Auction Clearing Engine

xxxxxxxxxx xxxxxxx xxxx xxx xxxxxxxxx, xxx xxx xxx'x xxx xxxx xxxxxxxxx xxxxxx xxxx xxxx xxxxx xxxxxxxx: xxx xxxxxxx xxx xxxxxxx xxxxxxx. xxx xxxxxx xxx xxxxxx, xxx xxxxxxxx xxxxx xx xxxxxxxx, xxx xxxxxxxxxx xxxxxxxxx xxxxxx xx xxxx xxxxxx xxxxx. xxx xxx xxxxxxx xxx xxxxxxxxxx xxxxxxxxx.

xxx xxx xxxxx xxx xxxxxxx xxxx xx xxx xxxxx xx xxxxx xxxxxx:

• xxxx: xxxx xx (xxxxx, xxx), xxxx xxxxxxx xx xxx xxx xx xxx xxxxxxxx xxxxx xx xx xxx xxxxxxxxx xxxxx.
• xxxx: xxxx xx (xxxxx, xxx), xxxx xxxxxxx xx xxxx xxx xx xxx xxxxxxxx xxxxx xxxx xx xxx xxxxxxxxx xxxxx.

xx x xxxxxxxxx xxxxxxxx xxxxx (x):

• xxxxxx (x(x)) = xxxxx xxx xxxxxxxx xxxx xxx xxxxx (xx x)
• xxxxxx (x(x)) = xxxxx xxx xxxxxxxx xxxx xxx xxxxx (xx x)
• xxxxxxxxxx xxxxxx (x(x) = xxx(x(x), x(x)))
• xxxxxxxxx (x(x) = x(x) - x(x))

xxxxxxxxx xxxxx_xxxxxxx(xxxx, xxxx) xxxxxxxx xxx xxxxxxxx xxxxx xxxxx xxx xxxxxx xxxx xxxxxx xx xxx xxxxxx, xx xxxxx xxxxx xx xxxxx:

x. xxxxxxxx xxxxxxxxxx xxxxxx (x(x)); x. xxxxx xxxx, xxxxxxxx xxx xxxxxxxx xxxxxxxxx (|x(x)|); x. xxxxx xxxx: xxxxxx xxx xxxxxx xxxx xxxxx.

xxxxxx xxx xxxxx (xxxxxxxx_xxxxx, xxxxxxxx_xxxxxx, xxxxxxxxx) xxx xxx xxxxxx xxxxx, xxxx xxx xxxxxxxxx xxxxxx ((x - x)). xx xxx xxxxxxx xxxxxxxxxx xxxxxx xx x (xxx xxxxxxx xxxx xxx xxxxx), xxxxxx (xxxx, x, x).

xxxxxxxx

xxxxx_xxxxxxx([(xxx, xx), (xxx, x)], [(xx, x), (xxx, x)])
# (xxx, xx, -x)
# xx xxx: xxxxxx xx (xxx xxx xxxx), xxxxxx xx (xxxx xx xx xxx xxx),
# xxxxxx xx. xxxxx xxx xxxx xx xxxxxx xxx xxxxxxxxx; xxx xx xxxxx.

xxxxx_xxxxxxx([(xx, xx)], [(xxx, xx)])
# (xxxx, x, x)
# xxxx xxx xx < xxxx xxx xxx: xxxxxxx xxxxxxx xx xxx xxxxx.

xxxxxxxxxxx

• xx xx (xx^x) xxxxxx xxxxxx xxxx xxxxx. xxxxxx xxx xxxxxxxxxx xxx xxxxxxxx xxxxxxxx; x xxxxx xxx xxxxxx xxxxxx xxx xxxxxx xxxxx (xxxxxxxxx xxx xxxxxxxxxx).
• xxxxxxxxxx xxxxx xxxxxxxxx xxxxx xx xxxxxxxxxx xxxxx xxxxx xx (x(x^x)) xxx xxxx xxx xxxxxx xx xxx xxxxxx xxxxxxxxxxx xxxx. xxx xxxx xxxx xxxxxxxxxx xxxx xxxxxxxxx xxx xxxxxxxxxx xx xxx xxxxx.
• xxxxxx, xxxxxxxxx, xxx xxxxxx xxx xxxxx xxxxxxxx; xx xxxxxxxx xxxxx xx xxxxxxxx xxxxxxxx.