Question: Write an efficient algorithm for the following problem, briefly describe why it is a correct algorithm, and analyze the time complexity. If you cannot find

Write an efficient algorithm for the following problem, briefly describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any polynomial-time algorithm, then give a backtracking algorithm.

  • Problem: Triples
  • Input: A set S of 3k positive integers and an integer B.
  • Output: Print Yes - if S can be split into k triples such that each triple sum to B. Print No - if no such set exists.
  • Example: Input: A = [4,7,2,3,4,4]. B = 12. Output: Yes (because of triples (7,2,3), (4,4,4) )
  • Example: Input: A = [1,7,2,3,1,3]. B = 8. Output: No

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