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>> [Music kucheza]

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00:00:03,346 --> 00:00:05,258

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>> DOUG LLOYD: zote haki.

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Hivyo search binary ni
algorithm tunaweza kutumia

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00:00:08,140 --> 00:00:10,530
kupata kipengele ndani ya safu.

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Tofauti na tafuta linear, inahitaji
hali maalum kuwa alikutana kabla,

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lakini ni hivyo ufanisi mkubwa zaidi kama
kwamba hali ni, kwa kweli, alikutana.

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>> Kwa hiyo kile ni wazo hapa?

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00:00:20,470 --> 00:00:21,780
ni mgawanyiko na kushinda.

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Tunataka kupunguza ukubwa wa
eneo la na nusu kila wakati

11
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ili kupata idadi ya lengo.

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Hii ni pale ambapo hali hiyo
linachukua nafasi, ingawa.

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Tunaweza kujiinua nguvu ya pekee
kuondoa nusu ya mambo

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bila hata kuangalia
yao kama safu ni Iliyopangwa.

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00:00:36,070 --> 00:00:39,200
>> Kama ni kamili mchanganyiko up,
hatuwezi tu na mikono

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00:00:39,200 --> 00:00:42,870
kuondokana na nusu ya vipengele, kwa sababu
hatujui nini sisi ni kutupa.

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Lakini kama safu ni yamepangwa,
tunaweza kufanya hivyo, kwa sababu sisi

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tunajua kwamba kila kitu
kushoto ya ambapo sisi sasa ni

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Lazima kuwa chini zaidi kuliko
thamani tuko sasa katika.

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Na kila kitu kwa
haki ya ambapo sisi ni

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lazima kuwa kubwa kuliko thamani
sasa tuko kuangalia.

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>> Basi nini pseudocode
hatua kwa kutafuta binary?

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00:00:58,710 --> 00:01:02,310
Sisi kurudia utaratibu huu mpaka
safu au, kama sisi kuendelea kupitia,

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arrays ndogo, vipande vidogo vya
awali safu, ni ya kawaida 0.

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00:01:07,740 --> 00:01:10,960
Mahesabu ya midpoint
ya sasa ya ndogo safu.

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>> Kama thamani wewe kutafuta ni
kwa kuwa kipengele cha safu, kuacha.

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Wewe kupatikana.

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Hiyo ni kubwa.

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Vinginevyo, kama lengo ni
chini ya nini katikati,

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hivyo kama thamani sisi ni kuangalia
kwa ni chini ya kile sisi kuona,

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kurudia utaratibu huu tena, lakini
mabadiliko hatua ya mwisho, badala

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ya kuwa awali
kukamilisha safu kamili,

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kwa kuwa tu wa kushoto
ya ambapo sisi tu inaonekana.

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>> Sisi alijua kwamba katikati kilikuwa juu sana,
au lengo ilikuwa chini ya katikati,

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na hivyo ni lazima kuwepo, ikiwa ni
ipo wakati wote katika safu,

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mahali fulani kwa upande wa kushoto wa midpoint.

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Na hivyo tutaweza kuweka safu
eneo tu kwa upande wa kushoto

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ya midpoint kama mpya hatua ya mwisho.

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Kinyume chake, kama lengo ni
kubwa kuliko nini katikati,

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tunafanya exact
mchakato, lakini badala yake sisi

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mabadiliko kuanza hatua ya kuwa
tu na haki ya midpoint

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sisi tu mahesabu.

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Na kisha, sisi kuanza mchakato tena.

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>> Hebu taswira hii, sawa?

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Hivyo kuna mengi kwenda na juu ya hapa,
lakini hapa ni safu ya vipengele 15.

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Na tunakwenda kuwa kuweka wimbo
ya mengi zaidi mambo wakati huu.

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Hivyo katika kutafuta linear, tulikuwa
tu kujali juu ya lengo.

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Lakini wakati huu tunataka
huduma ya juu ambapo ni sisi

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mapya ya kuangalia, ambapo
ni sisi kuacha kuangalia,

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na nini midpoint
wa safu ya sasa.

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Hivyo hapa sisi kwenda na kutafuta binary.

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Sisi ni pretty much vizuri kwenda, haki?

