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Modified merge sort that counts inversions during the merge step:
when an element from the right half is selected, the remaining
elements of the left half (mid - i + 1) all form inversions with
that right element.
count_inv [|8; 4; 2; 1; 3; 5; 7; 6|] = 12
Inversions of [8;4;2;1;3;5;7;6]:
with 8: (8,4)(8,2)(8,1)(8,3)(8,5)(8,7)(8,6) = 7
with 4: (4,2)(4,1)(4,3) = 3
with 2: (2,1) = 1
with 7: (7,6) = 1
total = 12
Tests: let rec ... and ... mutual recursion, while + ref + array
mutation, in-place sort with auxiliary scratch array.
145 baseline programs total.