How do you solve Minimum Time to Collect All Apples in a Tree on LeetCode?

Minimum Time to Collect All Apples in a Tree (LeetCode #1443) 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: Only traverse paths that lead to apples to minimize time.

What is the time complexity of Minimum Time to Collect All Apples in a Tree?

The optimal solution for Minimum Time to Collect All Apples in a Tree runs in O(n) time and uses O(n) space. This complexity arises because we visit each node exactly once during the DFS traversal, making it linear with respect to the number of nodes.

What is the brute force solution for Minimum Time to Collect All Apples in a Tree?

The brute force approach for Minimum Time to Collect All Apples in a Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves exploring all paths from the root to each apple, calculating the total time taken to collect all apples and return. This method is straightforward but inefficient as it checks every possible path. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Minimum Time to Collect All Apples in a Tree?

Clarify the problem requirements and constraints before diving into coding. Think about edge cases, such as trees with no apples. Explain your thought process clearly while coding; this helps interviewers follow your logic.

What are common mistakes when solving Minimum Time to Collect All Apples in a Tree?

Not considering the return trip when calculating time. Failing to handle the parent-child relationship correctly in DFS.

#1443

Minimum Time to Collect All Apples in a Tree

Medium

Hash TableTreeDepth-First SearchBreadth-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)

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Intuition

Time O(n)Space O(n)

The optimal solution uses Depth-First Search (DFS) to traverse the tree and only counts the time for edges that lead to apples. This avoids unnecessary traversal and efficiently calculates the minimum time.

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Algorithm

3 steps

1Step 1: Build a graph representation of the tree using adjacency lists.
2Step 2: Use DFS to traverse the tree, starting from the root.
3Step 3: For each node, check if it or any of its descendants have apples; if so, add the time to traverse that edge (2 seconds for round trip).

solution.py14 lines

1def minTime(n, edges, hasApple):
2    graph = {i: [] for i in range(n)}
3    for u, v in edges:
4        graph[u].append(v)
5        graph[v].append(u)
6    def dfs(node, parent):
7        total_time = 0
8        for neighbor in graph[node]:
9            if neighbor != parent:
10                time = dfs(neighbor, node)
11                if time > 0 or hasApple[neighbor]:
12                    total_time += time + 2
13        return total_time
14    return dfs(0, -1)

ℹ

Complexity note: This complexity arises because we visit each node exactly once during the DFS traversal, making it linear with respect to the number of nodes.

1Only traverse paths that lead to apples to minimize time.
2A depth-first search is effective for tree structures.

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