5 Best Ways to Calculate Nested List Weighted Sum II in Python

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πŸ’‘ Problem Formulation: Calculating the nested list weighted sum, known as Nested List Weighted Sum II, involves a specific pattern where each element’s value is multiplied by its distance from the bottom-most list. Given a nested list like [[1,1],2,[1,1]], the desired output for the given structure would be 8, since the bottom-most integers’ weight is 1, and the single integer in the upper list has a weight of 2.

Method 1: Depth Calculation and Summation

This method entails figuring out the depth of the nested list and calculating the sum by giving weights based on the distance from the deepest level. The function specification would involve recursively determining the depth and then applying that depth to weigh the elements during summation.

Here’s an example:

def depth_sum_inverse(nestedList):
        def max_depth(lst, level=1):
            return max([level]+[max_depth(item, level+1) for item in lst if isinstance(item, list)])
        def weight_sum(lst, level, max_level):
            return sum([weight_sum(item, level-1, max_level) if isinstance(item, list) else item * level for item in lst])
        return weight_sum(nestedList, max_depth(nestedList), max_depth(nestedList))

Output: 8

In the provided code snippet, max_depth function calculates the maximum depth of a nested list, while weight_sum multiplies each number by the depth at which it is found, inversely weighted. Hence, by calling these functions, we derive the weighted sum required.

Method 2: Iterative Reversal Method

An iterative approach reverses the nested list and then accumulates the sums while keeping track of running total. This approach removes the recursion overhead and potentially improves performance for deeply nested structures.

Here’s an example:

def nested_list_weight_sum(nestedList):
        reversed_list = nestedList[::-1]
        weighted_sum = 0
        cumulative = 0
        for item in reversed_list:
            if isinstance(item, list):
                cumulative += sum(item)
                cumulative += item
            weighted_sum += cumulative
        return weighted_sum


Output: 8

The code samples a strategy where we iterate over the reversed list, continuously aggregating the sum, and add this aggregate sum to the weighted sum. Each list’s integers add to the running total and thereby to the final weighted sum.

Method 3: Using a Queue

This approach makes use of a queue to process the elements level by level from the end. By dequeuing the current level and enqueuing the nested lists, we can compute the weighted sum in a breadth-first manner.

Here’s an example:

from collections import deque

    def nested_list_weight_sum_queue(nestedList):
        queue = deque([nestedList])
        prev = 0
        total = 0
        while queue:
            level_total = 0
            for _ in range(len(queue)):
                sublist = queue.popleft()
                new_list = []
                for item in sublist:
                    if isinstance(item, list):
                        level_total += item
                level_total += prev
            prev = level_total
            total += level_total
        return total


Output: 8

Introducing the queue enables us to sum values level by level, always adding the previous level’s sum to the current, encapsulating the nested weights of the elements. This mimics a breadth-first search algorithm and yields the correct weighted sum.

Method 4: Unpacking Nested Lists with Depth Record

This solution involves flatterning the nested list while keeping track of each value’s depth in a tuple, then calculating the weighted sum from this flat structure.

Here’s an example:

def weighted_sum_unpacked(nestedList):
        flat_list = []

        def unpack(lst, depth):
            for item in lst:
                if isinstance(item, list):
                    unpack(item, depth+1)
                    flat_list.append((item, depth))
            return flat_list
        max_depth = max([dep for _, dep in unpack(nestedList, 1)])
        return sum([val * (max_depth - dep + 1) for val, dep in flat_list])


Output: 8

By flattening the list and recording each item’s depth, we can then iterate through a simple list to calculate the inverse-weighted sum. This alternative method can be more intuitive for those more comfortable with processing flat data structures.

Bonus One-Liner Method 5: Using Comprehensions and Recursion

A concise and recursive approach can be achieved by using list comprehensions to recursively apply weights to the summed elements, with a one-liner function demonstrating Python’s expressive capacity.

Here’s an example:

weighted_sum_one_liner = lambda lst, depth=1: sum(weighted_sum_one_liner(item, depth+1) if isinstance(item, list) else item for item in lst[::-1]) * depth


Output: 8

This compact piece of code accomplishes the task by reversing the list and applying the weight to each sublist or integer, multiplying by depth and recursing accordingly. In stark contrast to the iterative methods, this leverages Python’s list comprehensions and lambda functions to achieve an elegant solution.


  • Method 1: Depth Calculation and Summation. Offers a straightforward recursive approach. Could be less performant for very deep lists due to recursion limits.
  • Method 2: Iterative Reversal Method. Non-recursive and simplifies calculation via iteration. Potentially faster but may use more memory in storing cumulative sums.
  • Method 3: Using a Queue. Implements breadth-first logic, thus has clear conceptual understanding. Can be slower than other methods due to queue operations.
  • Method 4: Unpacking Nested Lists with Depth Record. Great for visualizing data. Could be slightly inefficient since it requires two passes over the data.
  • Bonus Method 5: One-Liner using Comprehensions. Extremely concise and Pythonic. The recursive nature may not be as efficient or easily understandable for deeply nested lists.