Date: 2024-06-29
The "Alien Dictionary" problem involves determining the order of characters in an alien language based on a sorted list of words in that language. Given a list of words sorted lexicographically by the rules of this new language, you need to derive the order of letters in the alien alphabet.
Understand the Problem Requirements:
You are given a list of words sorted lexicographically by the rules of the alien language.
Your task is to determine the order of characters in the alien language.
Model the Problem as a Graph:
Treat each character as a node in a directed graph.
Draw a directed edge from character u to character v if u comes before v in the alien language.
Build the Graph:
Iterate through the list of words and for each pair of adjacent words, find the first character that differs.
Add a directed edge from the first differing character of the first word to the first differing character of the second word.
Keep track of the in-degree (number of incoming edges) for each character.
Perform Topological Sorting:
Use topological sorting to find a valid order of characters in the directed graph.
Characters with zero in-degrees are placed at the beginning of the order, and their edges are removed from the graph.
Continue the process until all nodes are processed.
Detect Cycles:
If there is a cycle in the graph, it indicates a contradiction in the given words, and it is impossible to determine a valid character order.
Ensure cycle detection is part of your topological sort implementation.
Return the Result:
If a valid topological sort is found, return the characters in the sorted order.
If not, return an indication that no valid order exists (e.g., an empty string).
Initialize the Graph:
Use a dictionary to represent the adjacency list of the graph.
Use another dictionary to count the in-degrees of each character.
Build the Graph from Words:
Compare each pair of adjacent words to build the graph.
Update the adjacency list and in-degree counts accordingly.
Topological Sorting Using Kahn's Algorithm:
Initialize a queue with all characters having zero in-degrees.
Process each character, append it to the result, and reduce the in-degrees of its neighbors.
Add neighbors with zero in-degrees to the queue.
Detect if all characters are processed; otherwise, a cycle exists.
Handle Edge Cases:
Consider edge cases such as single-word input, multiple identical words, and inconsistent character orders.
By following this structured approach, you can systematically solve the "Alien Dictionary" problem, ensuring both correctness and efficiency.
Number of Islands (Leetcode 200)
Category: Easy 🌟
Why it helps: This problem helps you practice graph traversal techniques like Depth-First Search (DFS) and Breadth-First Search (BFS) on a grid.
Knowledge and practice gain: You will gain familiarity with traversing a graph-like structure, marking visited nodes, and understanding connected components, which are essential for understanding the dependencies in the "Alien Dictionary."
Link: Number of Islands
Course Schedule (Leetcode 207)
Category: Medium ⭐⭐
Why it helps: This problem introduces you to detecting cycles in a directed graph using topological sorting, which is directly applicable to the "Alien Dictionary."
Knowledge and practice gain: You will learn about topological sorting, cycle detection, and the use of DFS and BFS in the context of directed graphs.
Link: Course Schedule
Find the Town Judge (Leetcode 997)
Category: Easy 🌟
Why it helps: This problem involves understanding relationships in a graph where you need to find a node with specific properties (e.g., in-degree and out-degree).
Knowledge and practice gain: You will practice identifying nodes based on their connections, which can be useful for understanding how characters depend on each other in the "Alien Dictionary."
Link: Find the Town Judge
Graph Valid Tree (Leetcode 261)
Category: Medium ⭐⭐
Why it helps: This problem requires you to determine if a graph is a valid tree, focusing on graph connectivity and the absence of cycles.
Knowledge and practice gain: You will understand how to verify the structure of a graph, ensuring there are no cycles and that it is fully connected, both of which are important for processing graph data structures.
Link: Graph Valid Tree
Find Whether Path Exists in Graph (Leetcode 1971)
Category: Easy 🌟
Why it helps: This problem involves determining if there is a path between two nodes in an undirected graph using graph traversal.
Knowledge and practice gain: You will practice basic graph traversal techniques and pathfinding, which are useful for ensuring all dependencies are met in the "Alien Dictionary."
Course Schedule II (Leetcode 210)
Category: Medium ⭐⭐
Why it helps: This problem extends the "Course Schedule" problem by requiring you to return the order of courses, which is a direct application of topological sorting.
Knowledge and practice gain: You will gain a deeper understanding of topological sorting and how to construct a valid order of nodes in a directed graph, a key skill for the "Alien Dictionary."
Link: Course Schedule II
Minimum Height Trees (Leetcode 310)
Category: Medium ⭐⭐
Why it helps: This problem requires you to find the roots of the minimum height trees, involving central nodes in a graph.
Knowledge and practice gain: You will learn about handling trees and understanding the centrality of nodes, which can help in visualizing and processing hierarchical data structures.
Link: Minimum Height Trees
All Paths From Source to Target (Leetcode 797)
Category: Medium ⭐⭐
Why it helps: This problem involves finding all paths in a directed acyclic graph (DAG), similar to finding all valid orderings in the "Alien Dictionary."
Knowledge and practice gain: You will practice working with DAGs and understanding multiple paths, which is useful for comprehending all possible character orders in the "Alien Dictionary."
Reconstruct Itinerary (Leetcode 332)
Category: Medium ⭐⭐
Why it helps: This problem involves reconstructing an itinerary from a list of flights, requiring careful traversal of edges.
Knowledge and practice gain: You will understand how to manage and reconstruct sequences based on given constraints, which helps in forming valid character sequences in the "Alien Dictionary."
Link: Reconstruct Itinerary
Sequence Reconstruction (Leetcode 444)
Category: Medium ⭐⭐
Why it helps: This problem involves determining if a sequence can be uniquely reconstructed from subsequences, closely related to determining unique ordering in the "Alien Dictionary."
Knowledge and practice gain: You will practice topological sorting in the context of unique sequence reconstruction, directly applicable to determining a valid character order in the "Alien Dictionary."
Link: Sequence Reconstruction