From 0da5ceafd9867889064e0de59263050e73608625 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Thu, 20 Feb 2020 18:03:31 +0700
Subject: [PATCH 01/11] added doctests in modular_exponential.py

---
 dynamic_programming/coin_change.py | 17 +++++++++++++++--
 linear_algebra/src/lib.py          | 22 ++++++++++++----------
 maths/modular_exponential.py       | 22 +++++++++++++++++++---
 3 files changed, 46 insertions(+), 15 deletions(-)

diff --git a/dynamic_programming/coin_change.py b/dynamic_programming/coin_change.py
index a85d8e08dbb1..2d7106f0cc6f 100644
--- a/dynamic_programming/coin_change.py
+++ b/dynamic_programming/coin_change.py
@@ -8,6 +8,18 @@
 
 
 def dp_count(S, m, n):
+    """
+    >>> dp_count([1, 2, 3], 3, 4)
+    4
+    >>> dp_count([1, 2, 3], 3, 7)
+    8
+    >>> dp_count([2, 5, 3, 6], 4, 10)
+    5
+    >>> dp_count([10], 1, 99)
+    0
+    >>> dp_count([4, 5, 6], 3, 0)
+    1
+    """
 
     # table[i] represents the number of ways to get to amount i
     table = [0] * (n + 1)
@@ -26,5 +38,6 @@ def dp_count(S, m, n):
 
 
 if __name__ == "__main__":
-    print(dp_count([1, 2, 3], 3, 4))  # answer 4
-    print(dp_count([2, 5, 3, 6], 4, 10))  # answer 5
+    import doctest
+
+    doctest.testmod()
diff --git a/linear_algebra/src/lib.py b/linear_algebra/src/lib.py
index 5ce0f696ad71..bf9e0d302a89 100644
--- a/linear_algebra/src/lib.py
+++ b/linear_algebra/src/lib.py
@@ -27,7 +27,7 @@
 
 class Vector(object):
     """
-        This class represents a vector of arbitray size.
+        This class represents a vector of arbitrary size.
         You need to give the vector components. 
         
         Overview about the methods:
@@ -37,7 +37,7 @@ class Vector(object):
         __str__() : toString method
         component(i : int): gets the i-th component (start by 0)
         __len__() : gets the size of the vector (number of components)
-        euclidLength() : returns the eulidean length of the vector.
+        euclidLength() : returns the euclidean length of the vector.
         operator + : vector addition
         operator - : vector subtraction
         operator * : scalar multiplication and dot product
@@ -46,11 +46,13 @@ class Vector(object):
         TODO: compare-operator
     """
 
-    def __init__(self, components=[]):
+    def __init__(self, components=None):
         """
             input: components or nothing
             simple constructor for init the vector
         """
+        if components is None:
+            components = []
         self.__components = list(components)
 
     def set(self, components):
@@ -86,9 +88,9 @@ def __len__(self):
         """
         return len(self.__components)
 
-    def eulidLength(self):
+    def euclidLength(self):
         """
-            returns the eulidean length of the vector
+            returns the euclidean length of the vector
         """
         summe = 0
         for c in self.__components:
@@ -112,7 +114,7 @@ def __sub__(self, other):
         """
             input: other vector
             assumes: other vector has the same size
-            returns a new vector that represents the differenz.
+            returns a new vector that represents the difference.
         """
         size = len(self)
         if size == len(other):
@@ -136,7 +138,7 @@ def __mul__(self, other):
                 summe += self.__components[i] * other.component(i)
             return summe
         else:  # error case
-            raise Exception("invalide operand!")
+            raise Exception("invalid operand!")
 
