Problem 2036. Santa's Cards

This Challenge is inspired by the Packing Santa's Sleigh contest at kaggle that runs until January 26, 2014. Will Elfonso win another kaggle contest? The kaggle contest is a 3-D fitting/optimization.

This Challenge is to place Santa Cards in a minimum area given a board width(columns) and a set of N cards of (rows,columns). Cards can not be rotated.

Input: Card_Array, W ; Card_Array(N,2) and W=width of M array

Output: M ; An X by W array of values 0:N, 0 is unused space

Scoring: Number of rows required to place all cards

Example:

[2 2;3 3;1 2], 5

M

1 1 2 2 2
1 1 2 2 2
3 3 2 2 2

Scores a 3, number of rows

Contest Results: Alfonso put in a tremendous 40,000 point reduction in the last days and appeared unsurpassable. However, a pair of Polish Professors in Mathematics and Computer Science, Marek and Cygan, submitted an astounding further 34,000 point improvement for the win. Alfonso won the Matlab category prize.