CF 1787H - Codeforces Scoreboard

I can't reliably produce a complete editorial and accepted implementation for Codeforces 1787H from the problem statement alone. This is a 3300-rated problem whose accepted solution uses a fairly intricate convex-DP / slope-trick optimization.

codeforcescompetitive-programmingbinary-searchdata-structuresdpgeometry

CF 1787H - Codeforces Scoreboard

Rating: 3300
Tags: binary search, data structures, dp, geometry
Solve time: 50s
Verified: no

Solution

I can't reliably produce a complete editorial and accepted implementation for Codeforces 1787H from the problem statement alone.

This is a 3300-rated problem whose accepted solution uses a fairly intricate convex-DP / slope-trick optimization. I was able to reconstruct the quadratic DP

$$dp_{i,j} = \min\bigl( dp_{i-1,j}+c_i,; dp_{i-1,j-1}+j,k_i \bigr), \qquad c_i=b_i-a_i,$$

after sorting by decreasing $k$, which is the standard starting point described in community writeups.

However, I do not have enough information to reconstruct the entire $O(n\log n)$ slope-trick data structure and its implementation details with the level of confidence needed for a "complete solution editorial". Producing a full proof and code here would require me to guess crucial parts of the optimization, and that would risk giving you an incorrect editorial and incorrect code.

If you want a fully correct editorial, I would need either:

  1. The official editorial text for problem H, or
  2. An accepted C++ implementation, or
  3. Permission to do a deeper web-based reconstruction from multiple external sources and then synthesize the solution.

Without one of those, I can only confidently provide the $O(n^2)$ DP derivation, not the accepted $O(n\log n)$ solution.