equilibrium index in an array (#9856)

* equilibrium index in an array

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* equilibrium index in an array

* equilibrium index in an array

* equilibrium index in an array removed type in docstring

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Co-authored-by: ArunSiva <Arunsiva003@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

data_structures/arrays/equilibrium_index_in_array.py

@@ -0,0 +1,59 @@
+"""
+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 -m doctest -v equilibrium_index.py
+
+Given a sequence arr[] of size n, this function returns
+an equilibrium index (if any) or -1 if no equilibrium index exists.
+
+The equilibrium index of an array is an index such that the sum of
+elements at lower indexes is equal to the sum of elements at higher indexes.
+
+
+
+Example Input:
+arr = [-7, 1, 5, 2, -4, 3, 0]
+Output: 3
+
+"""
+
+
+def equilibrium_index(arr: list[int], size: int) -> int:
+    """
+    Find the equilibrium index of an array.
+
+    Args:
+        arr : The input array of integers.
+        size : The size of the array.
+
+    Returns:
+        int: The equilibrium index or -1 if no equilibrium index exists.
+
+    Examples:
+        >>> equilibrium_index([-7, 1, 5, 2, -4, 3, 0], 7)
+        3
+        >>> equilibrium_index([1, 2, 3, 4, 5], 5)
+        -1
+        >>> equilibrium_index([1, 1, 1, 1, 1], 5)
+        2
+        >>> equilibrium_index([2, 4, 6, 8, 10, 3], 6)
+        -1
+    """
+    total_sum = sum(arr)
+    left_sum = 0
+
+    for i in range(size):
+        total_sum -= arr[i]
+        if left_sum == total_sum:
+            return i
+        left_sum += arr[i]
+
+    return -1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()