Algorithm: Calculating Product Sum from a Special Array with Nested Structures

DIRECTORY.md

@@ -166,6 +166,7 @@
   * Arrays
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
+    * [Product Sum Array](data_structures/arrays/product_sum.py)
   * Binary Tree
     * [Avl Tree](data_structures/binary_tree/avl_tree.py)
     * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py)

data_structures/arrays/product_sum.py

@@ -0,0 +1,70 @@
+"""
+Calculate Product Sum from an Array.
+reference: https://dev.to/sfrasica/algorithms-product-sum-from-an-array-dc6
+
+For doctests run following command:
+python -m doctest -v product_sum.py
+
+We need to create a function that calculates the product sum of a "special" array.
+This array can contain integers or nested arrays. The product sum is obtained by
+adding all the elements together and multiplying by their respective depth.
+
+For example, in the array [x, y], the product sum is (x + y). In the array [x, [y, z]],
+the product sum is x + 2 * (y + z). In the array [x, [y, [z]]],
+the product sum is x + 2 * (y + 3z).
+
+Example Input:
+
+[5, 2, [-7, 1], 3, [6, [-13, 8], 4]]
+"""
+
+
+def product_sum(arr: list[int | list], depth: int) -> int:
+    """
+    Recursively calculates the product sum of an array.
+
+    The product sum of an array is defined as the sum of its elements multiplied by
+    their respective depths.If an element is a list, its product sum is calculated
+    recursively by multiplying the sum of its elements with its depth plus one.
+
+    Args:
+        arr: The array of integers and nested lists.
+        depth: The current depth level.
+
+    Returns:
+        int: The product sum of the array.
+    """
+    total_sum = 0
+    for ele in arr:
+        if isinstance(ele, list):
+            total_sum += product_sum(ele, depth + 1)
+        else:
+            total_sum += ele
+    return total_sum * depth
+
+
+def product_sum_array(array: list[int | list]) -> int:
+    """
+    Calculates the product sum of an array.
+
+    Args:
+        array (List[Union[int, List]]): The array of integers and nested lists.
+
+    Returns:
+        int: The product sum of the array.
+
+    Examples:
+        >>> product_sum_array([1, 2, 3])
+        6
+        >>> product_sum_array([1, [2, 3]])
+        11
+        >>> product_sum_array([1, [2, [3, 4]]])
+        47
+    """
+    return product_sum(array, 1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()