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()
26 >>> round(median.get_stdev(), 2)
31 self.lowers, self.highers = [], []
34 def add_number(self, number: float):
35 if not self.highers or number > self.highers[0]:
36 heappush(self.highers, number)
38 heappush(self.lowers, -number) # for lowers we need a max heap
39 self.aggregate += number
43 if len(self.lowers) - len(self.highers) > 1:
44 heappush(self.highers, -heappop(self.lowers))
45 elif len(self.highers) - len(self.lowers) > 1:
46 heappush(self.lowers, -heappop(self.highers))
48 def get_median(self) -> float:
49 if len(self.lowers) == len(self.highers):
50 return (-self.lowers[0] + self.highers[0]) / 2
51 elif len(self.lowers) > len(self.highers):
52 return -self.lowers[0]
54 return self.highers[0]
56 def get_mean(self) -> float:
57 count = len(self.lowers) + len(self.highers)
58 return self.aggregate / count
60 def get_stdev(self) -> float:
61 mean = self.get_mean()
65 variance += (n - mean) ** 2
66 for n in self.highers:
67 variance += (n - mean) ** 2
68 return math.sqrt(variance)
71 def gcd_floats(a: float, b: float) -> float:
73 return gcd_floats(b, a)
78 return gcd_floats(b, a - math.floor(a / b) * b)
81 def gcd_float_sequence(lst: List[float]) -> float:
83 raise ValueError("Need at least one number")
87 gcd = gcd_floats(lst[0], lst[1])
88 for i in range(2, len(lst)):
89 gcd = gcd_floats(gcd, lst[i])
93 def truncate_float(n: float, decimals: int = 2):
95 Truncate a float to a particular number of decimals.
97 >>> truncate_float(3.1415927, 3)
101 assert 0 < decimals < 10
102 multiplier = 10**decimals
103 return int(n * multiplier) / multiplier
106 def percentage_to_multiplier(percent: float) -> float:
107 """Given a percentage (e.g. 155%), return a factor needed to scale a
108 number by that percentage.
110 >>> percentage_to_multiplier(155)
112 >>> percentage_to_multiplier(45)
114 >>> percentage_to_multiplier(-25)
118 multiplier = percent / 100
123 def multiplier_to_percent(multiplier: float) -> float:
124 """Convert a multiplicative factor into a percent change.
126 >>> multiplier_to_percent(0.75)
128 >>> multiplier_to_percent(1.0)
130 >>> multiplier_to_percent(1.99)
138 percent = 1.0 - percent
143 @functools.lru_cache(maxsize=1024, typed=True)
144 def is_prime(n: int) -> bool:
146 Returns True if n is prime and False otherwise. Obviously(?) very slow for
147 very large input numbers.
153 >>> is_prime(51602981)
157 if not isinstance(n, int):
158 raise TypeError("argument passed to is_prime is not of 'int' type")
166 # This is checked so that we can skip middle five numbers in below
168 if n % 2 == 0 or n % 3 == 0:
173 if n % i == 0 or n % (i + 2) == 0:
179 if __name__ == '__main__':