IOI Aliens - DP Formulation

Let $dp[i][j]$ = minimum total area to cover the first $i$ points using exactly $j$ photos. Transition: $dp[i][j] = \min_{p < i}(dp[p][j-1] + squareArea(p+1, i) - overlap(p, p+1))$. You cover points $p+1$ through $i$ with one photo, add its area, and subtract the overlap with the previous photo. The overlap term handles double-counting when adjacent photos share cells.

This is critical for correctness. Without it, overlapping cells would be counted twice. Complexity: $O(n^2 k)$. With $n = 100{,}000$ and $k = 100{,}000$, that's $10^{15}$ operations. Completely infeasible.