How do you solve Maximum Number of K-Divisible Components on LeetCode?

Maximum Number of K-Divisible Components (LeetCode #2872) 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: Understanding tree structure is crucial for optimizing DFS traversal.

What is the brute force solution for Maximum Number of K-Divisible Components?

The brute force approach for Maximum Number of K-Divisible Components is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible ways to remove edges and counting the resulting components. This is straightforward but inefficient, as it doesn't leverage the tree's structure. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Number of K-Divisible Components?

Maximum Number of K-Divisible Components uses the following concepts: Tree, Depth-First Search. The recommended patterns to study are: Depth-First Search, Tree Traversal.

What are the interview tips for Maximum Number of K-Divisible Components?

Always clarify the problem constraints and edge cases with the interviewer. Explain your thought process and reasoning as you code. Practice DFS and tree traversal problems to build intuition.

What are common mistakes when solving Maximum Number of K-Divisible Components?

Not considering edge cases where all nodes are leaves. Failing to correctly track visited nodes during DFS.

#2872

Maximum Number of K-Divisible Components

Hard

TreeDepth-First SearchDepth-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)

The optimal solution uses Depth-First Search (DFS) to calculate the sum of values in each subtree while checking divisibility by k. This allows us to efficiently determine where to split the tree without generating all combinations.

⚙️

Algorithm

4 steps

1Step 1: Build the graph representation of the tree using an adjacency list.
2Step 2: Perform a DFS to calculate the sum of values for each subtree.
3Step 3: If the sum of a subtree is divisible by k, increment the component count and return 0 (indicating this subtree can be split).
4Step 4: If not, return the sum of the subtree to its parent.

solution.py25 lines

1# Full working Python code
2
3def maxKDivisibleComponents(n, edges, values, k):
4    from collections import defaultdict
5
6    graph = defaultdict(list)
7    for a, b in edges:
8        graph[a].append(b)
9        graph[b].append(a)
10
11    components = 0
12
13    def dfs(node, parent):
14        nonlocal components
15        total = values[node]
16        for neighbor in graph[node]:
17            if neighbor != parent:
18                total += dfs(neighbor, node)
19        if total % k == 0:
20            components += 1
21            return 0  # This subtree can be split
22        return total
23
24    dfs(0, -1)
25    return components

ℹ

Complexity note: The time complexity is O(n) because we perform a single DFS traversal of the tree, visiting each node once. The space complexity is O(n) due to the graph representation and the recursion stack.

1Understanding tree structure is crucial for optimizing DFS traversal.
2Divisibility checks can be efficiently integrated into the DFS process.

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