Merge Operations for Minimum Travel Time

You have fixed distances between signs and per-km times on each segment; each merge removes an internal sign and adds its time to the next segment, so after exactly k merges you group adjacent segments (reducing the segment count by k) and want the grouping that minimizes the total sum(length × time). Core challenge: choose which adjacent merges to perform (an optimal partitioning of consecutive segments) — typically solved with DP over cuts/merges to minimize the weighted sum.