How can I find the maximum sum of a sub-sequence using dynamic programming?

Question

I\'m re-reading Skiena\'s Algorithm Design Manual to catch up on some stuff I\'ve forgotten since school, and I\'m a little baffled by his descriptions of Dynamic Programmin

Answer 1

There is a solution like, first sort the array in to some auxiliary memory, then apply Longest Common Sub-Sequence method to the original array and the sorted array, with sum(not the length) of common sub-sequence in the 2 arrays as the entry into the table (Memoization). This can also solve the problem

Total running time is O(nlogn)+O(n^2) => O(n^2) Space is O(n) + O(n^2) => O(n^2)

This is not a good solution when memory comes into picture. This is just to give a glimpse on how problems can be reduced to one another.