Inversion Count for an array indicates – how far (or close) the array is from being sorted.
If array is already sorted then inversion count is 0. If array is sorted in reverse order that inversion count is the maximum.
Formally speaking, two elements
a[j] form an inversion if
a[i] > a[j] and
i < j.
2, 4, 1, 3, 5 has three inversions
Yeah I think this question is identical to
327. Count of Range Sum
315. Count of Smaller Numbers After Self
Prove the following Lemma and you will know how to count inversion using merge sort.
Lemma: The number of inversion in array A[1..n] equals the number of inversion in array A[1..m] plus the number of inversion in array A[m+1..n] plus the number of inversion in array Sort(A[1..m]) + Sort(A[m+1..n]).
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