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train55's blog

By train55, history, 2 months ago, In English,

Can anyone give me the solution or send me the solution to this problem: I have an integer s I want to know the number of ways to express s as a sum of different elements from the array a[].(without repetition). Thank you!!

 
 
 
 
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2 months ago, # |
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constrains?

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2 months ago, # |
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Maybe this is what you need, link

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    2 months ago, # ^ |
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    He said no repetitions. In that case, try all subsets of a[ ]. Unless the problem limits the values of s and values in the array, I'm not aware of any polynomial-time algorithm.

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      2 months ago, # ^ |
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      So where is a way repeated in the solution(link)?

      Like if as given $$$s$$$=$$$4$$$ and $$$a$$$ = {1,2,3}.

      $$$ways$$$:
      1.{1,1,1,1}
      2.{1,1,2}
      3.{1,3}
      4.{2,2}
      These are the $$$4$$$ possible ways.right?

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        2 months ago, # ^ |
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        In the first way, you're using 1 4 times. I think that's what the OP meant by repetition.

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2 months ago, # |
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This is just basic knapsack dp. Essentially you do the coin change dp solution mentioned above except iterate through the array backwards to avoid repetition.