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Distinct Subsequences

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 12

Write a C++ program to count the number of distinct subsequences of a given string. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Example 1
    
  
  • Input: s = "abc"
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  • Output: 8
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  • Explanation: 
      
      
    • The distinct subsequences are "", "a", "b", "c", "ab", "ac", "bc", and "abc".
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    •
Example 2
    
  
  • Input: s = "aba"
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  • Output: 7
    • 
  
  • Explanation: 
      
      
    • The distinct subsequences are "", "a", "b", "aa", "ab", "ba", "aba".
      • 
      
    • Note that "a" appears twice as a subsequence but is counted only once.
      • 
    
    •
Constraints
    
  
  • 1 ≤ s.length ≤ 1000
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  • s consists of lowercase English letters
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  • Time Complexity: O(n²)
    • 
  
  • Space Complexity: O(n²)
    •
StringsDynamic Programming CapgeminiApple
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Hint
Solution

Solution Hints

    
  
  • Use dynamic programming to solve this problem
    • 
  
  • Consider using a map or array to keep track of last occurrence of characters
    • 
  
  • Calculate number of distinct subsequences ending at each position
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  • Be careful about handling duplicates in the string
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  • Consider empty string as a valid subsequence
    •

Steps to solve by this approach:

 Step 1: Initialize a dp array where dp[i] represents the number of distinct subsequences ending at position i.
 Step 2: Initialize dp[0] = 1 to account for the empty subsequence.
 Step 3: For each character, the number of subsequences doubles (we can either include or exclude it).
 Step 4: Track the last occurrence of each character to handle duplicates.
 Step 5: For duplicates, subtract the count of subsequences that would be counted twice.
 Step 6: Update the last occurrence map for each character.
 Step 7: Return dp[n] - 1 to exclude the empty subsequence if not counting it.

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