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Find the Longest Common Subsequence (LCS) of Two Strings.

Certification: Advanced Level Accuracy: 100% Submissions: 2 Points: 15

Write a Python program that finds the longest common subsequence (LCS) between two given strings.

Example 1
    
  
  • Input 1: "ABCDEF"
    • 
  
  • Input 2: "AEBDF"
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  • Output: "ABDF"
    • 
  
  • Explanation:
    
      
      
    • Step 1: Take the input strings.
      • 
      
    • Step 2: Find the longest common subsequence.
      • 
      
    • Step 3: Return the LCS as the result.
      • 
    
    
  
    •
Example 2
    
  
  • Input 1: "AGGTAB"
    • 
  
  • Input 2: "GXTXAYB"
    • 
  
  • Output: "GTAB"
    • 
  
  • Explanation:
    
      
      
    • Step 1: Take the input strings.
      • 
      
    • Step 2: Find the longest common subsequence.
      • 
      
    • Step 3: Return the LCS as the result.
      • 
    
    
  
    •
Constraints
    
  
  • 1 ≤ len(str1), len(str2) ≤ 1000
    • 
  
  • Strings consist of uppercase English letters only.
    • 
  
  • Time Complexity: O(m*n), where m and n are the lengths of the strings.
    • 
  
  • Space Complexity: O(m*n)
    •
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Hint
Solution

Solution Hints

    
  
  • Use dynamic programming to solve this problem.
    • 
  
  • Create a 2D array dp where dp[i][j] represents the length of the LCS of str1[0:i] and str2[0:j].
    • 
  
  • Fill the dp table by comparing characters of both strings.
    • 
  
  • Reconstruct the LCS from the dp table.
    •

Steps to solve by this approach:

 Step 1: Create a 2D DP table where dp[i][j] represents the LCS length of str1[0...i-1] and str2[0...j-1].

 Step 2: Fill the DP table using bottom-up approach with recurrence relation.

 Step 3: If characters match, dp[i][j] = dp[i-1][j-1] + 1.

 Step 4: If characters don't match, dp[i][j] = max(dp[i-1][j], dp[i][j-1]).

 Step 5: Backtrack through the DP table to reconstruct the actual LCS.

 Step 6: Return the longest common subsequence string.

Submitted Code :