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00:02:25,290 --> 00:02:28,650
Mimi tu kwenda kuweka chini
chini hapa seti ya fahirisi.

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Hii ni kimsingi tu kile kipengele
wa safu tunazungumzia.

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Pamoja na tafuta linear, sisi
huduma, kwa vile sisi

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haja ya kujua jinsi wengi
mambo tuko iterating juu,

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lakini sisi si kweli huduma ya kile
kipengele tuko sasa kuangalia.

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Katika kutafuta binary, sisi kufanya.

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Na hivyo wale ni tu
kuna kama mwongozo kidogo.

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>> Ili tuweze kuanza, sawa?

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00:02:44,910 --> 00:02:46,240
Naam, si kabisa.

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Kumbuka kile alisema
kuhusu tafuta binary?

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Hatuwezi kufanya hivyo juu ya
zisizochambuliwa safu au mwingine,

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sisi si kuhakikisha kuwa
mambo fulani au maadili si

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kuwa ajali
kuondolewa wakati sisi tu

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kuamua kupuuza nusu ya safu.

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>> Hivyo hatua moja kwa binary tafuta
ni lazima uwe na safu yamepangwa.

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Na unaweza kutumia yoyote ya kuchagua
algorithms tumekuwa aliyesema kuhusu

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kupata wewe nafasi hiyo.

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Hivyo sasa, tuko katika nafasi ambapo
tunaweza kufanya search binary.

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>> Basi hebu kurudia utaratibu
hatua kwa hatua na kuweka

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wimbo wa nini kinatokea kama sisi kwenda.

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Hivyo kwanza tunahitaji kufanya ni mahesabu ya
midpoint wa safu ya sasa.

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Naam, tutaweza kusema tuko, kwanza ya
zote, kuangalia kwa thamani 19.

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Sisi ni kujaribu kupata idadi 19.

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Sehemu ya kwanza ya hii
safu iko katika ripoti sifuri,

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na kipengele mwisho wa hii
safu iko katika ripoti 14.

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Na hivyo tutaweza kuwaita wale mwanzo na mwisho.

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>> Hivyo sisi mahesabu ya midpoint na
kuongeza 0 pamoja na 14 kugawanywa na 2;

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pretty moja kwa moja midpoint.

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Na tunaweza kusema kwamba
midpoint ni sasa 7.

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Hivyo ni 15 nini sisi ni kuangalia kwa?

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Hakuna, siyo.

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Sisi ni kuangalia kwa 19.

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Lakini tunajua kwamba 19 ni mkubwa
kuliko yale sisi kupatikana katika katikati.

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>> Hivyo nini tunaweza kufanya ni
mabadiliko kuanza hatua

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kwa kuwa tu na haki ya
midpoint, na kurudia utaratibu tena.

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Na wakati sisi kufanya hivyo, sisi sasa wanasema
mpya kuanza hatua ni safu eneo 8.

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Nini tumekuwa kufanyika ni ufanisi
kupuuzwa kila kitu kwa upande wa kushoto wa 15.

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Tumekuwa kuondolewa nusu
ya tatizo, na sasa,

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badala ya kuwa na kutafuta
zaidi ya 15 vipengele katika safu yetu,

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sisi tu kuwa na kutafuta juu ya 7.

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Hivyo 8 ni mpya kuanza hatua.

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14 bado ni hatua ya mwisho.

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>> Na sasa, sisi kwenda juu hii tena.

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Sisi mahesabu midpoint mpya.

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8 pamoja na 14 ni 22, kugawanywa na 2 ni 11.

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00:04:27,130 --> 00:04:28,660
Je, hii ni nini sisi ni kuangalia kwa?

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Hakuna, siyo.

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Sisi ni kuangalia kwa thamani hiyo ni
chini ya kile sisi tu kupatikana.

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Hivyo sisi ni kwenda kurudia
mchakato tena.

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Tunakwenda kubadili hatua ya mwisho kwa
kuwa tu kwa upande wa kushoto wa midpoint.

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Kwa hiyo mpya hatua ya mwisho inakuwa 10.

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Na sasa, hiyo ni sehemu tu ya
safu tuna aina kupitia.

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00:04:44,780 --> 00:04:48,460
Hivyo tuna sasa kuondolewa
12 ya vipengele 15.

