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.

Describe how backtracking in DFS affects space complexity.

• It reduces space complexity

• It increases space complexity

• It has no effect

• It depends on the number of nodes

What is the maximum space taken in the call stack during the first call of DFS?

• 1

• 2

• 3

• 4

Explain the worst-case scenario for space complexity in DFS.

• When all nodes are in a straight line

• When the tree is balanced

• When there are no nodes

• When the tree is full

What is the time complexity of Depth First Search (DFS) in terms of the number of nodes?

• O(1)

• O(n)

• O(n^2)

• O(log n)

How does the space complexity of DFS depend on the structure of the tree?

• It is always constant

• It depends on the depth of the tree

• It is proportional to the number of nodes

• It is irrelevant