Mastering Algorithmic Challenges

What is a Trie and how is it used for auto-complete?

• A Trie is a type of database used for storing large datasets.

• A Trie is a graph-based structure used for image processing.

• A Trie is a tree-like data structure used for efficient prefix-based searching, commonly utilized in auto-complete features.

• A Trie is a linear data structure used for sorting data.

Implement a function to insert a word into a Trie.

• def add_word(root, word):

• def insert_word(root, word):

• def insert(root, word): node = root for char in word: if char not in node.children: node.children[char] = TrieNode() node = node.children[char] node.is_end_of_word = True

• def place_word(root, word):

How do you search for a prefix in a Trie?

• Use a hash map to store the prefixes instead of a Trie.

• Search for the prefix using a binary search algorithm.

• Traverse the Trie character by character, checking for child nodes corresponding to each character of the prefix.

• Count the number of nodes in the Trie before searching.

Write a recursive function to find all permutations of a string.

• def generate_permutations(s): return list(s)

• def permute(s): return sorted(s)

• def permute(s): if len(s) == 0: return [''] permutations = [] for i in range(len(s)): current_char = s[i] remaining_chars = s[:i] + s[i+1:] for p in permute(remaining_chars): permutations.append(current_char + p) return permutations

• def permute(s): return [s]

What is the base case for generating permutations recursively?

• The base case is when the list is sorted.

• The base case is when the list has two elements.

• The base case is when the list is empty or has one element.

• The base case is when the list contains only unique elements.

Explain the N-Queens problem and its constraints.

• The N-Queens problem allows queens to be placed anywhere on the board without restrictions.

• The N-Queens problem requires placing N queens on an N x N board with the constraint that no two queens can attack each other.

• The N-Queens problem involves placing N knights on a chessboard.

• The N-Queens problem requires placing N queens on a 2 x 2 board.

How can backtracking be applied to solve the N-Queens problem?

• Backtracking can be applied by placing queens row by row and checking for conflicts, backtracking when necessary.

• Randomly placing queens on the board without any checks for conflicts.

• Using a greedy algorithm to place queens in the first available position.

• Placing all queens in the first row and checking for conflicts afterwards.

What is a directed graph and how can cycles be detected in it?

• A directed graph is a graph with undirected edges, and cycles can be detected using breadth-first search.

• A directed graph is a graph where edges have a direction, and cycles can be detected using DFS with a recursion stack or Kahn's algorithm.

• A directed graph is a graph with no edges, and cycles can be detected using linear search.

• A directed graph is a graph where all nodes are isolated, and cycles can be detected using Dijkstra's algorithm.

Describe the depth-first search (DFS) method for cycle detection.

• DFS can detect cycles in a graph by using a visited set and a recursion stack to track the path.

• DFS requires a queue to track visited nodes.

• DFS can only detect cycles in directed graphs.

• DFS uses a breadth-first approach to find cycles.

What is the significance of articulation points in a graph?

• Articulation points are irrelevant in directed graphs.

• Articulation points indicate critical connections in a graph whose removal would disrupt connectivity.

• Articulation points help in finding the shortest path between two nodes.

• Articulation points are used to measure the weight of edges in a graph.