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_14/sol1.py

@@ -1,21 +1,73 @@
+# -*- coding: utf-8 -*-
+"""
+Problem Statement:
+The following iterative sequence is defined for the set of positive integers:
+
+    n → n/2 (n is even)
+    n → 3n + 1 (n is odd)
+
+Using the rule above and starting with 13, we generate the following sequence:
+
+    13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+
+It can be seen that this sequence (starting at 13 and finishing at 1) contains
+10 terms. Although it has not been proved yet (Collatz Problem), it is thought
+that all starting numbers finish at 1.
+
+Which starting number, under one million, produces the longest chain?
+"""
 from __future__ import print_function
-largest_number = 0
-pre_counter = 0
 
-for input1 in range(750000,1000000):
-    counter = 1
-    number = input1
+try:
+    raw_input  # Python 2
+except NameError:
+    raw_input = input  # Python 3
 
-    while number > 1:
-        if number % 2 == 0:
-            number /=2
-            counter += 1
-        else:
-            number = (3*number)+1
-            counter += 1
 
-    if counter > pre_counter:
-        largest_number = input1
-        pre_counter = counter
+def solution(n):
+    """Returns the number under n that generates the longest sequence using the
+    formula:
+    n → n/2 (n is even)
+    n → 3n + 1 (n is odd)
+ 
+    >>> solution(1000000)
+    {'counter': 525, 'largest_number': 837799}
+    >>> solution(200)
+    {'counter': 125, 'largest_number': 171}
+    >>> solution(5000)
+    {'counter': 238, 'largest_number': 3711}
+    >>> solution(15000)
+    {'counter': 276, 'largest_number': 13255}
+    """
+    largest_number = 0
+    pre_counter = 0
 
-print(('Largest Number:',largest_number,'->',pre_counter,'digits'))
+    for input1 in range(n):
+        counter = 1
+        number = input1
+
+        while number > 1:
+            if number % 2 == 0:
+                number /= 2
+                counter += 1
+            else:
+                number = (3 * number) + 1
+                counter += 1
+
+        if counter > pre_counter:
+            largest_number = input1
+            pre_counter = counter
+    return {"counter": pre_counter, "largest_number": largest_number}
+
+
+if __name__ == "__main__":
+    result = solution(int(raw_input().strip()))
+    print(
+        (
+            "Largest Number:",
+            result["largest_number"],
+            "->",
+            result["counter"],
+            "digits",
+        )
+    )