UVa 10810 - Ultra-QuickSort

10810 - Ultra-QuickSort

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Summary
To find number of adjacent swaps necessary to sort a given sequence of integers.

Explanation
In a sequence $$A$$, the pair $$(i, j)$$ is an inversion of $$A$$ if $$i < j$$ and $$A_i > A_j$$. You have to find the inversions count of given sequences of length $$n < 500000$$.

$$n$$ is huge; a brute-force $$O(n^2)$$ bubble sort algorithm won't pass. Similar to UVa 10327, exploit the merge sort algorithm to calculate inversions count.

Note
In the worst case of a completely unsorted list, ($$i, j$$ $$ < n $$, $$i < j$$, $$A_i \ge A_j$$), number of swaps will equal:
 * $$(n - 1) + (n - 2) + (n - 3) + \ldots + (n - (n - 1)) = \frac{n(n-1)}{2}$$

where $$n$$ is the string length. Remembering that we have a huge $$n < 5000000$$, maximum number of swaps will equal:
 * $$\frac{(5000000 -1)(5000000 - 2)}{2} = 12499992500001$$

which far exceeds the capacity of a 32-bit integer. Thus, use 64-bit integers for the inversions count.

Input
5 9 1 0 5 4 3 1 2 3 5 5 2 3 4 1 0

Output
6 0 7