refactor(math): pascals triangle

pymath/pascals_triangle/README.md

@@ -1 +1,14 @@
-# Pascal's Triangle
+# Pascal's Triangle
+
+Given an index k, return the kth row of the Pascal's triangle.
+Pascal's triangle: To generate A[C] in row R, sum up A'[C] and A'[C-1] from previous row R - 1.
+
+```text
+Example:
+
+Input : k = 3
+
+Return : [1,3,3,1]
+```
+
+Note: k is 0 based. k = 0, corresponds to the row [1]. 

pymath/pascals_triangle/__init__.py

@@ -1,3 +1,4 @@
+from typing import List
 from math import factorial as fac
 
 
@@ -8,30 +9,30 @@ def binomial(x, y):
         return 0
 
 
-def pascals_triangle(nth: int) -> list:
+def pascals_triangle(nth: int) -> List[List[int]]:
     """
     Generate Pascal's triangle of binomial coefficients upto the nth row
     :param nth: Nth row to generate Pascal's triangle
     :return: returns list of lists of each row or binomial coefficients of Pascal's triangle
     """
-    result = []
+    result: List[List[int]] = []
     for x in range(nth + 1):
         result.append([binomial(x, y) for y in range(x + 1)])
 
     return result
 
 
-def pascal_nth_row(nth: int) -> list:
+def pascal_nth_row(nth: int) -> List[int]:
     """
-    Get's Pascal's Triangle Nth row and returns it
-    This is much faster than calculating the whole triangle and then fetching by it's index.
-    Instead we use the formula
-    NCr = (NCr - 1 * (N - r + 1)) / r where 1 ≤ r ≤ N
-    as the nth row consists of the following sequence:
-    NC0, NC1, ......, NCN - 1, NCN
+    Gets Pascal's Triangle Nth row and returns it
+    This is much faster than calculating the whole triangle and then fetching by its index.
+    We instead use the formula:
+        NCr = (NCr - 1 * (N - r + 1)) / r where 1 ≤ r ≤ N
+        as the nth row consists of the following sequence:
+        NC0, NC1, ......, NCN - 1, NCN
     """
     ncr_1 = 1
-    row = [ncr_1]
+    row: List[int] = [ncr_1]
 
     for i in range(1, nth + 1):
         ncr = (ncr_1 * (nth - i + 1)) // i

pymath/pascals_triangle/test_pascals_triangle.py

@@ -0,0 +1,15 @@
+import unittest
+from . import pascals_triangle, pascal_nth_row
+
+
+class PascalsTriangleTestCase(unittest.TestCase):
+    def test_1(self):
+        """k=3 should return [1, 3, 3, 1]"""
+        k = 3
+        expected = [1, 3, 3, 1]
+        actual = pascal_nth_row(k)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == '__main__':
+    unittest.main()