     def copy(self):
         """
@@ -223,7 +225,7 @@ class Matrix(object):
 
     def __init__(self, matrix, w, h):
         """
-            simple constructor for initialzes 
+            simple constructor for initializing
             the matrix with components.
         """
         self.__matrix = matrix
@@ -249,7 +251,7 @@ def changeComponent(self, x, y, value):
         """
             changes the x-y component of this matrix
         """
-        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+        if 0 <= x < self.__height and 0 <= y < self.__width:
             self.__matrix[x][y] = value
         else:
             raise Exception("changeComponent: indices out of bounds")
@@ -258,7 +260,7 @@ def component(self, x, y):
         """
             returns the specified (x,y) component
         """
-        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+        if 0 <= x < self.__height and 0 <= y < self.__width:
             return self.__matrix[x][y]
         else:
             raise Exception("changeComponent: indices out of bounds")
diff --git a/maths/modular_exponential.py b/maths/modular_exponential.py
index 8715e17147ff..5a3493669a19 100644
--- a/maths/modular_exponential.py
+++ b/maths/modular_exponential.py
@@ -1,8 +1,19 @@
-"""Modular Exponential."""
-
+"""
+    Modular Exponential.
+    Modular exponentiation is a type of exponentiation performed over a modulus. 
+"""
 
+"""Calculate Modular Exponential."""
 def modular_exponential(base, power, mod):
-    """Calculate Modular Exponential."""
+    """
+    >>> modular_exponential(5, 0, 10)
+    1
+    >>> modular_exponential(2, 8, 7)
+    4
+    >>> modular_exponential(3, -2, 9)
+    -1
+    """
+
     if power < 0:
         return -1
     base %= mod
@@ -13,6 +24,7 @@ def modular_exponential(base, power, mod):
             result = (result * base) % mod
         power = power >> 1
         base = (base * base) % mod
+
     return result
 
 
@@ -22,4 +34,8 @@ def main():
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
     main()

From 4183239405ad4c20b293774ab74a597c082ff714 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Thu, 20 Feb 2020 18:11:35 +0700
Subject: [PATCH 02/11] added doctests in modular_exponential.py

---
 maths/modular_exponential.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/modular_exponential.py b/maths/modular_exponential.py
index 5a3493669a19..0fd35d65b780 100644
--- a/maths/modular_exponential.py
+++ b/maths/modular_exponential.py
@@ -4,7 +4,7 @@
 """
 
 """Calculate Modular Exponential."""
-def modular_exponential(base, power, mod):
+def modular_exponential(base : int, power : int, mod : int):
     """
     >>> modular_exponential(5, 0, 10)
     1

From 3856fa064d97ee70cdfd0db0dfdeabc4db1474e2 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Thu, 20 Feb 2020 18:19:59 +0700
Subject: [PATCH 03/11] added URL link

---
 maths/modular_exponential.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/modular_exponential.py b/maths/modular_exponential.py
index 0fd35d65b780..91fa0e462a49 100644
--- a/maths/modular_exponential.py
+++ b/maths/modular_exponential.py
@@ -1,6 +1,7 @@
 """
     Modular Exponential.
     Modular exponentiation is a type of exponentiation performed over a modulus. 
+    For more explanation, please check https://en.wikipedia.org/wiki/Modular_exponentiation
 """
 
 """Calculate Modular Exponential."""

From cb8ab389ee70461911c35f8d48bfdf95a972224c Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 3 Oct 2020 15:27:05 +0000
Subject: [PATCH 04/11] updating DIRECTORY.md

---
 DIRECTORY.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 37eaadb89786..9e33eb6c00ba 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -547,6 +547,8 @@
   * Problem 11
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_11/sol1.py)
     * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_11/sol2.py)
+  * Problem 112
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_112/sol1.py)
   * Problem 12
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_12/sol1.py)
     * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_12/sol2.py)

From 7824282d8885db24ab6d92ea8cb2c2f91c651026 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Sat, 3 Oct 2020 22:27:40 +0700
Subject: [PATCH 05/11] Add problem 50 solution

