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 = [], []
30 def add_number(self, number: float):
31 if not self.highers or number > self.highers[0]:
32 heappush(self.highers, number)
34 heappush(self.lowers, -number) # for lowers we need a max heap
35 self.aggregate += number
39 if len(self.lowers) - len(self.highers) > 1:
40 heappush(self.highers, -heappop(self.lowers))
41 elif len(self.highers) - len(self.lowers) > 1:
42 heappush(self.lowers, -heappop(self.highers))
44 def get_median(self) -> float:
45 if len(self.lowers) == len(self.highers):
46 return (-self.lowers[0] + self.highers[0]) / 2
47 elif len(self.lowers) > len(self.highers):
48 return -self.lowers[0]
50 return self.highers[0]
52 def get_mean(self) -> float:
53 count = len(self.lowers) + len(self.highers)
54 return self.aggregate / count
56 def get_stdev(self) -> float:
57 mean = self.get_mean()
60 variance += (n - mean) ** 2
61 for n in self.highers:
62 variance += (n - mean) ** 2
63 return math.sqrt(variance)
66 def gcd_floats(a: float, b: float) -> float:
68 return gcd_floats(b, a)
73 return gcd_floats(b, a - math.floor(a / b) * b)
76 def gcd_float_sequence(lst: List[float]) -> float:
78 raise ValueError("Need at least one number")
82 gcd = gcd_floats(lst[0], lst[1])
83 for i in range(2, len(lst)):
84 gcd = gcd_floats(gcd, lst[i])
88 def truncate_float(n: float, decimals: int = 2):
90 Truncate a float to a particular number of decimals.
92 >>> truncate_float(3.1415927, 3)
96 assert 0 < decimals < 10
97 multiplier = 10**decimals
98 return int(n * multiplier) / multiplier
101 def percentage_to_multiplier(percent: float) -> float:
102 """Given a percentage (e.g. 155%), return a factor needed to scale a
103 number by that percentage.
105 >>> percentage_to_multiplier(155)
107 >>> percentage_to_multiplier(45)
109 >>> percentage_to_multiplier(-25)
113 multiplier = percent / 100
118 def multiplier_to_percent(multiplier: float) -> float:
119 """Convert a multiplicative factor into a percent change.
121 >>> multiplier_to_percent(0.75)
123 >>> multiplier_to_percent(1.0)
125 >>> multiplier_to_percent(1.99)
133 percent = 1.0 - percent
138 @functools.lru_cache(maxsize=1024, typed=True)
139 def is_prime(n: int) -> bool:
141 Returns True if n is prime and False otherwise. Obviously(?) very slow for
142 very large input numbers.
148 >>> is_prime(51602981)
152 if not isinstance(n, int):
153 raise TypeError("argument passed to is_prime is not of 'int' type")
161 # This is checked so that we can skip middle five numbers in below
163 if n % 2 == 0 or n % 3 == 0:
168 if n % i == 0 or n % (i + 2) == 0:
174 if __name__ == '__main__':