I just solved this problem in uva.onlignejudge 10664 a classical dp problem ( you have n weights and you want to find a way to distribute these weights equally between 2 people ) so you only need a simple dp to find (total sum of weights ) / 2 using given weights .

but what if we decided to shares these weight between k people how to solve that ? do we have to keep track on the chosen weights ??

Solved the problem : http://lightoj.com/volume_showproblem.php?problem=1147 The problem is almost similar to your question . Thanks .

obviously you didn't read my statement will , i was able to solve that problem for 2 people now i'am asking how we solve it for k people ??

You can do brute-force for

O(k^{n}) or dp for O(k^{2}*MAXSUM^{k — 1}).I dont think it's possible to solve it faster.

can you give your dp approach ??

dp[i][val1][val2]...[val k -1] is it possible to distribute birst k items, so first have val1, second — val2 and so on. There are

k*MAXSUM^{}(k- 1) states and you need O(k) to do step, you simply choose who takes ith item.