How do you solve Sum of Distances in Tree on LeetCode?

Sum of Distances in Tree (LeetCode #834) 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 traversal is crucial for solving tree-related problems efficiently.

What is the time complexity of Sum of Distances in Tree?

The optimal solution for Sum of Distances in Tree runs in O(n) time and uses O(n) space. The time complexity is O(n) because we perform two DFS traversals of the tree, each visiting every node once.

What is the brute force solution for Sum of Distances in Tree?

The brute force approach for Sum of Distances in Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute-force approach, we calculate the distance from each node to every other node individually. This is straightforward but inefficient, as it involves repeated calculations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Sum of Distances in Tree?

Sum of Distances in Tree uses the following concepts: Dynamic Programming, Tree, Depth-First Search, Graph Theory. The recommended patterns to study are: Depth-First Search (DFS), Dynamic Programming on Trees.

What are the interview tips for Sum of Distances in Tree?

Always clarify the problem and constraints before diving into coding. Think about edge cases, especially with trees (like single-node trees). Explain your thought process while coding; it helps interviewers understand your reasoning.

What are common mistakes when solving Sum of Distances in Tree?

Not considering the tree structure and its properties, leading to inefficient solutions. Failing to account for the parent-child relationship during traversal.

#834

Sum of Distances in Tree

Hard

Dynamic ProgrammingTreeDepth-First SearchGraph TheoryDepth-First Search (DFS)Dynamic Programming on Trees

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 approach leverages the tree structure to calculate distances efficiently. By using a two-pass DFS, we can compute the distances in linear time.

⚙️

Algorithm

3 steps

1Step 1: Perform a DFS from an arbitrary root (e.g., node 0) to calculate the initial distances and subtree sizes.
2Step 2: Use the results from the first DFS to compute the distances for all nodes based on the parent's distance.
3Step 3: Return the final distances for all nodes.

solution.py26 lines

1def sumOfDistancesInTree(n, edges):
2    from collections import defaultdict
3    graph = defaultdict(list)
4    for a, b in edges:
5        graph[a].append(b)
6        graph[b].append(a)
7
8    answer = [0] * n
9    count = [1] * n
10
11    def dfs1(node, parent):
12        for neighbor in graph[node]:
13            if neighbor != parent:
14                dfs1(neighbor, node)
15                count[node] += count[neighbor]
16                answer[node] += answer[neighbor] + count[neighbor]
17
18    def dfs2(node, parent):
19        for neighbor in graph[node]:
20            if neighbor != parent:
21                answer[neighbor] = answer[node] - count[neighbor] + (n - count[neighbor])
22                dfs2(neighbor, node)
23
24    dfs1(0, -1)
25    dfs2(0, -1)
26    return answer

ℹ

Complexity note: The time complexity is O(n) because we perform two DFS traversals of the tree, each visiting every node once.

1Understanding tree traversal is crucial for solving tree-related problems efficiently.
2Using properties of trees (like subtree sizes) can help optimize calculations.

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