Improved Equilibrium Index of an Array. (#10899)

* Improved Equilibrium Index of an Array.

This is the modifications made to the original code:

1. Create Doctest Instructions: Python "doctest" can be executed by running the following command: python -m doctest -v equilibrium_index.py.

2. Deleted Argument {size}: Deleted the `size` argument because `len(arr)} allows the array's length to be determined inside the function, simplifying and improving the readability of the function signature.

3. Used {enumerate}: To improve code readability and indicate that we're working with element-index pairs, we iterated through the array using both elements and their indices using the `enumerate` function.

4. Optimized the Loop: To prevent pointless additions, the loop was improved by initializing {left_sum} with the value of the first element (arr[0]). Furthermore, since the beginning and last items (0 and size - 1) cannot be equilibrium indices, there is no need to check them, saving further computations.

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

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

data_structures/arrays/equilibrium_index_in_array.py

@@ -2,7 +2,7 @@
 Find the Equilibrium Index of an Array.
 Reference: https://www.geeksforgeeks.org/equilibrium-index-of-an-array/
 
-Python doctests can be run with the following command:
+Python doctest can be run with the following command:
 python -m doctest -v equilibrium_index.py
 
 Given a sequence arr[] of size n, this function returns
@@ -20,35 +20,34 @@ Output: 3
 """
 
 
-def equilibrium_index(arr: list[int], size: int) -> int:
+def equilibrium_index(arr: list[int]) -> int:
     """
     Find the equilibrium index of an array.
 
     Args:
-        arr : The input array of integers.
-        size : The size of the array.
+        arr (list[int]): The input array of integers.
 
     Returns:
         int: The equilibrium index or -1 if no equilibrium index exists.
 
     Examples:
-        >>> equilibrium_index([-7, 1, 5, 2, -4, 3, 0], 7)
+        >>> equilibrium_index([-7, 1, 5, 2, -4, 3, 0])
         3
-        >>> equilibrium_index([1, 2, 3, 4, 5], 5)
+        >>> equilibrium_index([1, 2, 3, 4, 5])
         -1
-        >>> equilibrium_index([1, 1, 1, 1, 1], 5)
+        >>> equilibrium_index([1, 1, 1, 1, 1])
         2
-        >>> equilibrium_index([2, 4, 6, 8, 10, 3], 6)
+        >>> equilibrium_index([2, 4, 6, 8, 10, 3])
         -1
     """
     total_sum = sum(arr)
     left_sum = 0
 
-    for i in range(size):
-        total_sum -= arr[i]
+    for i, value in enumerate(arr):
+        total_sum -= value
         if left_sum == total_sum:
             return i
-        left_sum += arr[i]
+        left_sum += value
 
     return -1