Bin Packing
Description:
A set of n 1-dimensional items have to be packed in identical bins. All bins have exactly the same length l and each item i has length li<=l . We look for a minimal number of bins q such that
- each bin contains at most 2 items,
- each item is packed in one of the q bins,
- the sum of the lengths of the items packed in a bin does not exceed l .
You are requested, given the integer values n , l , l1 , ..., ln , to compute the optimal number of bins q .
Input:
The first line of the input contains the number of items n (1<=n<=105) . The second line contains one integer that corresponds to the bin length l<=10000 . We then have n lines containing one integer value that represents the length of the items.
Output:
Your program has to write the minimal number of bins required to pack all items.
Sample Input:
10 80 70 15 30 35 10 80 20 35 10 30
Sample Output:
6
Hint:
The sample instance and an optimal solution is shown in the figure below. Items are numbered from 1 to 10 according to the input order.
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