Added solution to problem 148 in Project Euler

project_euler/problem_148/sol1.py

@@ -4,27 +4,35 @@
 Author:	Sai Teja Manchi
 
 Problem Statement:
-We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7:
+We can easily verify that none of the entries in the
+first seven rows of Pascal's triangle are divisible by 7:
 
- 	 	 	 	 	 	 1
- 	 	 	 	 	 1	 	 1
- 	 	 	 	 1	 	 2	 	 1
- 	 	 	 1	 	 3	 	 3	 	 1
- 	 	 1	 	 4	 	 6	 	 4	 	 1
- 	 1	 	 5	 	10	 	10	 	 5	 	 1
-1	 	 6	 	15	 	20	 	15	 	 6	 	 1
-However, if we check the first one hundred rows, we will find that only 2361 of the 5050 entries are not divisible by 7.
+                               1
+                          1          1
+                     1          2          1
+                1          3          3          1
+           1          4          6          4          1
+      1          5         10         10          5          1
+1          6         15         20         15          6          1
+However, if we check the first one hundred rows, we will find that
+only 2361 of the 5050 entries are not divisible by 7.
 
-Find the number of entries which are not divisible by 7 in the first one billion (109) rows of Pascal's triangle.
+Find the number of entries which are not divisible by 7
+in the first one billion (109) rows of Pascal's triangle.
 
 Solution:
 We Generate each row in the pascal triangle one-by-one.
-Since Pascal's triangle is vertically-symmetric we only need to generate half of the values.
+Since Pascal's triangle is vertically-symmetric,
+we only need to generate half of the values
 We then count the values which are not divisible by 7.
 We only store the remainders(when divided by 7) in the list to reduce memory usage..
+
+Note: In the original problem, we need to calucalte for 10^9
+      but we took 10^6 here by default.
 """
 
-def solution(n: int = 10**9) -> int:
+
+def solution(pascal_row_count: int = 10**5) -> int:
     """
     To evaluate the solution, use solution()
     >>> solution(3)
@@ -34,39 +42,40 @@ def solution(n: int = 10**9) -> int:
     >>> solution(100)
     2361
     """
-    
-    #Initializing pascal row and count
+
+    # Initializing pascal row and count
     pascal_row = [1, 2]
     cnt = 6
-    
-    #To keep track of length of the pascal row
+
+    # To keep track of length of the pascal row
     l = 2
-    
-    for i in range(3, n):
+
+    for i in range(3, pascal_row_count):
         j = 1
-        
-        #Generating the next pascal row
+
+        # Generating the next pascal row
         while j < l:
-            pascal_row[j-1] = (pascal_row[j - 1] + pascal_row[j]) % 7
+            pascal_row[j - 1] = (pascal_row[j - 1] + pascal_row[j]) % 7
             if pascal_row[j - 1] != 0:
                 cnt += 2
             j += 1
-            
-        #Adding the middle element for even rows        
+
+        # Adding the middle element for even rows
         if i % 2 == 0:
             pascal_row[-1] = pascal_row[-1] * 2
             l += 1
             if pascal_row[-1] % 7 != 0:
                 cnt += 1
-        #Deleting the last element for odd rows since 1 is added at beginning
+        # Deleting the last element for odd rows since 1 is added at beginning
         else:
             del pascal_row[-1]
         pascal_row.insert(0, 1)
-        
-        #Adding 2 to the count for the Additonal 1's in the new pascal row
+
+        # Adding 2 to the count for the Additonal 1's in the new pascal row
         cnt += 2
-    
+
     return cnt
 
+
 if __name__ == "__main__":
-    print(f"{solution()}")
+    print(f"{solution()}")