Added doctest and more explanation about Dijkstra execution. (#1014)

* Added doctest and more explanation about Dijkstra execution.

* tests were not passing with python2 due to missing __init__.py file at number_theory folder

* Removed the dot at the beginning of the imported modules names because 'python3 -m doctest -v data_structures/hashing/*.py' and 'python3 -m doctest -v data_structures/stacks/*.py' were failing not finding hash_table.py and stack.py modules.

* Moved global code to main scope and added doctest for project euler problems 1 to 14.

* Added test case for negative input.

* Changed N variable to do not use end of line scape because in case there is a space after it the script will break making it much more error prone.

* Added problems description and doctests to the ones that were missing. Limited line length to 79 and executed python black over all scripts.

* Changed the way files are loaded to support pytest call.

* Added __init__.py to problems to make them modules and allow pytest execution.

* Added project_euler folder to test units execution

* Changed 'os.path.split(os.path.realpath(__file__))' to 'os.path.dirname()'

project_euler/problem_03/sol1.py

@@ -1,39 +1,61 @@
-'''
+"""
 Problem:
-The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N?
-e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
-'''
-from __future__ import print_function, division
+The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
+of a given number N?
 
+e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
+"""
+from __future__ import print_function, division
 import math
 
+try:
+    raw_input  # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+
 def isprime(no):
-    if(no==2):
+    if no == 2:
         return True
-    elif (no%2==0):
+    elif no % 2 == 0:
         return False
-    sq = int(math.sqrt(no))+1
-    for i in range(3,sq,2):
-        if(no%i==0):
+    sq = int(math.sqrt(no)) + 1
+    for i in range(3, sq, 2):
+        if no % i == 0:
             return False
     return True
 
-maxNumber = 0
-n=int(input())
-if(isprime(n)):
-    print(n)
-else:
-    while (n%2==0):
-        n=n/2
-    if(isprime(n)):
-        print(n)
+
+def solution(n):
+    """Returns the largest prime factor of a given number n.
+    
+    >>> solution(13195)
+    29
+    >>> solution(10)
+    5
+    >>> solution(17)
+    17
+    """
+    maxNumber = 0
+    if isprime(n):
+        return n
     else:
-        n1 = int(math.sqrt(n))+1
-        for i in range(3,n1,2):
-            if(n%i==0):
-                if(isprime(n/i)):
-                    maxNumber = n/i
-                    break
-                elif(isprime(i)):
-                    maxNumber = i
-        print(maxNumber)
+        while n % 2 == 0:
+            n = n / 2
+        if isprime(n):
+            return int(n)
+        else:
+            n1 = int(math.sqrt(n)) + 1
+            for i in range(3, n1, 2):
+                if n % i == 0:
+                    if isprime(n / i):
+                        maxNumber = n / i
+                        break
+                    elif isprime(i):
+                        maxNumber = i
+            return maxNumber
+    return int(sum)
+
+
+if __name__ == "__main__":
+    print(solution(int(raw_input().strip())))

project_euler/problem_03/sol2.py

@@ -1,18 +1,40 @@
-'''
+"""
 Problem:
-The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N?
-e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
-'''
+The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
+of a given number N?
 
-from __future__ import print_function
-n=int(input())
-prime=1
-i=2
-while(i*i<=n):
-    while(n%i==0):
-        prime=i
-        n//=i
-    i+=1
-if(n>1):
-    prime=n
-print(prime)
+e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
+"""
+from __future__ import print_function, division
+import math
+
+try:
+    raw_input  # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+
+def solution(n):
+    """Returns the largest prime factor of a given number n.
+    
+    >>> solution(13195)
+    29
+    >>> solution(10)
+    5
+    >>> solution(17)
+    17
+    """
+    prime = 1
+    i = 2
+    while i * i <= n:
+        while n % i == 0:
+            prime = i
+            n //= i
+        i += 1
+    if n > 1:
+        prime = n
+    return int(prime)
+
+
+if __name__ == "__main__":
+    print(solution(int(raw_input().strip())))