---
 project_euler/problem_50/__init__.py |   0
 project_euler/problem_50/sol1.py     | 100 +++++++++++++++++++++++++++
 2 files changed, 100 insertions(+)
 create mode 100644 project_euler/problem_50/__init__.py
 create mode 100644 project_euler/problem_50/sol1.py

diff --git a/project_euler/problem_50/__init__.py b/project_euler/problem_50/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/project_euler/problem_50/sol1.py b/project_euler/problem_50/sol1.py
new file mode 100644
index 000000000000..c7f21a3baf9c
--- /dev/null
+++ b/project_euler/problem_50/sol1.py
@@ -0,0 +1,100 @@
+from math import floor, sqrt
+
+"""
+Consecutive prime sum
+
+Problem 50
+
+The prime 41, can be written as the sum of six consecutive primes:
+
+41 = 2 + 3 + 5 + 7 + 11 + 13
+
+This is the longest sum of consecutive primes that adds to
+a prime below one-hundred.
+
+The longest sum of consecutive primes below one-thousand that adds to a prime,
+contains 21 terms, and is equal to 953.
+
+Which prime, below one-million, can be written as the sum of
+the most consecutive primes?
+"""
+
+"""
+Solution:
+
+First of all, we need to generate all prime numbers
+from 2 to the closest prime number with 1000000.
+Then, use sliding window to get the answer.
+"""
+
+
+def is_prime(number: int) -> bool:
+    """
+    function to check whether a number is a prime or not.
+    >>> is_prime(2)
+    True
+    >>> is_prime(6)
+    False
+    >>> is_prime(1)
+    False
+    """
+
+    if number < 2:
+        return False
+
+    for n in range(2, floor(sqrt(number)) + 1):
+        if number % n == 0:
+            return False
+
+    return True
+
+
+def solution():
+    """
+    Return the problem solution.
+    >>> solution()
+    997651
+    """
+
+    prime_list = [2] + [x for x in range(3, 10 ** 6, 2) if is_prime(x)]
+
+    cumulative_sum = []
+    tmp = 0
+    for x in prime_list:
+        tmp += x
+        if tmp < 10 ** 6:
+            cumulative_sum.append(tmp)
+        else:
+            break
+
+    upper_limit_idx = 0
+    for i in range(len(prime_list)):
+        if prime_list[i] < 10 ** 6:
+            upper_limit_idx = i
+        else:
+            break
+
+    max_count = -1
+    answer = 0
+    for number in reversed(cumulative_sum):
+        count_prime = cumulative_sum.index(number) + 1
+
+        if not is_prime(number):
+            tmp = number
+
+            for i in range(upper_limit_idx):
+                count_prime -= 1
+                tmp -= prime_list[i]
+
+                if is_prime(tmp) or tmp < 0:
+                    break
+
+        if max_count < count_prime:
+            max_count = count_prime
+            answer = tmp
+
+    return answer
+
+
+if __name__ == "__main__":
+    print(solution())

From c933fe88804f4e89c67c7d942ef2f52048b2e365 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 3 Oct 2020 15:28:26 +0000
Subject: [PATCH 06/11] updating DIRECTORY.md

---
 DIRECTORY.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 9e33eb6c00ba..16f0688f957c 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -633,6 +633,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_47/sol1.py)
   * Problem 48
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_48/sol1.py)
+  * Problem 50
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_50/sol1.py)
   * Problem 52
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_52/sol1.py)
   * Problem 53

From a2acaf88184620fd8606ac9ef68b4d10c6a4f9d5 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Sun, 4 Oct 2020 21:46:55 +0700
Subject: [PATCH 07/11] Fix some mistakes

---
 project_euler/problem_50/sol1.py | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/project_euler/problem_50/sol1.py b/project_euler/problem_50/sol1.py
index c7f21a3baf9c..7760ff9c5df4 100644
--- a/project_euler/problem_50/sol1.py
+++ b/project_euler/problem_50/sol1.py
@@ -17,9 +17,7 @@
 
 Which prime, below one-million, can be written as the sum of
 the most consecutive primes?
-"""
 
-"""
 Solution:
 
 First of all, we need to generate all prime numbers
@@ -37,6 +35,10 @@ def is_prime(number: int) -> bool:
     False
     >>> is_prime(1)
     False
+    >>> is_prime(-7000)
+    False
+    >>> is_prime(104729)
+    True
     """
 
     if number < 2:
@@ -60,8 +62,8 @@ def solution():
 
     cumulative_sum = []
     tmp = 0
-    for x in prime_list:
-        tmp += x
+    for prime in prime_list:
+        tmp += prime
         if tmp < 10 ** 6:
             cumulative_sum.append(tmp)
         else:

