import math

def b(n, p, k):
    return (math.factorial(n)/(math.factorial(n-k)*math.factorial(k))*math.pow(p, k)*math.pow(1-p, n-k))

def f(n, p, k):
    x = 0
    for i in range(0, k+1):
        x += b(n, p, i)
    return x

def ls(n, p, a):
    g = int(n*p)
    while f(n, p, g) > a:
        g-=1
    print("H0: p≥" + str(p))
    print("H1: p<" + str(p))
    print("An(H0) = [" + str(g+1) + ";" + str(n) + "]")
    print("Ab(H0) = [0;" + str(g) + "]")
    print("P(Fehler 1. Art) = " + str(f(n, p, g)))
    return g

def rs(n, p, a):
    g = int(n*p)
    while f(n, p, g-1) < (1-a):
        g+=1
    print("H0: p≤" + str(p))
    print("H1: p>" + str(p))
    print("An(H0) = [0;" + str(g-1) + "]")
    print("Ab(H0) = [" + str(g) + ";" + str(n) + "]")
    print("P(Fehler 1. Art) = " + str(1-f(n, p, g-1)))
    return g

def bs(n, p, a):
    l = int(n*p)
    while f(n, p, l) > a/2:
        l-=1
    r = int(n*p)
    while f(n, p, r-1) < (1-a/2):
        r+=1
    print("H0: p=" + str(p))
    print("H1: p≠" + str(p))
    print("An(H0) = [" + str(l+1) + ";" + str(r-1) + "]")
    print("Ab(H0) = [0;" + str(l) + "] oder [" + str(r) + ";" + str(n) + "]")
    print("P(Fehler 1. Art) = " + str(1-f(n, p, r-1) + f(n, p, l)))