What is the optimal time complexity of solving DFS?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for DFS?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in DFS?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for DFS?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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DSA SectionEasy

DFS

Learn how to solve the 'DFS' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function dfs_traversal(graph, start) that performs a Depth-First Search traversal on a graph (represented as an adjacency list of neighbor lists) starting from the node start. Return a list of nodes in the order they were first visited. In case of multiple neighbors, visit them in the order they appear in the adjacency list.

Constraints

•1 <= V <= 500
•0 <= E <= 1000

Examples

Example 1

Input

graph = {0: [1, 2], 1: [2], 2: [0, 3], 3: [3]}, start = 2

Output

[2, 0, 1, 3]

Explanation

From 2, we visit neighbor 0. From 0, we visit neighbor 1. Neighbor 2 of 1 is already visited. Backtrack to 0, then to 2, then visit neighbor 3.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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