Question

I was wondering what the best way is to batch a given set of numbers in terms of a processing time.
Take items: 9, 18, 7, 8, 4, 9, 11, 15, 3, 8,
(item 1 has a processing time of 9, item 2 has a processing time of 18, etc.)

If the batch processing time limit is set to say 20, then a possible grouping of the items into batches would be:{1, 3, 5} {2} {4, 6} {8, 9} {7, 10} (group 1 is 9+7+4=20) etc so 5 batches of items have been made where the contents are <= 20.

Ideally i want it to sort them into as fewer groups as possible. Above’s case is a minimum of 5 groups with a content limit of 20…

Thanks

Answer 1

If the batch processing time limit is set to say 20,…

So I assume that there is no element greater than batch processing time limit. Here is my approach:

• Firstly sort the items. Then get 2 pointers for the list, one is at
  index 0 (left-pointer) and the other one at the last index
  (right-pointer).
• Take the element of right-pointer and add it to a sublist. Take the
  element of left-pointer and add it to the same sublist. If the sum of
  the elements in sublist is less than limit, update left-pointer (set
  it to next element) and try adding it. Continue this process until a
  sublist is filled.
• Then start filling the next sublist. Consume all elements to
  construct sublists.

Implementation in Java:

int[] input = { 9, 18, 7, 8, 4, 9, 11, 15, 3, 8 }; // Input items.
Arrays.sort(input); // Sort the items.
int left = 0, right = input.length - 1; // Left and right pointers.
int remainder = 0, limit = 20;

// list of groups.
ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();

while (right >= left) 
{
    ArrayList<Integer> subList = new ArrayList<Integer>();
    list.add(subList);
    // Add the current maximum element.
    subList.add(input[right]);
    if (right == left)
        break;
    remainder = limit - input[right];
    right--;

    // Add small elements until limit is reached.
    while (remainder > input[left]) {
        subList.add(input[left]);
        remainder = remainder - input[left];
        left++;
    }

    remainder = 0; // Reset the remainder.
}

Printing the groups:

for (ArrayList<Integer> subList : list) 
{
    for (int i : subList)
        System.out.print(i + " ");
    System.out.println();
}

Output: (Each line denotes a group of numbers)

18 
15 3 
11 4 
9 7 
9 8
8