improved prime numbers implementation (#1606)

* improved prime numbers implementation

* fixup! Format Python code with psf/black push

* fix type hint

* fixup! Format Python code with psf/black push

* fix doctests

* updating DIRECTORY.md

* added prime tests with negative numbers

* using for instead filter

* updating DIRECTORY.md

* Remove unused typing.List

* Remove tab indentation

* print("Sorted order is:", " ".join(a))

DIRECTORY.md

@@ -133,6 +133,7 @@
     * [Gaussian Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/gaussian_filter.py)
     * [Median Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/median_filter.py)
     * [Sobel Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/sobel_filter.py)
+  * [Index Calculation](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/index_calculation.py)
   * Rotation
     * [Rotation](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/rotation/rotation.py)
   * [Test Digital Image Processing](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/test_digital_image_processing.py)
@@ -216,6 +217,7 @@
 ## Hashes
   * [Chaos Machine](https://github.com/TheAlgorithms/Python/blob/master/hashes/chaos_machine.py)
   * [Enigma Machine](https://github.com/TheAlgorithms/Python/blob/master/hashes/enigma_machine.py)
+  * [Hamming Code](https://github.com/TheAlgorithms/Python/blob/master/hashes/hamming_code.py)
   * [Md5](https://github.com/TheAlgorithms/Python/blob/master/hashes/md5.py)
   * [Sha1](https://github.com/TheAlgorithms/Python/blob/master/hashes/sha1.py)
 
@@ -234,6 +236,7 @@
   * [Linear Discriminant Analysis](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/linear_discriminant_analysis.py)
   * [Linear Regression](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/linear_regression.py)
   * [Logistic Regression](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/logistic_regression.py)
+  * [Multilayer Perceptron Classifier](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/multilayer_perceptron_classifier.py)
   * [Polymonial Regression](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/polymonial_regression.py)
   * [Scoring Functions](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/scoring_functions.py)
   * [Sequential Minimum Optimization](https://github.com/TheAlgorithms/Python/blob/master/machine_learning/sequential_minimum_optimization.py)
@@ -252,6 +255,7 @@
   * [Binomial Coefficient](https://github.com/TheAlgorithms/Python/blob/master/maths/binomial_coefficient.py)
   * [Ceil](https://github.com/TheAlgorithms/Python/blob/master/maths/ceil.py)
   * [Collatz Sequence](https://github.com/TheAlgorithms/Python/blob/master/maths/collatz_sequence.py)
+  * [Eulers Totient](https://github.com/TheAlgorithms/Python/blob/master/maths/eulers_totient.py)
   * [Explicit Euler](https://github.com/TheAlgorithms/Python/blob/master/maths/explicit_euler.py)
   * [Extended Euclidean Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/extended_euclidean_algorithm.py)
   * [Factorial Python](https://github.com/TheAlgorithms/Python/blob/master/maths/factorial_python.py)
@@ -286,6 +290,7 @@
   * [Prime Factors](https://github.com/TheAlgorithms/Python/blob/master/maths/prime_factors.py)
   * [Prime Numbers](https://github.com/TheAlgorithms/Python/blob/master/maths/prime_numbers.py)
   * [Prime Sieve Eratosthenes](https://github.com/TheAlgorithms/Python/blob/master/maths/prime_sieve_eratosthenes.py)
+  * [Pythagoras](https://github.com/TheAlgorithms/Python/blob/master/maths/pythagoras.py)
   * [Qr Decomposition](https://github.com/TheAlgorithms/Python/blob/master/maths/qr_decomposition.py)
   * [Quadratic Equations Complex Numbers](https://github.com/TheAlgorithms/Python/blob/master/maths/quadratic_equations_complex_numbers.py)
   * [Radix2 Fft](https://github.com/TheAlgorithms/Python/blob/master/maths/radix2_fft.py)
@@ -499,11 +504,11 @@
   * [I Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/i_sort.py)
   * [Insertion Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/insertion_sort.py)
   * [Merge Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_sort.py)
-  * [Merge Sort Fastest](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_sort_fastest.py)
   * [Odd Even Transposition Parallel](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_transposition_parallel.py)
   * [Odd Even Transposition Single Threaded](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_transposition_single_threaded.py)
   * [Pancake Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/pancake_sort.py)
   * [Pigeon Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/pigeon_sort.py)
+  * [Pigeonhole Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/pigeonhole_sort.py)
   * [Quick Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/quick_sort.py)
   * [Quick Sort 3 Partition](https://github.com/TheAlgorithms/Python/blob/master/sorts/quick_sort_3_partition.py)
   * [Radix Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/radix_sort.py)
@@ -516,6 +521,7 @@
   * [Tim Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/tim_sort.py)
   * [Topological Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/topological_sort.py)
   * [Tree Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/tree_sort.py)
+  * [Unknown Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/unknown_sort.py)
   * [Wiggle Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/wiggle_sort.py)
 
