Solving the 0/1 Knapsack Problem by a Biomolecular DNA Computer

Algorithm 1

(1) For 𝑖=𝑛 to 𝑛+𝑊−1

   For 𝑗=𝑖 down to 𝑛

      Separate (𝑇_𝑗−𝑛,𝑖+1)→(𝑇_{(𝑗−𝑛+1)′},𝑇_𝑗−𝑛)

      Combine (𝑇_{𝑗−𝑛+1},𝑇_{𝑗−𝑛+1},𝑇_{(𝑗−𝑛+1)′})

(2) The capacity of knapsack is 𝐶,

  Discard tubes 𝑇_𝑐+1,𝑇_𝑐+2,𝑇_𝑐+3,…,𝑇_𝑊

  Combine (𝑇₀,𝑇₀,𝑇₁,𝑇₂,…,𝑇_𝑐)

(3) For 𝑖=𝑛+𝑊 to 𝑛+𝑊+𝑉−1

   For 𝑗=𝑖 down to 𝑛+𝑊

      Separate (𝑇_{𝑗−𝑛−𝑊},𝑖+1)→(𝑇_{(𝑗−𝑛−𝑊+1)′},𝑇_{𝑗−𝑛−𝑊})

      Combine (𝑇_{𝑗−𝑛−𝑊+1},𝑇_{𝑗−𝑛−𝑊+1},𝑇_{(𝑗−𝑛−𝑊+1)′})

(4) Read 𝑇_𝑉; else if it was empty then:

  Read 𝑇_𝑉−1; else if it was empty then:

  Read 𝑇_𝑉−2; else if it was empty then:

   ⋮

  Read 𝑇₂; else if it was empty then:

  Read 𝑇₁;