Improve documentation for linear search algorithm

maths/modular_division.py

@@ -28,9 +28,13 @@ def modular_division(a: int, b: int, n: int) -> int:
     4
 
     """
-    assert n > 1
-    assert a > 0
-    assert greatest_common_divisor(a, n) == 1
+    if n <= 1:
+        raise ValueError("Modulus n must be greater than 1")
+    if a <= 0:
+        raise ValueError("Divisor a must be a positive integer")
+    if greatest_common_divisor(a, n) != 1:
+        raise ValueError("a and n must be coprime (gcd(a, n) = 1)")
+
     (_d, _t, s) = extended_gcd(n, a)  # Implemented below
     x = (b * s) % n
     return x

searches/linear_search.py

@@ -1,4 +1,19 @@
 """
+Linear Search Algorithm
+
+Linear search is a simple searching technique that checks each element in the collection
+sequentially until the target element is found or the collection is exhausted.
+It is also known as sequential search.
+
+Characteristics:
+- Works on both sorted and unsorted collections
+- Time complexity: O(n)
+- Space complexity: O(1)
+- Simple and reliable for small datasets
+
+For large datasets or sorted collections, binary search or other logarithmic search
+algorithms are usually more efficient.
+
 This is pure Python implementation of linear search algorithm
 
 For doctests run following command: