3 """Mathematical helpers."""
7 from heapq import heappop, heappush
8 from typing import List
11 class RunningMedian(object):
12 """A running median computer.
14 >>> median = RunningMedian()
15 >>> median.add_number(1)
16 >>> median.add_number(10)
17 >>> median.add_number(3)
18 >>> median.get_median()
20 >>> median.add_number(7)
21 >>> median.add_number(5)
22 >>> median.get_median()
27 self.lowers, self.highers = [], []
29 def add_number(self, number):
30 if not self.highers or number > self.highers[0]:
31 heappush(self.highers, number)
33 heappush(self.lowers, -number) # for lowers we need a max heap
37 if len(self.lowers) - len(self.highers) > 1:
38 heappush(self.highers, -heappop(self.lowers))
39 elif len(self.highers) - len(self.lowers) > 1:
40 heappush(self.lowers, -heappop(self.highers))
43 if len(self.lowers) == len(self.highers):
44 return (-self.lowers[0] + self.highers[0]) / 2
45 elif len(self.lowers) > len(self.highers):
46 return -self.lowers[0]
48 return self.highers[0]
51 def gcd_floats(a: float, b: float) -> float:
53 return gcd_floats(b, a)
58 return gcd_floats(b, a - math.floor(a / b) * b)
61 def gcd_float_sequence(lst: List[float]) -> float:
63 raise ValueError("Need at least one number")
67 gcd = gcd_floats(lst[0], lst[1])
68 for i in range(2, len(lst)):
69 gcd = gcd_floats(gcd, lst[i])
73 def truncate_float(n: float, decimals: int = 2):
75 Truncate a float to a particular number of decimals.
77 >>> truncate_float(3.1415927, 3)
81 assert 0 < decimals < 10
82 multiplier = 10**decimals
83 return int(n * multiplier) / multiplier
86 def percentage_to_multiplier(percent: float) -> float:
87 """Given a percentage (e.g. 155%), return a factor needed to scale a
88 number by that percentage.
90 >>> percentage_to_multiplier(155)
92 >>> percentage_to_multiplier(45)
94 >>> percentage_to_multiplier(-25)
98 multiplier = percent / 100
103 def multiplier_to_percent(multiplier: float) -> float:
104 """Convert a multiplicative factor into a percent change.
106 >>> multiplier_to_percent(0.75)
108 >>> multiplier_to_percent(1.0)
110 >>> multiplier_to_percent(1.99)
118 percent = 1.0 - percent
123 @functools.lru_cache(maxsize=1024, typed=True)
124 def is_prime(n: int) -> bool:
126 Returns True if n is prime and False otherwise. Obviously(?) very slow for
127 very large input numbers.
133 >>> is_prime(51602981)
137 if not isinstance(n, int):
138 raise TypeError("argument passed to is_prime is not of 'int' type")
146 # This is checked so that we can skip middle five numbers in below
148 if n % 2 == 0 or n % 3 == 0:
153 if n % i == 0 or n % (i + 2) == 0:
159 if __name__ == '__main__':