feat: more statistics + a simple exercise

src/main.py

@@ -1,4 +1,5 @@
 from sympy import diff, limit, oo, symbols
+import unittest
 
 from modules.math import (
 	test_math_module
@@ -12,8 +13,8 @@ from modules.statistics import (
 from modules.strings import t_strings
 
 if __name__=="__main__":
-	t_strings()
+	# t_strings()
-
 	# test_math_module()
 	# test_probability_module()
-	test_statistics_module()
+	# test_statistics_module()
+	# test_exercises_module()

src/modules/exercises/essentials.py

@@ -0,0 +1,11 @@
+def maximum_subarray_sum(input_array: list[int]):
+	max_sum = input_array[0]
+	subarray = [input_array[0]]
+	for origin in range(0, len(input_array)):
+		for end in range(origin + 1, len(input_array) + 1):
+			temp_subarray = input_array[origin:end]
+			temp_sum = sum(temp_subarray)
+			if (temp_sum > max_sum):
+				max_sum = temp_sum
+				subarray = temp_subarray
+	return [max_sum, subarray]

src/modules/statistics.py

@@ -1,2 +1,39 @@
+from math import sqrt, pi, e
+
+def population_variance(difference_list, mean):
+	summatory = 0.0
+	for diff in difference_list:
+		summatory += (diff - mean) ** 2
+	return summatory / len(difference_list)
+
+def population_variance_inline(difference_list):
+	return sum((v - (sum(difference_list) / len(difference_list))) ** 2 for v in difference_list) / len(difference_list)
+
+def sample_variance(difference_list):
+	mean = sum(difference_list) / len(difference_list)
+	return sum((diff - mean) ** 2 for diff in difference_list) / (len(difference_list) - 1)
+
+def population_standard_deviation(difference_list):
+	return sqrt(population_variance_inline(difference_list))
+
+def sample_standard_deviation(difference_list):
+	return sqrt(sample_variance(difference_list))
+
+def standard_deviation(difference_list, is_sample):
+	return sample_standard_deviation(difference_list) if is_sample else population_standard_deviation(difference_list)
+
+# PDF generates the Normal Distribution (symetric arround the mean)
+def probability_density_function(x: float, mean: float, standard_deviation: float):
+	return (1 / (standard_deviation * sqrt(2 * pi))) * (e ** ((-1/2) * (x - (mean ** 2)) / standard_deviation))
+
+
 def test_statistics_module():
 	print("=== Statistics module ===")
+	differences = [ -6.571, -5.571, -1.571, 0.429, 2.429, 3.429, 7.429 ]
+	print("The population variance is", population_variance(differences, sum(differences) / len(differences)), population_variance_inline(differences))
+	print("The standard deviation is", standard_deviation(differences, False))
+	sample = differences.copy()
+	del sample[3]
+	del sample[1]
+	print("The sample variance for a population is", sample_variance(sample))
+	print("The standard deviation for a population is", standard_deviation(sample, True))

tests/test_essentials.py

@@ -0,0 +1,19 @@
+import pytest
+
+from src.modules.exercises.essentials import *
+
+def test_subarray_sum():
+	input = [2,3,-8,7,-1,2,3]
+	result = maximum_subarray_sum(input)
+	expected = [11, [7, -1, 2, 3]]
+	assert result == expected
+	input = [-2,-4]
+	result = maximum_subarray_sum(input)
+	expected = [-2, [-2]]
+	assert result == expected
+	input = [5,4,1,7,8]
+	result = maximum_subarray_sum(input)
+	expected = [25, [5,4,1,7,8]]
+	assert result == expected
+
+