JavaScript algorithm for determining the most optimal combination (with the fewest items) of lengths that are under a specified threshold

What is the optimal way to select a combination of n values so that their sum (n1+n2+n3+n4+n5) is minimized?

maxDiff = D
requiredLength = L

lengthArray = [l1, l2, l3, l4, l5, l6]

1st constraint,
diff = L - (n1*l1 + n2*l2 + n3*l3 + n4*l4 + n5*l5)

2nd constraint,
0 >= diff <= D

In this scenario, the l values represent various sheet lengths (e.g. 1000mm, 1100mm, ..., 2000mm, etc.) The user inputs the maximum required length, represented by L. The goal is to determine the best combination of n values (greater than or equal to 0) that will minimize the number of sheets needed.

If there is a difference, it signifies the gap between the sheets and could potentially be zero.

javascriptarraysalgorithmcombinationspermutation

Answer №1

If you're looking for a solution using dynamic programming, here's how to approach it:

Start by creating an array A of length L+1 with item counters set to 0 and the last added item.

Iterate through the array from index range k, going from A[i] to A[l].

If adding item li to A[k-li] results in a better count in the cell A[k] (lower value), update the current value in A[k]. Here's the pseudocode:

if (A[k-l[i]].count + 1 < A[k].count) 
   {
     A[k].count = A[k-l[i]].count + 1; 
     A[k].item =  l[i];
   }

Finally, check if the item set in A[L] can be found. If not, backtrack to find the nearest result.

To retrieve the items, move down by A[k].item steps.

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