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_29/solution.py

@@ -1,33 +1,51 @@
-def main():
+"""
+Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:
+
+2^2=4,  2^3=8,   2^4=16,  2^5=32
+3^2=9,  3^3=27,  3^4=81,  3^5=243
+4^2=16, 4^3=64,  4^4=256, 4^5=1024
+5^2=25, 5^3=125, 5^4=625, 5^5=3125
+
+If they are then placed in numerical order, with any repeats removed, we get
+the following sequence of 15 distinct terms:
+
+4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
+
+How many distinct terms are in the sequence generated by ab
+for 2 <= a <= 100 and 2 <= b <= 100?
+"""
+from __future__ import print_function
+
+
+def solution(n):
+    """Returns the number of distinct terms in the sequence generated by a^b
+    for 2 <= a <= 100 and 2 <= b <= 100.
+ 
+    >>> solution(100)
+    9183
+    >>> solution(50)
+    2184
+    >>> solution(20)
+    324
+    >>> solution(5)
+    15
+    >>> solution(2)
+    1
+    >>> solution(1)
+    0
     """
-    Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:
-
-    22=4, 23=8, 24=16, 25=32
-    32=9, 33=27, 34=81, 35=243
-    42=16, 43=64, 44=256, 45=1024
-    52=25, 53=125, 54=625, 55=3125
-    If they are then placed in numerical order, with any repeats removed,
-    we get the following sequence of 15 distinct terms:
-
-    4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
-
-    How many distinct terms are in the sequence generated by ab
-    for 2 <= a <= 100 and 2 <= b <= 100?
-    """
-
     collectPowers = set()
 
     currentPow = 0
 
-    N = 101     # maximum limit
+    N = n + 1  # maximum limit
 
     for a in range(2, N):
         for b in range(2, N):
-            currentPow = a**b   # calculates the current power
-            collectPowers.add(currentPow)   # adds the result to the set
-
-    print("Number of terms ", len(collectPowers))
+            currentPow = a ** b  # calculates the current power
+            collectPowers.add(currentPow)  # adds the result to the set
+    return len(collectPowers)
 
 
-if __name__ == '__main__':
-    main()
+if __name__ == "__main__":
+    print("Number of terms ", solution(int(str(input()).strip())))