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Alien Dictionary

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

Write a C++ program to solve the Alien Dictionary problem. In an alien language, words are sorted lexicographically based on the alien alphabet. Given a sorted dictionary of alien words, derive the order of letters in the alien alphabet. Return a string representing the order of the alien alphabet. If there is no valid order, return an empty string.

Example 1
    
  
  • Input: words = ["wrt", "wrf", "er", "ett", "rftt"]
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  • Output: "wertf"
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  • Explanation: 
      
      
    • From "wrt" and "wrf", we know 't' comes before 'f'
      • 
      
    • From "wrf" and "er", we know 'w' comes before 'e'
      • 
      
    • From "er" and "ett", we know 'r' comes before 't'
      • 
      
    • From "ett" and "rftt", we know 'e' comes before 'r'
      • 
      
    • Combining all relationships: "wertf"
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    •
Example 2
    
  
  • Input: words = ["z", "x", "z"]
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  • Output: ""
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  • Explanation: 
      
      
    • Since "z" appears both before and after "x", there's a contradiction.
      • 
      
    • No valid alphabet order exists.
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    •
Constraints
    
  
  • 1 ≤ words.length ≤ 100
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  • 1 ≤ words[i].length ≤ 100
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  • words[i] consists of only lowercase English letters
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  • Time Complexity: O(C) where C is the total length of all words
    • 
  
  • Space Complexity: O(1) or O(U^2) where U is the number of unique characters
    •
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Hint
Solution

Solution Hints

    
  
  • Extract character order relationships from adjacent words
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  • Create a directed graph where edges represent order relationships
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  • Check for cycles in the graph (which would indicate an invalid order)
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  • Perform a topological sort on the graph
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  • The topological sort result is the order of the alien alphabet
    •

Steps to solve by this approach:

 Step 1: Create a set of all unique characters in the words.
 Step 2: Build a directed graph where edges represent the ordering relationships between characters.
 Step 3: For each pair of adjacent words, find the first differing character and add an edge.
 Step 4: Check for invalid orderings (e.g., if a longer word is a prefix of a shorter word).
 Step 5: Perform a topological sort using Kahn's algorithm with a queue of nodes with 0 in-degree.
 Step 6: Build the result string by appending characters in topological order.
 Step 7: Validate the result by checking if all characters are included (indicating no cycles).

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