) / (y * x)
            res.append((ratio,x,y))
            data_dict['x'].append(x)
            data_dict['y'].append(y)
            rt_to_add = ratio*2 if ratio!=1 else ratio+0.1  # scaling for scatter plot
            data_dict['ratio'].append(rt_to_add)
    res.sort(reverse=True)
    if prnt:
        for x in res:
            print('y: {} x: {} ratio: {:.6}'.format(x[2],x[1], x[0]))
    return res, data_dict

if __name__ == "__main__":
    # tests()
    try:
        assert len(sys.argv)==4
        n, x, y = int(sys.argv[1]), int(sys.argv[2]), int(sys.argv[3])
        res = discover_weekly_prob(n,x,y)
        ratio = (30*res) / (y * x)
        print('With n={}, x={} & y={}\nThe probability of listening to every song is ~{:.0%}\nProbability/time ratio is {:.4}'.format(n,x,y,res,ratio))
    except Exception as e:
        print("Something went wrong...")
        if len(sys.argv)!=4:
            print("It looks like you haven't passed three arguments!")
        elif y>n:
            print('y cannot be bigger then n!')
        else:
            print('Your error is: ', e)
        print('Correct syntax looks like this: "python spot.py 30 14 5"')

For context see my post.

USAGE

You need to have Python installed. Both 2.7+ and 3+ versions are supported.

If you are on mac - don't worry you should have Python 2.7 already installed. Otherwise - read this.

Once you have Python installed, download the above file. Then open Terminal and go to the folder where you saved the file.

Example for mac users:

If you downloaded the file to your "Downloads" folder, you should simply type cd ~/Downloads in Terminal and you should be good to go.

Once you're there you just run the script and pass the values for n, x and y by typing for example:

python spot.py 30 14 6

this will print the probability for n=30 x=14 and y=6 as well as it's ratio measure.

Have fun! :)