How do you solve Maximum Score After Applying Operations on a Tree on LeetCode?

Maximum Score After Applying Operations on a Tree (LeetCode #2925) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Dynamic programming helps break down the problem into manageable subproblems.

What is the time complexity of Maximum Score After Applying Operations on a Tree?

The optimal solution for Maximum Score After Applying Operations on a Tree runs in O(n) time and uses O(n) space. This complexity is linear because we visit each node exactly once during the DFS traversal, making it efficient for trees.

What is the brute force solution for Maximum Score After Applying Operations on a Tree?

The brute force approach for Maximum Score After Applying Operations on a Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we explore all possible combinations of nodes we can pick to maximize the score while ensuring the tree remains healthy. This means we will check every node and its children recursively to see if we can include them in our score. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Score After Applying Operations on a Tree?

Maximum Score After Applying Operations on a Tree uses the following concepts: Dynamic Programming, Tree, Depth-First Search. The recommended patterns to study are: Dynamic Programming, Depth-First Search, Tree Traversal.

What are the interview tips for Maximum Score After Applying Operations on a Tree?

Always clarify the problem constraints and edge cases. Think aloud while coding to show your thought process. Practice tree traversal techniques to become comfortable with DFS and BFS.

What are common mistakes when solving Maximum Score After Applying Operations on a Tree?

Not considering the health condition of the tree when selecting nodes. Failing to properly handle the parent-child relationship during DFS.

#2925

Maximum Score After Applying Operations on a Tree

Medium

Dynamic ProgrammingTreeDepth-First SearchDynamic ProgrammingDepth-First SearchTree Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

In the optimal approach, we use dynamic programming with depth-first search (DFS) to calculate the maximum score for each subtree while keeping track of the sum of values. This allows us to efficiently determine which nodes to include in the score without violating the health condition of the tree.

⚙️

Algorithm

3 steps

1Step 1: Build the tree structure from the edges.
2Step 2: Use DFS to calculate the maximum score for each node while keeping track of the sum of values in the subtree.
3Step 3: For each node, decide whether to include its value based on the sum of its children's values.

solution.py23 lines

1# Full working Python code
2class Solution:
3    def maxScore(self, edges, values):
4        from collections import defaultdict
5        tree = defaultdict(list)
6        for a, b in edges:
7            tree[a].append(b)
8            tree[b].append(a)
9
10        def dfs(node, parent):
11            total = values[node]
12            score = 0
13            for child in tree[node]:
14                if child != parent:
15                    child_score, child_sum = dfs(child, node)
16                    score += child_score
17                    total += child_sum
18            if total > 0:
19                score += total
20            return score, total
21
22        max_score, _ = dfs(0, -1)
23        return max_score

ℹ

Complexity note: This complexity is linear because we visit each node exactly once during the DFS traversal, making it efficient for trees.

1Dynamic programming helps break down the problem into manageable subproblems.
2Understanding tree traversal is crucial for efficiently solving tree-related problems.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.