Depth-first Search Complexity

The video tutorial discusses the time and space complexity of Depth First Search (DFS) algorithms, focusing on preorder, inorder, and postorder traversals. It explains that the time complexity is O(n) due to the need to visit each node, while space complexity depends on the tree's depth, potentially reaching O(d) in the worst case. The tutorial also covers the concept of activation records in the call stack, emphasizing the impact of tree structure on space usage. Practical tips are provided for implementing DFS without unnecessary arrays, using print statements instead. The session concludes with a recap of key points.

What is the time complexity of DFS for preorder, inorder, and postorder traversals?

• O(n^2)

• O(1)

• O(log n)

• O(n)

In the worst-case scenario, what is the space complexity of DFS?

• O(log n)

• O(n)

• O(1)

• O(n^2)

How does the space complexity of DFS relate to the tree's structure?

• It is independent of the tree's structure.

• It depends on the depth of the tree.

• It depends on the number of nodes.

• It is always constant.

If a tree is a straight line with 10 nodes, how many activation records will DFS use?

• 5

• 20

• 10

• 15

What is a practical tip for outputting DFS results without using extra space?

• Use a linked list.

• Use a print statement instead of an array.

• Use a larger array.

• Store results in a file.