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Tunajua kwamba kama 19
lipo katika safu,

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lazima kuwepo mahali fulani kati ya kipengele
idadi 8 na kipengele namba 10.

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>> Hivyo sisi mahesabu ya midpoint mpya tena.

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00:04:59,400 --> 00:05:02,900
8 pamoja na 10 ni 18, kugawanywa na 2 ni 9.

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Na katika kesi hii, angalia,
Lengo ni katikati.

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00:05:05,074 --> 00:05:06,740
Tulikuta nini hasa sisi ni kuangalia kwa.

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00:05:06,740 --> 00:05:07,780
Tunaweza kuacha.

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Sisi mafanikio ya kumaliza
tafuta binary.

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Sawa.

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00:05:11,060 --> 00:05:13,930
Hivyo tunajua algorithm hii
kazi kama lengo ni

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mahali fulani ndani ya safu.

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00:05:16,070 --> 00:05:19,060
Je, hii kazi algorithm kama
Lengo siyo katika safu?

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00:05:19,060 --> 00:05:20,810
Naam, hebu kuanza yake
tena, na wakati huu,

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hebu angalia kwa kipengele
16, ambayo kuibua tunaweza kuona

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haipo popote katika safu.

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00:05:25,620 --> 00:05:27,110
>> Kuanza hatua ni tena 0.

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00:05:27,110 --> 00:05:28,590
Hatua ya mwisho ni tena 14.

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Hayo ni fahirisi ya kwanza na
mambo ya mwisho wa safu kamili.

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Na tutaweza kwenda kupitia mchakato sisi tu
safari kwa kupitia tena, kujaribu kupata 16,

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ingawa kuibua, tunaweza tayari
kuwaambia kwamba si kwenda kuwa huko.

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Sisi tu wanataka kuhakikisha algorithm hii
itakuwa, kwa kweli, bado kazi katika baadhi ya njia

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na si tu kutuacha
kukwama katika kitanzi usio.

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00:05:46,310 --> 00:05:48,190
>> Basi nini hatua ya kwanza?

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00:05:48,190 --> 00:05:50,230
Mahesabu ya midpoint
wa safu ya sasa.

130
00:05:50,230 --> 00:05:52,790
Nini midpoint
wa safu ya sasa?

131
00:05:52,790 --> 00:05:54,410
Naam, ni 7, sawa?

132
00:05:54,410 --> 00:05:57,560
14 pamoja na 0 kugawanywa na 2 ni 7.

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00:05:57,560 --> 00:05:59,280
Ni 15 nini sisi ni kuangalia kwa?

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00:05:59,280 --> 00:05:59,780
Hakuna

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Ni pretty karibu, lakini sisi tunataka
kwa thamani kubwa kidogo kuliko hiyo.

136
00:06:02,930 --> 00:06:06,310
>> Hivyo tunajua kwamba itakuja
kuwa mahali pa kushoto ya 15.

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00:06:06,310 --> 00:06:08,540
Lengo ni mkubwa kuliko
nini katika midpoint.

138
00:06:08,540 --> 00:06:12,450
Na hivyo sisi kuweka mpya kuanza hatua ya
kuwa tu na haki ya katikati.

139
00:06:12,450 --> 00:06:16,130
Midpoint sasa 7, hivyo
hebu sema mpya kuanza hatua ni 8.

140
00:06:16,130 --> 00:06:18,130
Na nini tumekuwa ufanisi
amefanya tena ni kupuuzwa

141
00:06:18,130 --> 00:06:21,150
nzima kushoto nusu ya safu.

142
00:06:21,150 --> 00:06:23,750
>> Sasa, sisi kurudia
mchakato mara moja zaidi.

143
00:06:23,750 --> 00:06:24,910
Mahesabu ya midpoint mpya.

144
00:06:24,910 --> 00:06:29,350
8 pamoja na 14 ni 22, kugawanywa na 2 ni 11.

145
00:06:29,350 --> 00:06:31,060
Ni 23 nini sisi ni kuangalia kwa?

146
00:06:31,060 --> 00:06:31,870
Kwa bahati mbaya, hakuna.

147
00:06:31,870 --> 00:06:34,930
Sisi ni kuangalia kwa thamani
kuwa ni chini ya 23.