From e75158b3b0fde2e424cdb42aa578a9dc79d6b5a0 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Mon, 5 Oct 2020 08:04:30 +0700
Subject: [PATCH 08/11] Move the import statement lower

---
 project_euler/problem_50/sol1.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_50/sol1.py b/project_euler/problem_50/sol1.py
index 7760ff9c5df4..760f49260091 100644
--- a/project_euler/problem_50/sol1.py
+++ b/project_euler/problem_50/sol1.py
@@ -1,5 +1,3 @@
-from math import floor, sqrt
-
 """
 Consecutive prime sum
 
@@ -25,6 +23,8 @@
 Then, use sliding window to get the answer.
 """
 
+from math import floor, sqrt
+
 
 def is_prime(number: int) -> bool:
     """

From eebca1e45af4d6e7708f1e7403e0b629cd93bc42 Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Sun, 11 Oct 2020 14:56:30 +0700
Subject: [PATCH 09/11] Add default argument into main function

---
 project_euler/problem_50/sol1.py | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/project_euler/problem_50/sol1.py b/project_euler/problem_50/sol1.py
index 760f49260091..3febfc68bdd2 100644
--- a/project_euler/problem_50/sol1.py
+++ b/project_euler/problem_50/sol1.py
@@ -51,27 +51,27 @@ def is_prime(number: int) -> bool:
     return True
 
 
-def solution():
+def solution(constraint=10 ** 6):
     """
     Return the problem solution.
-    >>> solution()
-    997651
+    >>> solution(1000)
+    953
     """
 
-    prime_list = [2] + [x for x in range(3, 10 ** 6, 2) if is_prime(x)]
+    prime_list = [2] + [x for x in range(3, constraint, 2) if is_prime(x)]
 
     cumulative_sum = []
     tmp = 0
     for prime in prime_list:
         tmp += prime
-        if tmp < 10 ** 6:
+        if tmp < constraint:
             cumulative_sum.append(tmp)
         else:
             break
 
     upper_limit_idx = 0
     for i in range(len(prime_list)):
-        if prime_list[i] < 10 ** 6:
+        if prime_list[i] < constraint:
             upper_limit_idx = i
         else:
             break

From c45bfe36ecdaf004c7b8b07369426c8641dfc9fc Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Mon, 12 Oct 2020 12:54:04 +0700
Subject: [PATCH 10/11] Improve the code

* Add type hint
* Add more tests
* Add problem link
---
 project_euler/problem_50/sol1.py | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_50/sol1.py b/project_euler/problem_50/sol1.py
index 3febfc68bdd2..64436a2d436b 100644
--- a/project_euler/problem_50/sol1.py
+++ b/project_euler/problem_50/sol1.py
@@ -2,6 +2,7 @@
 Consecutive prime sum
 
 Problem 50
+https://projecteuler.net/problem=50
 
 The prime 41, can be written as the sum of six consecutive primes:
 
@@ -51,11 +52,15 @@ def is_prime(number: int) -> bool:
     return True
 
 
-def solution(constraint=10 ** 6):
+def solution(constraint: int = 10 ** 6):
     """
     Return the problem solution.
+    >>> solution(10000)
+    9521
     >>> solution(1000)
     953
+    >>> solution(50)
+    58
     """
 
     prime_list = [2] + [x for x in range(3, constraint, 2) if is_prime(x)]
@@ -99,4 +104,4 @@ def solution(constraint=10 ** 6):
 
 
 if __name__ == "__main__":
-    print(solution())
+    print(solution(50))

From e51429f1785481e7cefb7b87ab05760302d66cee Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Mon, 12 Oct 2020 12:58:17 +0700
Subject: [PATCH 11/11] Small fix

---
 project_euler/problem_50/sol1.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/project_euler/problem_50/sol1.py b/project_euler/problem_50/sol1.py
index 64436a2d436b..de5f81ad2b89 100644
--- a/project_euler/problem_50/sol1.py
+++ b/project_euler/problem_50/sol1.py
@@ -104,4 +104,4 @@ def solution(constraint: int = 10 ** 6):
 
 
 if __name__ == "__main__":
-    print(solution(50))
+    print(solution())