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Assign a value for marbles of each color.Sort them O(nlogn).
If the no of colors are 2 or 3 then we can do it in O(n)

sry i am not clear with question pls give one input and output test case for this problem.

It resembles to concept of bucket sort as commented about assign a value to each color say red = 0.1 blue = 0.2 etc

let a[] be the array of marbles scattered (0.1,0.2,0.1,0.4,0.2....)
for(int i=0; i<n; i++)
insert a[i] into b[n*a[i]]
where n is total number of colors

insert in to b using a linklist

refer CLRS pg 174 Bucketsort

that does it in O(n) with space complexity n+ (total no of marbles)/n

This is an example of Dutch National Flag problem.
Try Wikipedia search

As per my interpretation, the boxes of the marbles are not labelled with any particular colour. As an example consider two boxes B1 and B2
B1 has 70 Green and 20 Red balls
B2 has 30 Green and 10 Red balls
Optimal way would be to put 30 Green from box B2 to B1 and 20 Red from B1 to B2.