148
00:06:34,930 --> 00:06:37,850
Na hivyo katika kesi hii, tunakwenda
kubadili hatua ya mwisho kwa kuwa tu

149
00:06:37,850 --> 00:06:40,035
upande wa kushoto wa midpoint ya sasa.

150
00:06:40,035 --> 00:06:43,440
Midpoint sasa ni 11, na
hivyo tutaweza kuweka mpya hatua ya mwisho

151
00:06:43,440 --> 00:06:46,980
kwa mara ya pili, twende
kupitia utaratibu huu hadi 10.

152
00:06:46,980 --> 00:06:48,660
>> Tena, sisi kupitia mchakato tena.

153
00:06:48,660 --> 00:06:49,640
Mahesabu ya midpoint.

154
00:06:49,640 --> 00:06:53,100
8 pamoja na 10 kugawanywa na 2 ni 9.

155
00:06:53,100 --> 00:06:54,750
Ni 19 nini sisi ni kuangalia kwa?

156
00:06:54,750 --> 00:06:55,500
Kwa bahati mbaya, hakuna.

157
00:06:55,500 --> 00:06:58,050
Sisi ni bado kuangalia kwa
idadi kidogo kuliko hivyo.

158
00:06:58,050 --> 00:07:02,060
Hivyo tutaweza kubadili hatua ya mwisho wakati huu
kwa kuwa tu kwa upande wa kushoto wa midpoint.

159
00:07:02,060 --> 00:07:05,532
Midpoint sasa 9,
hivyo hatua ya mwisho itakuwa 8.

160
00:07:05,532 --> 00:07:07,920
Na sasa, sisi ni kuangalia tu
katika moja ya kipengele safu.

161
00:07:07,920 --> 00:07:10,250
>> Nini midpoint wa safu hii?

162
00:07:10,250 --> 00:07:13,459
Naam, ni kuanza saa 8, ni
kuishia katika 8, midpoint ni 8.

163
00:07:13,459 --> 00:07:14,750
Ni kwamba kile sisi ni kuangalia kwa?

164
00:07:14,750 --> 00:07:16,339
Je, sisi kuangalia kwa 17?

165
00:07:16,339 --> 00:07:17,380
Hapana, sisi ni kuangalia kwa ajili ya 16.

166
00:07:17,380 --> 00:07:20,160
Hivyo kama ipo katika safu,
ni lazima kuwepo mahali fulani

167
00:07:20,160 --> 00:07:21,935
upande wa kushoto wa ambapo sisi sasa ni.

168
00:07:21,935 --> 00:07:23,060
Kwa hiyo kile ni sisi kwenda kufanya?

169
00:07:23,060 --> 00:07:26,610
Vizuri, tutaweza kuweka hatua ya mwisho kwa kuwa tu
upande wa kushoto wa midpoint ya sasa.

170
00:07:26,610 --> 00:07:29,055
Hivyo tutaweza kubadili hatua ya mwisho kwa 7.

171
00:07:29,055 --> 00:07:32,120
Je, unaweza kuona nini tu
kilichotokea hapa, ingawa?

172
00:07:32,120 --> 00:07:33,370
Angalia hapa sasa.

173
00:07:33,370 --> 00:07:35,970
>> Mwanzo ni sasa zaidi kuliko mwisho.

174
00:07:35,970 --> 00:07:39,620
Kwa ufanisi, ncha mbili
wa safu yetu wamevuka,

175
00:07:39,620 --> 00:07:42,252
na kuanza hatua ni
sasa baada ya hatua ya mwisho.

176
00:07:42,252 --> 00:07:43,960
Naam, hiyo haina
maana yoyote, sawa?

177
00:07:43,960 --> 00:07:47,960
Hivyo sasa, nini tunaweza kusema sisi ni
na safu ndogo ya ukubwa 0.

178
00:07:47,960 --> 00:07:50,110
Na mara moja sisi ni wamezipata kwa
hatua hii, tunaweza sasa

179
00:07:50,110 --> 00:07:53,940
kuhakikisha kwamba kipengele 16
haipo katika safu,

180
00:07:53,940 --> 00:07:56,280
kwa sababu kuanza hatua
na hatua ya mwisho wamevuka.

