You are given a nested list of integers. Each element is either an integer or a list whose elements may also be integers or other lists. The depth of an integer is defined as the number of lists that it is inside of. For example, the integer 3
in [[1,1],2,[1,1]]
has a depth of 2, while the integer 2
has a depth of 1.
Your task is to compute the weighted sum of all the integers in the list, where the weight of an integer is defined as maxDepth - depth(integer) + 1
. The maxDepth
is the maximum depth of any integer in the entire nested list. In other words, elements at the deepest level have weight 1, and elements at the shallowest level have the greatest weight.
For example:
[[1,1],2,[1,1]]
, the maxDepth
is 2. The weighted sum would be 1*2 + 1*2 + 2*1 + 1*2 + 1*2 = 10
.[1,[4,[6]]]
, the maxDepth
is 3. The weighted sum would be 1*3 + 4*2 + 6*1 = 3 + 8 + 6 = 17
.Write a function that takes a nested list of integers as input and returns the weighted sum as described. You can assume the existence of a NestedInteger
class or interface with the following methods:
isInteger() -> bool
: Returns true
if this NestedInteger
holds a single integer, rather than a nested list.getInteger() -> int
: Returns the single integer that this NestedInteger
holds, if it holds a single integer. Returns None
if this NestedInteger
holds a nested list.getList() -> List[NestedInteger]
: Returns the nested list that this NestedInteger
holds, if it holds a nested list. Returns None
if this NestedInteger
holds a single integer.When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:
The brute force approach involves figuring out the depth of each number within the nested structure. We'll determine the maximum depth first, then use that to weight each number based on its level of nesting.
Here's how the algorithm would work step-by-step:
def nested_list_weight_sum_two(nested_list):
def get_depth(nested_list):
maximum_depth_so_far = 1
for element in nested_list:
if isinstance(element, list):
maximum_depth_so_far = max(maximum_depth_so_far, 1 + get_depth(element))
return maximum_depth_so_far
maximum_depth = get_depth(nested_list)
# Need maximum depth to apply weights
def calculate_weighted_sum(nested_list, current_depth):
weighted_sum = 0
for element in nested_list:
if isinstance(element, list):
weighted_sum += calculate_weighted_sum(element, current_depth + 1)
else:
weight = maximum_depth - current_depth + 1
weighted_sum += element * weight
return weighted_sum
# Start the recursive calculation
return calculate_weighted_sum(nested_list, 1)
This problem asks us to calculate a weighted sum of integers within a nested list structure, where the weight is determined by the depth of the integer from the outermost list. The key idea is to traverse the nested list level by level, accumulating the unweighted sum of the integers at each level and then multiplying the cumulative sum by the level's depth.
Here's how the algorithm would work step-by-step:
def nested_list_weight_sum(nested_list):
def get_depth(nested_list_item):
if not isinstance(nested_list_item, list):
return 1
if not nested_list_item:
return 1
return 1 + max(get_depth(item) for item in nested_list_item)
maximum_depth = get_depth(nested_list)
level_sums = []
def calculate_level_sums(nested_list_item, depth):
if len(level_sums) < depth:
level_sums.append(0)
for item in nested_list_item:
if isinstance(item, int):
level_sums[depth - 1] += item
elif isinstance(item, list):
calculate_level_sums(item, depth + 1)
# Calculating sum for each level
calculate_level_sums(nested_list, 1)
total_weighted_sum = 0
# Multiplying each level sum by depth
for index, level_sum in enumerate(level_sums):
total_weighted_sum += level_sum * (maximum_depth - index)
return total_weighted_sum
Case | How to Handle |
---|---|
Null or empty nestedList input | Return 0 immediately as there are no integers to sum. |
Nested list containing only empty lists | Return 0 because the weighted sum will be zero due to no integers. |
Nested lists with extremely deep nesting levels | Ensure the recursion depth or iterative depth calculation doesn't lead to stack overflow or performance issues; consider an iterative approach if recursion depth becomes a concern. |
Nested list containing very large integer values (potential overflow) | Use appropriate data types (e.g., long) to avoid integer overflow when calculating the weighted sum. |
Nested list with integers having zero value | The zero values should contribute zero to the sum, and should be handled correctly by the weighting calculation. |
Nested List with only single integer at root level | Correctly compute depth and the single integer will be multiplied by the max depth. |
Nested Lists with varying depth distributions | The depth calculation and the weighted sum must correctly handle skewed depth distributions, ensuring that leaves have depth 1 and the root has the largest depth. |
Maximum sized nested list (memory considerations) | Iterative implementations will use less memory than recursive ones for large input lists. |