UVa 10616 - Divisible Group Sums

10616 - Divisible Group Sums

 * http://acm.uva.es/p/v106/10616.html

Summary
Count how many fixed size subset sums are divisible by a given divisor.

Explanation
We can use memoization to solve this problem. Let $$a_1, a_2, ... a_n$$ be the input numbers, and let $$d$$ be the desired divisor. The state space is current index, current sum mod d, numbers left to pick. When at index i, with mod j, and k numbers left to select, we can either take the item at index i, leaving us with at state $$i + 1, (j + a[i]) % d, k - 1$$, or we can pass on item i, leaving us at state $$i + 1, j, k$$. The total number of subsets at state i, j, k is simply the sum of the of counts at each branch.

Gotchas

 * The input is a signed integer, negative numbers will appear in the input.
 * The modulo (%) operator may not work as intended for negative numbers in your favorite langauge, try it.

Input
10 2 1 2 3 4 5 6 7 8 9 10 5 1 5 2 5 1 2 3 4 5 6 6 2 3 1 1 -1 3 2 0 0

Output
SET 1: QUERY 1: 2 QUERY 2: 9 SET 2: QUERY 1: 1 SET 3: QUERY 1: 1 SET 4: QUERY 1: 1