'Algorithm to find minimum number of days to color boxes by one or more robots

I have n boxes which should be colored. Each day robot can color one box or generate another robot, who works exactly as his parent starting next day.

i.e., if on Sunday I have one robot and 10 balls, on Monday:

  1. There is one robot, 1 colored boxes and 9 uncolored boxes, or

  2. There are 2 robots and 10 uncolored boxes.

I need to find the minimum number of days to color all boxes.

I thought to solve that using dynamic programming:

T(n,1) = min(T(n-1,1) + 1, T(n,2))

But I am not sure how to create a DP matrix and if DP is correct approach at all.

algorithmdynamic-programming


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