Maximize non-adjacent sum on an N-ary tree
Problem Description
You are tasked with finding the maximum possible sum of node values in an N-ary tree, subject to a specific constraint: no two selected nodes can be directly connected. This means if you select a node, you cannot select any of its children. Each node in the tree contains a non-negative integer value (0 or positive).
Requirements
- Implement a tree node structure. For example:
value: intchildren: List[Node]
- Implement a function
maxNonAdjacentTreeSum(root) -> intthat takes a pointer or reference to the root node (ornullfor an empty tree) and returns the maximum achievable sum.
Input / Output
- Input:
rootpointer/reference to the root node (ornullfor an empty tree). - Output: An integer representing the maximum achievable sum.
Example
Consider the following tree structure:
- Root node with value 3.
- Child 1 with value 2.
- Child of Child 1 with value 3.
- Child 2 with value 3.
- Child of Child 2 with value 1.
- Child 1 with value 2.
One optimal selection of non-adjacent nodes yields a sum of 7. This can be achieved by selecting the root (value 3), the grandchild under node 2 (value 3), and the grandchild under node 3 (value 1). (3 + 3 + 1 = 7).
Constraints
- The number of nodes
ncan be up to approximately 10^5. - The solution should aim for O(n) time complexity.
- Extra space complexity should be proportional to the recursion depth or explicit stack size.
AI interview prep
Core dilemma
The central engineering conflict is designing an efficient dynamic programming approach for N-ary trees that correctly propagates optimal choices (include or exclude current node) from children to parents, ensuring global optimality while adhering to the non-adjacency constraint and O(N) time complexity.
2 tradeoffs and 3 stress tests locked
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Maximize non-adjacent sum on an N-ary tree
Problem Description
You are tasked with finding the maximum possible sum of node values in an N-ary tree, subject to a specific constraint: no two selected nodes can be directly connected. This means if you select a node, you cannot select any of its children. Each node in the tree contains a non-negative integer value (0 or positive).
Requirements
- Implement a tree node structure. For example:
value: intchildren: List[Node]
- Implement a function
maxNonAdjacentTreeSum(root) -> intthat takes a pointer or reference to the root node (ornullfor an empty tree) and returns the maximum achievable sum.
Input / Output
- Input:
rootpointer/reference to the root node (ornullfor an empty tree). - Output: An integer representing the maximum achievable sum.
Example
Consider the following tree structure:
- Root node with value 3.
- Child 1 with value 2.
- Child of Child 1 with value 3.
- Child 2 with value 3.
- Child of Child 2 with value 1.
- Child 1 with value 2.
One optimal selection of non-adjacent nodes yields a sum of 7. This can be achieved by selecting the root (value 3), the grandchild under node 2 (value 3), and the grandchild under node 3 (value 1). (3 + 3 + 1 = 7).
Constraints
- The number of nodes
ncan be up to approximately 10^5. - The solution should aim for O(n) time complexity.
- Extra space complexity should be proportional to the recursion depth or explicit stack size.