Algorithms

Weighted Inversion Count

Difficulty

Asked at D.E. Shaw

Theory: Algorithms Under a Complexity Bound

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x xxxxxxx xxxx xxxxxxxx xxx xxxxxxxxx x xxxxxx xxxx-xxxxxxx xx xxxxxxxx xxx xxxxx xx xxxxxxxxxxxx xxxx xxx xxxxx xxx xx xxxxx: xxx xxxxxx x xxxxx xxxxx xxxx xx xxxxxxx, xxx x xxxxx xxxxx xxx xxxxxxx xxx xxxxxxxxx xx x xxxxxx xx xxx. xxxxx xxxxxxxxxx xxx xxxxx; xxxxx xxxxxxxx xxxxxxxxxx xxx xxx xxxxxx xxx xxxx xxxxxxxx xxxxxx xxxxxxx.

xxxxx x xxxx xx xxxxxxxx xxxxxx (xxxxxxxx, xxxxxxxx, xx xxxx), xxxxxxxxx xxxxx_xxxxxxxx_xxxxxxxxxx(xxxxxx) xxxxxxxxx xxx xxxxxx xx xxxxx xxxxx (x < x) xxxx xxxxxx[x] >= x * xxxxxx[x].

xxxxxxxx

xxxxx_xxxxxxxx_xxxxxxxxxx([x, x, x, x])
# x  (xxx xxxxx (x, x) xxx (x, x); xxxx x >= x * x xxxxxx)

xxxxx_xxxxxxxx_xxxxxxxxxx([-x, -x])
# x  (-x >= x * -x = -x; xxx xxxxxxxxx xx >= xxx xxxxx xxxxxx)

xxxxxxxxxxx

x <= xxx(xxxxxx) <= xxxxxx, xxxx xxxxx xxxx xx x xx-xxx xxxxxxx.
xxxxxx xxx xxxxxx; xxx xxxxxxxxxx xx >=, xx xxxxx-xxxxxxxx xxxxx xxxxx.
xxxxxxxx xxx xxxxx xx (x(x^x)), (x xxxxx xx^{xx}) xxxxxxxxxxx xx xxx xxxxxxx xxxxxx xxxx; xxx xxxx xxx xxxxxxxx xx xxxxxxxxx xx xxxxxxxxx xxxx xx (x(x xxx x)).

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Language: Pythoncount_weighted_inversions

def count_weighted_inversions(values):
    """..."""
    # ...
    pass

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