List
def example():
def insert(lst, *args):
for arg in args:
lst.append(arg)
def show(dataset):
for index, value in enumerate(dataset):
print(f"{index} => {value}")
onlineCourse = ['MIT OpenCourseWare', 'Coursera', 'edX']
insert(onlineCourse, 'Udemy', 'Udacity')
show(onlineCourse)
if __name__ == '__main__':
example()
Dictionaries
def example():
def insert(dataset, **kwargs):
for kw in kwargs:
dataset.update({kw: kwargs[kw]})
def show(dataset):
for key, value in dataset.items():
print(f"\"{key}\", url = {value}")
onlineCourse = {'MIT OpenCourseWare': 'https://ocw.mit.edu/',
'Coursera' : 'https://www.coursera.org/',
'edX' : 'https://www.edx.org/'}
print(type(onlineCourse))
show(onlineCourse)
insert(onlineCourse, Udemy = 'https://www.udemy.com/',
Udacity = 'https://www.udacity.com/')
show(onlineCourse)
if __name__ == '__main__':
example()
def example():
dataset = list(range(1, 10 + 1, 1))
xs = list(map((lambda x: x ** 2), dataset))
ys = list(map((lambda x: x ** 3), dataset))
print(dataset)
print(xs)
print(ys)
if __name__ == '__main__':
example()
def example():
dataset = list(range(-5, 5 + 1, 1))
pos_lst = list(filter((lambda x: x > 0), dataset))
neg_lst = list(filter((lambda x: x < 0), dataset))
print(dataset)
print(pos_lst)
print(neg_lst)
if __name__ == '__main__':
example()
from functools import reduce
import operator
def example():
dataset = list(range(-5, 5 + 1, 1))
pos_lst = list(filter(lambda x: x > 0, dataset))
div_lst = list(map(lambda x: x / 2, pos_lst))
result = reduce(operator.add, div_lst)
print(dataset)
print(pos_lst)
print(div_lst)
print(result)
if __name__ == '__main__':
example()
Primality Test
def is_prime(n):
for x in [i for i in range(2, n + 1, 1) if i <= n / i]:
if n % x == 0:
return False
return True
def find_prime(m, n):
return [i for i in range(m, n + 1, 1) if is_prime(i)]
def example():
print(find_prime(1, 30))
if __name__ == '__main__':
example()
Combination
Definition
Factorial
n!=n×(n−1)×(n−2)×...×2×1=n×(n−1)!
Number of k-Combinations
C(n,k)=Ckn=(kn)=k!(n−k)!n!
Example
import itertools as it
def factorial(n):
return 1 if n == 1 else n * factorial(n - 1)
def comb(n, k):
return factorial(n) / (factorial(k) * factorial(n - k))
def example():
dataset = [1, 2, 3, 4]
xs = list(it.combinations(dataset, 2))
ys = list(it.combinations(dataset, 3))
assert len(xs) == comb(len(dataset), 2)
assert len(ys) == comb(len(dataset), 3)
print(xs)
print(ys)
if __name__ == '__main__':
example()
Permutations
import itertools as it
def example():
def printAllPermutations(dataset):
for i in range(len(dataset)):
xs = list(it.permutations(dataset, i + 1))
print(xs)
dataset = list(range(1, 3 + 1, 1))
printAllPermutations(dataset)
if __name__ == '__main__':
example()
Use SymPy
to Compute Limits
Encapsulation of SymPy
import sympy as sy
class SymMath:
x = sy.Symbol("X")
@staticmethod
def limitOf(f, n):
return sy.limit(f, SymMath.x, n)
e=x→0lim(1+x)x1=n→∞lim(1+n1)n, x=n1
print(SymMath.limitOf((1 + SymMath.x) ** (1 / SymMath.x), 0))
print(SymMath.limitOf((1 + 1 / SymMath.x) ** SymMath.x, sy.S.Infinity))
x→0limxsin(x)=1
print(SymMath.limitOf((sy.sin(SymMath.x) / SymMath.x), 0))
x→0limxcos(x)−1=0
print(SymMath.limitOf(((sy.cos(SymMath.x) - 1) / SymMath.x), 0))
Complete Example Code
import sympy as sy
class SymMath:
x = sy.Symbol("X")
@staticmethod
def limitOf(f, n):
return sy.limit(f, SymMath.x, n)
def example():
print(SymMath.limitOf((1 + SymMath.x) ** (1 / SymMath.x), 0))
print(SymMath.limitOf((1 + 1 / SymMath.x) ** SymMath.x, sy.S.Infinity))
print(SymMath.limitOf((sy.sin(SymMath.x) / SymMath.x), 0))
print(SymMath.limitOf(((sy.cos(SymMath.x) - 1) / SymMath.x), 0))
if __name__ == '__main__':
example()
Random Integers Matrix
import numpy as np
class Matrix:
def __init__(self, rows, cols, start, stop):
assert rows > 0 and cols > 0
self.data = np.random.randint(start, stop + 1, size = (rows, cols))
self.row = self.data.shape[0]
self.colum = self.data.shape[1]
def __str__(self):
return f"Matrix = \n{self.data}"
def example():
m1 = Matrix(3, 4, -12345, 67890)
print(m1)
print(f"row = {m1.row}")
print(f"column = {m1.colum}")
if __name__ == '__main__':
example()