Implement DFS and tree algorithms

Part 1 (DFS on graph): Given an undirected graph with n nodes labeled 0..n-1 and an edge list, implement a function that returns all connected components using depth-first search. Each component should be returned as a list of node labels in ascending order; the list of components should be sorted by each component’s smallest label. Discuss time/space complexity and how you would handle very large sparse graphs. Part 2 (Binary tree): Given the root of a binary tree, implement (a) level-order traversal that returns values grouped by level, and (b) a function that determines whether the tree is height-balanced (for every node, the height difference between left and right subtrees is at most 1). Provide complexity and key test cases.