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_09/sol2.py

@@ -1,18 +1,44 @@
-"""A Pythagorean triplet is a set of three natural numbers, for which,
-a^2+b^2=c^2
-Given N, Check if there exists any Pythagorean triplet for which a+b+c=N
-Find maximum possible value of product of a,b,c among all such Pythagorean triplets, If there is no such Pythagorean triplet print -1."""
-#!/bin/python3
+"""
+Problem Statement:
+A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+    a^2 + b^2 = c^2
+For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
-product=-1
-d=0
-N = int(input())
-for a in range(1,N//3):
-    """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c """
-    b=(N*N-2*a*N)//(2*N-2*a)
-    c=N-a-b
-    if c*c==(a*a+b*b):
-        d=(a*b*c)
-        if d>=product:
-            product=d
-print(product)
+There exists exactly one Pythagorean triplet for which a + b + c = 1000.
+Find the product abc.
+"""
+from __future__ import print_function
+
+try:
+    raw_input  # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+
+def solution(n):
+    """
+     Return the product of a,b,c which are Pythagorean Triplet that satisfies
+     the following:
+     1. a < b < c
+     2. a**2 + b**2 = c**2
+     3. a + b + c = 1000
+    
+    >>> solution(1000)
+    31875000
+    """
+    product = -1
+    d = 0
+    for a in range(1, n // 3):
+        """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
+        """
+        b = (n * n - 2 * a * n) // (2 * n - 2 * a)
+        c = n - a - b
+        if c * c == (a * a + b * b):
+            d = a * b * c
+            if d >= product:
+                product = d
+    return product
+
+
+if __name__ == "__main__":
+    print(solution(int(raw_input().strip())))