Unclear on dp transition equation for Codeforces Problem 1666J

Revision en2, by butterflies, 2022-07-13 03:49:43

I'm confused on the editorial for 1666J - Job Lookup. View the editorial here

In the editorial for 1666J - Job Lookup, when transitioning from $$$a_{i,k - 1}$$$ and $$$a_{k + 1, j}$$$ to $$$a_{i,j},$$$ $$$c_{u, v}$$$ seems to be only added once (the number of messages going from $$$u$$$ to $$$v$$$, for all $$$u,v$$$ such that $$$i \le u \le k - 1$$$ and $$$k < v \le j$$$) even though the total cost should be $$$c_{u,v} \cdot d_{u,v}$$$. What is going on here?

Thank you for the help!

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en3 English butterflies 2022-07-13 03:49:53 0 (published)
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en1 English butterflies 2022-07-13 03:47:52 572 Initial revision (published)