181
00:07:56,280 --> 00:07:58,340
Na hivyo ni huko.

182
00:07:58,340 --> 00:08:01,340
Sasa, taarifa kwamba hii ni kidogo
tofauti na kuanza hatua na mwisho

183
00:08:01,340 --> 00:08:02,900
uhakika kuwa sawa.

184
00:08:02,900 --> 00:08:05,030
Kama tungekuwa kuangalia
kwa 17, ingekuwa

185
00:08:05,030 --> 00:08:08,870
wamekuwa katika safu, na kuanza hatua
na hatua ya mwisho ya kwamba iteration mwisho

186
00:08:08,870 --> 00:08:11,820
kabla pointi hizo shilingi,
tunataka wamegundua 17 huko.

187
00:08:11,820 --> 00:08:15,510
Ni wakati wao kuvuka kwamba tunaweza tu
kuhakikisha kwamba kipengele haina

188
00:08:15,510 --> 00:08:17,180
zipo katika safu.

189
00:08:17,180 --> 00:08:20,260
>> Basi hebu kuchukua mengi wachache
hatua ya kutafuta linear.

190
00:08:20,260 --> 00:08:23,250
Katika mazingira ya kesi mbaya, tulikuwa na
kugawa orodha ya mambo n

191
00:08:23,250 --> 00:08:27,770
mara kwa mara katika nusu ili kupata lengo,
ama kwa sababu lengo kipengele

192
00:08:27,770 --> 00:08:33,110
itakuwa mahali fulani katika mwisho
mgawanyiko, au haipo kabisa.

193
00:08:33,110 --> 00:08:37,830
Hivyo katika hali mbaya zaidi, tuna
wameigawanya array-- gani unajua?

194
00:08:37,830 --> 00:08:40,510
Fungua wa nyakati n; sisi
na kupunguza tatizo

195
00:08:40,510 --> 00:08:42,610
katika idadi fulani ya nyakati nusu.

196
00:08:42,610 --> 00:08:45,160
Hiyo idadi ya nyakati ni gogo n.

197
00:08:45,160 --> 00:08:46,510
>> Nini bora kesi mazingira?

198
00:08:46,510 --> 00:08:48,899
Naam, kwanza wakati sisi
mahesabu ya midpoint,

199
00:08:48,899 --> 00:08:50,190
tunaona nini sisi ni kuangalia kwa.

200
00:08:50,190 --> 00:08:52,150
Katika zote za awali
mifano juu ya kutafuta binary

201
00:08:52,150 --> 00:08:55,489
tumekuwa tu wamekwenda juu, kama tulikuwa na
wamekuwa kutafuta kipengele 15,

202
00:08:55,489 --> 00:08:57,030
tunataka wamegundua kwamba mara moja.

203
00:08:57,030 --> 00:08:58,321
Hiyo ilikuwa mwanzoni kabisa.

204
00:08:58,321 --> 00:09:01,200
Hiyo ilikuwa ni midpoint ya
jaribio la kwanza katika mgawanyiko

205
00:09:01,200 --> 00:09:03,950
ya mgawanyiko katika kutafuta mapacha.

206
00:09:03,950 --> 00:09:06,350
>> Na hivyo katika hali mbaya zaidi
kesi, tafuta binary anaendesha

207
00:09:06,350 --> 00:09:11,580
katika logi n, ambayo ina unafuu zaidi
kuliko tafuta linear, katika hali mbaya zaidi.

208
00:09:11,580 --> 00:09:16,210
Katika kesi bora, mapacha
search anaendesha katika omega ya 1.

209
00:09:16,210 --> 00:09:18,990
Hivyo search binary ni mengi
bora kuliko tafuta linear,

210
00:09:18,990 --> 00:09:23,270
lakini wewe kuwa na kushughulika na mchakato wa
kuchagua safu yako kwanza kabla unaweza

211
00:09:23,270 --> 00:09:26,140
kujiinua nguvu ya kutafuta binary.

212
00:09:26,140 --> 00:09:27,130
>> Mimi nina Doug Lloyd.

213
00:09:27,130 --> 00:09:29,470
Hii ni CS 50.

214
00:09:29,470 --> 00:09:31,070