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_12/sol1.py

@@ -1,9 +1,9 @@
-from __future__ import print_function
-from math import sqrt
-'''
+"""
 Highly divisible triangular numbers
 Problem 12
-The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
+The sequence of triangle numbers is generated by adding the natural numbers. So
+the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
+terms would be:
 
 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
 
@@ -18,31 +18,48 @@ Let us list the factors of the first seven triangle numbers:
 28: 1,2,4,7,14,28
 We can see that 28 is the first triangle number to have over five divisors.
 
-What is the value of the first triangle number to have over five hundred divisors?
-'''
+What is the value of the first triangle number to have over five hundred
+divisors?
+"""
+from __future__ import print_function
+from math import sqrt
+
 try:
-	xrange		#Python 2
+    xrange  # Python 2
 except NameError:
-	xrange = range	#Python 3
+    xrange = range  # Python 3
+
 
 def count_divisors(n):
-	nDivisors = 0
-	for i in xrange(1, int(sqrt(n))+1):
-		if n%i == 0:
-			nDivisors += 2
-	#check if n is perfect square 
-	if n**0.5 == int(n**0.5): 
-        	nDivisors -= 1
-	return nDivisors
+    nDivisors = 0
+    for i in xrange(1, int(sqrt(n)) + 1):
+        if n % i == 0:
+            nDivisors += 2
+    # check if n is perfect square
+    if n ** 0.5 == int(n ** 0.5):
+        nDivisors -= 1
+    return nDivisors
 
-tNum = 1
-i = 1
 
-while True:
-	i += 1
-	tNum += i
+def solution():
+    """Returns the value of the first triangle number to have over five hundred
+    divisors.
+    
+    >>> solution()
+    76576500
+    """
+    tNum = 1
+    i = 1
 
-	if count_divisors(tNum) > 500:
-		break
+    while True:
+        i += 1
+        tNum += i
 
-print(tNum)
+        if count_divisors(tNum) > 500:
+            break
+
+    return tNum
+
+
+if __name__ == "__main__":
+    print(solution())

project_euler/problem_12/sol2.py

@@ -1,8 +1,51 @@
-def triangle_number_generator(): 
-    for n in range(1,1000000):
-        yield n*(n+1)//2
-        
-def count_divisors(n): 
-    return sum([2 for i in range(1,int(n**0.5)+1) if n%i==0 and i*i != n])
+"""
+Highly divisible triangular numbers
+Problem 12
+The sequence of triangle numbers is generated by adding the natural numbers. So
+the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
+terms would be:
 
-print(next(i for i in triangle_number_generator() if count_divisors(i) > 500))
+1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+
+Let us list the factors of the first seven triangle numbers:
+
+ 1: 1
+ 3: 1,3
+ 6: 1,2,3,6
+10: 1,2,5,10
+15: 1,3,5,15
+21: 1,3,7,21
+28: 1,2,4,7,14,28
+We can see that 28 is the first triangle number to have over five divisors.
+
+What is the value of the first triangle number to have over five hundred
+divisors?
+"""
+from __future__ import print_function
+
+
+def triangle_number_generator():
+    for n in range(1, 1000000):
+        yield n * (n + 1) // 2
+
+
+def count_divisors(n):
+    return sum(
+        [2 for i in range(1, int(n ** 0.5) + 1) if n % i == 0 and i * i != n]
+    )
+
+
+def solution():
+    """Returns the value of the first triangle number to have over five hundred
+    divisors.
+    
+    >>> solution()
+    76576500
+    """
+    return next(
+        i for i in triangle_number_generator() if count_divisors(i) > 500
+    )
+
+
+if __name__ == "__main__":
+    print(solution())