Minimize the sum of errors of representative integers

Question

Given n integers between [0,10000] as D₁,D₂...,D_n, where there may be duplicates, and n can be huge:

I want to find k distinct represent

Answer 1

This is is similar to one-dimensional k-medians clustering.

The DP I suggested previously won't work; I think we need a table from (n', k', i) to the optimal solution on D₁ ≤ … ≤ D_n' with k' representatives of which the greatest is i. Given the bounds on D, the running time is on the order of n² k with a very large constant, so you should probably adapt one of the heuristics that people use for k-means.