 ## Strings

data_structures/data_structures/heap/heap_generic.py

@@ -30,7 +30,8 @@ class Heap(object):
         """Performs changes required for swapping two elements in the heap"""
         # First update the indexes of the items in index map.
         self.pos_map[self.arr[i][0]], self.pos_map[self.arr[j][0]] = (
-            self.pos_map[self.arr[j][0]], self.pos_map[self.arr[i][0]]
+            self.pos_map[self.arr[j][0]],
+            self.pos_map[self.arr[i][0]],
         )
         # Then swap the items in the list.
         self.arr[i], self.arr[j] = self.arr[j], self.arr[i]

digital_image_processing/index_calculation.py

@@ -176,10 +176,10 @@ class IndexCalculation:
 
     def ARVI2(self):
         """
-            Atmospherically Resistant Vegetation Index 2
-            https://www.indexdatabase.de/db/i-single.php?id=396
-            :return: index
-             	−0.18+1.17*(self.nir−self.red)/(self.nir+self.red)
+        Atmospherically Resistant Vegetation Index 2
+        https://www.indexdatabase.de/db/i-single.php?id=396
+        :return: index
+            −0.18+1.17*(self.nir−self.red)/(self.nir+self.red)
         """
         return -0.18 + (1.17 * ((self.nir - self.red) / (self.nir + self.red)))
 

maths/prime_numbers.py

@@ -1,28 +1,34 @@
-from typing import List
+from typing import Generator
 
 
-def primes(max: int) -> List[int]:
+def primes(max: int) -> Generator[int, None, None]:
     """
     Return a list of all primes numbers up to max.
-    >>> primes(10)
-    [2, 3, 5, 7]
-    >>> primes(11)
-    [2, 3, 5, 7, 11]
-    >>> primes(25)
+    >>> list(primes(0))
+    []
+    >>> list(primes(-1))
+    []
+    >>> list(primes(-10))
+    []
+    >>> list(primes(25))
     [2, 3, 5, 7, 11, 13, 17, 19, 23]
-    >>> primes(1_000_000)[-1]
-    999983
+    >>> list(primes(11))
+    [2, 3, 5, 7, 11]
+    >>> list(primes(33))
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
+    >>> list(primes(10000))[-1]
+    9973
     """
-    max += 1
-    numbers = [False] * max
-    ret = []
-    for i in range(2, max):
-        if not numbers[i]:
-            for j in range(i, max, i):
-                numbers[j] = True
-            ret.append(i)
-    return ret
+    numbers: Generator = (i for i in range(1, (max + 1)))
+    for i in (n for n in numbers if n > 1):
+        for j in range(2, i):
+            if (i % j) == 0:
+                break
+        else:
+            yield i
 
 
 if __name__ == "__main__":
-    print(primes(int(input("Calculate primes up to:\n>> "))))
+    number = int(input("Calculate primes up to:\n>> ").strip())
+    for ret in primes(number):
+        print(ret)

sorts/pigeonhole_sort.py

@@ -36,8 +36,9 @@ def pigeonhole_sort(a):
 
 
 def main():
-    pigeonhole_sort([8, 3, 2, 7, 4, 6, 8])
-    print("Sorted order is: ", " ", join(a))
+    a = [8, 3, 2, 7, 4, 6, 8]
+    pigeonhole_sort(a)
+    print("Sorted order is:", " ".join(a))
 
 
 if __name__ == "__main__":