Dividing a Sequence into K ranges

Problem Statement:
Say you have a sequence of N numbers and you want to partition the sequence into K groups such that after applying a cost function c(i) for each group the sum of all cost functions over all groups is minimized or maximized?

Approach:
To divide the sequence into ranges , we will use K keys . The key used to divide the group can be indices or values . If its values then numbers in the
sequence can be used along with values in the sequence to partition values into groups whose key is K.

One way to do this is to use K-for loops , if the key is value based then probable something like this would work:

for i = 1 to n
 for j = 1 to n
  for k = 1 to n
   for l = 1 to n{
    key1 = seq[i]
    key2 = seq[j]
    key3 = seq[k]
    key4 = seq[l]

 }

After dividing the sequence into keys, use the keys to apply and aggregate the result of individual cost functions . Depending upon the requirement reduce the cost functions using functions like min , max depending upon if you want to minimize or maximize your result.

There you go , now u have 1 simple way of dividing a sequence into groups