UVa 10871 - Primed Subsequence

Summary
Use an $$O(n^2)$$ algorithm with a sieve.

Explanation
First, we reduce the problem of finding the sum between two indices to $$O(1)$$ by linearly summing the elements - $$sum(n) = sum(n-1) + element(n)$$. We can then find the sum between two indices by simply taking the difference - $$sum(i,j) = sum(j) - sum(i)$$. Try out all possibilities of $$i$$ and $$j$$, cohering to the problem specs, and it should run within reasonable time.

Input
3 5 3 5 6 3 8 5 6 4 5 4 12 21 15 17 16 32 28 22 26 30 34 29 31 20 24 18 33 35 25 27 23 19 21

Output
Shortest primed subsequence is length 2: 5 6 Shortest primed subsequence is length 3: 4 5 4 This sequence is anti-primed.