Inverse-Depth Weighted Sum of a Nested Integer List

Question

The question asks the candidate to calculate the inverse-depth weighted sum of a nested integer list, where deeper integers contribute less to the overall sum.

Codemia · Accepted Answer

To solve the problem of calculating the inverse-depth weighted sum of a nested integer list, we need to traverse the list recursively. Each integer's contribution to the sum is inversely proportional to its depth in the nested structure. We will maintain a depth counter that increments as we go deeper into the nested lists.

The algorithm involves a recursive function that processes each element of the nested list. If the element is an integer, we add its value divided by its depth to the sum. If the element is a list, we recursively call the function on that list, increasing the depth by one. Here is a sample implementation in Python:

```python
def depthSumInverse(nestedList):
    def dfs(nestedList, depth):
        total = 0
        for elem in nestedList:
            if elem.isInteger():
                total += elem.getInteger() / depth
            else:
                total += dfs(elem.getList(), depth + 1)
        return total
    max_depth = 1  # Assume at least depth 1
    return dfs(nestedList, max_depth)
```

The time complexity of this algorithm is O(N), where N is the number of integers in the nested list. Each integer is processed once. For achieving O(1) query time for multiple queries, we can precompute the total weighted sum and store it, allowing us to return the result immediately for each query.

When implementing this solution, consider edge cases such as an empty nested list or lists containing only empty sublists. Ensure that the recursive function handles these cases gracefully without throwing errors.

To optimize further, we could preprocess the nested list to compute the maximum depth and store intermediate results. This would allow us to answer queries in constant time by leveraging precomputed values, reducing the need for repeated calculations.

Inverse-Depth Weighted Sum of a Nested Integer List

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