Project Euler problem148

project_euler/problem_148/sol1.py

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+"""
+Project Euler Problem 148 : https://projecteuler.net/problem=148
+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:
+                               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.
+
+Solution:
+We iteratively 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.
+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 calculate for 10^9 rows
+      but we took 10^4 rows here by default.
+"""
+
+
+def solution(pascal_row_count: int = 10**9) -> int:
+    """
+    To evaluate the solution, use solution()
+    >>> solution(3)
+    6
+    >>> solution(10)
+    40
+    >>> solution(100)
+    2361
+    """
+
+    # Initializing pascal row and count
+    pascal_row = [1, 2]
+    count = 6
+
+    # To keep track of length of the pascal row
+    l = 2
+
+    for i in range(3, pascal_row_count):
+        j = 1
+
+        # Generating the next pascal row
+        while j < l:
+            pascal_row[j - 1] = (pascal_row[j - 1] + pascal_row[j]) % 7
+            if pascal_row[j - 1] != 0:
+                count += 2
+            j += 1
+
+        # 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:
+                count += 1
+        # 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 Additional 1's in the new pascal row
+        count += 2
+
+    return count
+
+
+if __name__ == "__main__":
+    print(f"{solution()}")