Split k trades across two assets

Question

You are given two price paths, pricesa and pricesb, and a total budget of k round trips to split between them however you like (no overlapping positions on either asset). Return the maximum combined profit.

Accepted Answer

Solve each asset in isolation first, then combine. For a single path, the standard k-transaction machine already gives you, as a by-product, the best profit for every budget from 0 to k: sell[j] is the best you can do with at most j trades on that path (not trading is always allowed, so sell[j] is non-decreasing in j). Compute that whole array bestA[0..k] for asset A and bestB[0..k] for asset B. Now the only remaining choice is how many of the k trades go to A: give j to A and the rest to B. Because each array is non-decreasing, spending the full budget is never worse than leaving trades unus…

Split k trades across two assets

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