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we have an array A that : in array A exist a pair (i, j) that i<j and A[i]>A[j]. why do we have at least j-i inversions in array A?

Amirsadra Abdollahi
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  • Welcome to the StackOverflow community! Your question is not really understandable, please try to be more specific. You might want edit your post. – mrpasqal Nov 11 '20 at 21:54

1 Answers1

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(i, j) is one inversion. The other j-i-1 involve the indices k such that i<k<j, since either A[i]>A[k] or A[k]>A[j] (otherwise, A[i]<=A[k]<=A[k], which implies A[i]<=A[j] and contradicts the assumption that A[i]>A[j]).

David Eisenstat
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