Nested List Weight Sum
The given problem asks to calculate the sum of all integers in the nested list, each multiplied by its depth.
To solve this, we’ll write a recursive function that will traverse the given nested list and multiply each integer by its depth, adding the products together. The base case will be when an integer is found, at which point it is multiplied by its depth and returned.
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Explanation
dfs
Function: A depth-first search function that takes a NestedInteger object and the current depth. If the object is an integer, it returns the product of the integer and the depth. If it’s a list, it recursively calls itself for each element in the list, incrementing the depth by 1.Iterating through
nestedList
: We iterate through the givennestedList
, and for each NestedInteger, we call thedfs
function with depth 1.Returning the Sum: The sum of all the products is returned.
Key Takeaways
- The function makes use of recursion to handle the nested structure of the input.
- The time complexity of this code is (O(N)), where (N) is the total number of integers in the nested list, and the space complexity is (O(D)), where (D) is the maximum depth of the nested list.
System Analyst Hat
Understand the problem
Define the interface Input: NestedInteger[] nested_list Output: Integer
Define the term
- What is a nested list?
- What is a nested integer
- Nested list is an array of nested integers
- Is an array of NestedInteger objects
Terminology
- What is depth?
- Can you see the examples and define depth in simple terms?
- Pattern recognitions skill and ability to ask questions
- In example 1, the pair of ones is nested inside the array whereas 2 is by itself in the array as a single element.
- Depth means how deep the elements are nested inside the array
- What is a nested list?
What should we extract from this problem statement?
- What is implicit?
How can we derive the implicit info from the statement?
When we look at the input
- Input can have nesting that is multiple levels
- What is explicit?
- What is implicit?
How can we derive the implicit info from the statement?
When we look at the input
Programmer’s Hat
[[1,1],2,[1,1]] 2 * 1 + 2 * 2 + 2 * 2 = 10
1 + 42 + 63 1 * depth of 1 + 4 * depth of 4 + 6 * depth of 6
Analyze the concrete cases Generalize it to a valid expression
How to calculate the depth?
[NestedInteger, NestedInteger, NestedInteger] get_list
We can use is_integer to check if the element is an integer. depth = 1 Iterate that list and check if it is an integer
What to calculate the depth for 2 and 3.
- NestedInteger is_integer ? depth = 2
- NestedInteger false depth = 3
DFS comes handy
- Recursive Approach
Solution Outline
- We have to process each element in the list?
- Our unit of work is to process each element in the list
- Do we need to calculate depth for each element.
- We need to keep track of the depth for every recursive call
- Everytime we call the recursive call,
- Two conditions If it is just an integer
- Base Cases Empty array - return 0 Single integer - Example: [2] => Return the integer
Recurrence Relation
weight_sum(input) = weighted(input[1..-1] ) + input[0] * 1 if input[0] is an integer weighted(input[1..-1] ) + input[0] * depth?
if input[0] is a list1 + 42 + 63 = output 1 * depth of 1 + 4 * depth of 4 + 6 * depth of 6
[[1,1],2,[1,1]]
(1+1) * 2 + 2 * 1 + (1+1) * 2 = 10
1 * 2 + 1 * 2 + 2 * 1 + 2 * 1 + 1 * 2
summation * depth +
Time: O( ) Space: O( )
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