[pre-commit.ci] auto fixes from pre-commit.com hooks

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Author: pre-commit-ci[bot]

maths/sieve_of_sundaram.py

@@ -13,19 +13,19 @@
 def sieve_of_sundaram(limit: int) -> List[int]:
     """
     Generate all prime numbers up to the given limit using Sieve of Sundaram.
-    
+
     The algorithm works by creating a list of integers and marking composite numbers,
     then extracting the remaining unmarked numbers which represent primes.
-    
+
     Args:
         limit: Upper bound (exclusive) for finding primes
-        
+
     Returns:
         List of all prime numbers less than the limit
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+
     Raises:
         ValueError: If limit is negative
-        
+
     Examples:
         >>> sieve_of_sundaram(30)
         [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
@@ -46,42 +46,42 @@ def sieve_of_sundaram(limit: int) -> List[int]:
     """
     if limit < 0:
         raise ValueError("limit must be non-negative")
-    
+
     if limit <= 2:
         return []
-    
+
     # Calculate the range for Sundaram sieve
     # We need to find primes up to 'limit', so we work with (limit-1)//2
     n = (limit - 1) // 2
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+
     # Create a boolean array and initialize all entries as not marked (False)
     # marked[i] represents whether (2*i + 1) is composite
     marked = [False] * (n + 1)
-    
+
     # Mark numbers using Sundaram's formula: i + j + 2*i*j
     # where i <= j and i + j + 2*i*j <= n
     for i in range(1, n + 1):
         j = i
         while i + j + 2 * i * j <= n:
             marked[i + j + 2 * i * j] = True
             j += 1
-    
+
     # Collect unmarked numbers and transform them to get primes
     primes = [2]  # 2 is the only even prime
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     for i in range(1, n + 1):
         if not marked[i]:
             primes.append(2 * i + 1)
-    
+
     return primes
 
 
 if __name__ == "__main__":
     print("Sieve of Sundaram Demo")
     print("-" * 20)
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     test_limits = [10, 30, 50, 100]
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     for limit in test_limits:
         primes = sieve_of_sundaram(limit)
         print(f"Primes up to {limit}: {primes}")