5 from typing import List
6 from heapq import heappush, heappop
10 """A running median computer.
12 >>> median = RunningMedian()
13 >>> median.add_number(1)
14 >>> median.add_number(10)
15 >>> median.add_number(3)
16 >>> median.get_median()
18 >>> median.add_number(7)
19 >>> median.add_number(5)
20 >>> median.get_median()
25 self.lowers, self.highers = [], []
27 def add_number(self, number):
28 if not self.highers or number > self.highers[0]:
29 heappush(self.highers, number)
31 heappush(self.lowers, -number) # for lowers we need a max heap
35 if len(self.lowers) - len(self.highers) > 1:
36 heappush(self.highers, -heappop(self.lowers))
37 elif len(self.highers) - len(self.lowers) > 1:
38 heappush(self.lowers, -heappop(self.highers))
41 if len(self.lowers) == len(self.highers):
42 return (-self.lowers[0] + self.highers[0])/2
43 elif len(self.lowers) > len(self.highers):
44 return -self.lowers[0]
46 return self.highers[0]
49 def gcd_floats(a: float, b: float) -> float:
51 return gcd_floats(b, a)
56 return gcd_floats(b, a - math.floor(a / b) * b)
59 def gcd_float_sequence(lst: List[float]) -> float:
61 raise ValueError("Need at least one number")
65 gcd = gcd_floats(lst[0], lst[1])
66 for i in range(2, len(lst)):
67 gcd = gcd_floats(gcd, lst[i])
71 def truncate_float(n: float, decimals: int = 2):
73 Truncate a float to a particular number of decimals.
75 >>> truncate_float(3.1415927, 3)
79 assert decimals > 0 and decimals < 10
80 multiplier = 10 ** decimals
81 return int(n * multiplier) / multiplier
84 def percentage_to_multiplier(percent: float) -> float:
85 """Given a percentage (e.g. 155%), return a factor needed to scale a
86 number by that percentage.
88 >>> percentage_to_multiplier(155)
90 >>> percentage_to_multiplier(45)
92 >>> percentage_to_multiplier(-25)
96 multiplier = percent / 100
101 def multiplier_to_percent(multiplier: float) -> float:
102 """Convert a multiplicative factor into a percent change.
104 >>> multiplier_to_percent(0.75)
106 >>> multiplier_to_percent(1.0)
108 >>> multiplier_to_percent(1.99)
116 percent = 1.0 - percent
121 @functools.lru_cache(maxsize=1024, typed=True)
122 def is_prime(n: int) -> bool:
124 Returns True if n is prime and False otherwise. Obviously(?) very slow for
125 very large input numbers.
131 >>> is_prime(51602981)
135 if not isinstance(n, int):
136 raise TypeError("argument passed to is_prime is not of 'int' type")
144 # This is checked so that we can skip middle five numbers in below
146 if (n % 2 == 0 or n % 3 == 0):
151 if (n % i == 0 or n % (i + 2) == 0):
157 if __name__ == '__main__':