I'm trying to come up with a recursive solution for this problem but I haven't been able to so far. Any advice/pointers here?
I tried 0-1 knapsack style but there is an issue with backtracking the array.
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It appears that the statement is actually asking for the number of permutations of 1... n with k inversions. If In(t) is the number of permutations of size n with t inversions, then
. This recurrence can be calculated in O(nt) using prefix sums on In.