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Alien Dictionary Problem

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 15

You are given a sorted dictionary of an alien language that has its own order of characters. The dictionary consists of a list of words sorted lexicographically by the rules of this alien language. Derive the order of characters in this alien language.

You have to assume all letters are in lowercase and there are no duplicates in the alien dictionary.

Example 1
    

  • Input: words = ["wrt", "wrf", "er", "ett", "rftt"]
    • 

  • Output: "wertf"
    • 

  • Explanation: 
      

    • Step 1: Compare adjacent words to find character relationships.
      • 

    • Step 2: From "wrt" and "wrf", we know 't' comes before 'f'.
      • 

    • Step 3: From "wrt" and "er", we know 'w' comes before 'e'.
      • 

    • Step 4: From "er" and "ett", we know 'r' comes before 't'.
      • 

    • Step 5: From "ett" and "rftt", we know 'e' comes before 'r'.
      • 

    • Step 6: These relationships form a directed graph: w->e->r->t->f.
      • 

    • Step 7: Performing a topological sort gives us "wertf".
      • 

    

    •
Example 2
    

  • Input: words = ["z", "x"]
    • 

  • Output: "zx"
    • 

  • Explanation: 
      

    • Step 1: Compare adjacent words to find character relationships.
      • 

    • Step 2: From "z" and "x", we know 'z' comes before 'x'.
      • 

    • Step 3: These relationships form a directed graph: z->x.
      • 

    • Step 4: Performing a topological sort gives us "zx".
      • 

    

    •
Constraints
    

  • 1 ≤ words.length ≤ 100
    • 

  • 1 ≤ words[i].length ≤ 100
    • 

  • words[i] consists of only lowercase English letters.
    • 

  • The input is guaranteed to produce a valid order of characters (no cycles).
    • 

  • Time Complexity: O(total number of characters in all words)
    • 

  • Space Complexity: O(1) or O(unique characters) since there are at most 26 unique characters
    •
GraphDictionaries PwCSwiggy
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Hint
Solution

Solution Hints

    
  
  • Model this problem as a graph where characters are vertices and their ordering constraints are edges.
    • 
  
  • Compare adjacent words to derive the character ordering.
    • 
  
  • Use topological sorting to find the order of characters.
    • 
  
  • Check for inconsistencies in the input that would make the alien dictionary invalid.
    • 
  
  • Handle edge cases like words that are prefixes of other words.
    •

Steps to solve by this approach:

 Step 1: Create a graph where each character is a vertex and ordering relationships are edges.

 Step 2: Compare adjacent words in the dictionary to derive character ordering constraints.

 Step 3: Add directed edges from one character to another based on their relative order.

 Step 4: Track in-degree of each vertex (character) for topological sorting.

 Step 5: Use BFS or Kahn's algorithm to perform topological sorting of characters.

 Step 6: Start with characters having zero in-degree (no characters come before them).

 Step 7: As each character is processed, reduce the in-degree of its neighbors.

 Step 8: Append characters to the result in the order they are processed.

 Step 9: Check if all characters are included in the output to verify a valid ordering exists.

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