UVa 10131 - Is Bigger Smarter?

10131 - Is Bigger Smarter

 * http://acm.uva.es/p/v101/10131.html

Summary
A standard Dynamic Programming (Longest Increasing Subsequence) problem.

Explanation
This can also be viewed as a Graph Theory problem, as the Longest Increasing Subsequence problem reduces to finding the longest path in a Directed Acyclic Graph. Therefore, this problem can be solved in $$O(n log n)$$. Using each elephant as a vertex, an edge can be drawn from a bigger, smarter (strictly) elephant to one that is less so.

Input
6008 1300 6000 2100 500 2000 1000 4000 1100 3000 6000 2000 8000 1400 6000 1200 2000 1900

Output
4 4 5 9 7