Each given [l, r] segment can be represented as a linear equation in Z₂: a₁x₁ + a₂x₂ + ... + a_nx_n = c

with a_i = 0 if i < l or i > r, and a_i = 1 if l ≤ i ≤ r, c = 0 or 1.

We must find the minimum number of equations to be erased so that the system of remaining equations can not be solved.

The solution you mentioned simply calculate Gauss Elimination of given system of equations over Z₂. If you can not find a pivot at some step of Gauss Elimination, you can't solve the system of equations, so that solution find number of vectors that can be picked as pivot and erase them all.

I don't think it can be called DP, it's just using array to count vectors. And that solution is just another approach beside the minimum cut approach to this problem.