1
00:00:00,000 --> 00:00:07,800

2
00:00:07,800 --> 00:00:10,190
>> ZAMYLA: Ili kuelewa
kujirudia, lazima

3
00:00:10,190 --> 00:00:13,820
kwanza kuelewa recursion.

4
00:00:13,820 --> 00:00:17,280
Kuwa na kujirudia katika kubuni programu njia
kwamba una binafsi-rejea

5
00:00:17,280 --> 00:00:18,570
ufafanuzi.

6
00:00:18,570 --> 00:00:21,520
Kujirudia miundo data, kwa mfano,
ni miundo data kwamba

7
00:00:21,520 --> 00:00:23,990
pamoja na wao wenyewe katika
ufafanuzi yao.

8
00:00:23,990 --> 00:00:27,160
Lakini leo, sisi ni kwenda kuzingatia
juu ya kazi ya kujirudia.

9
00:00:27,160 --> 00:00:31,160
>> Kumbuka kwamba kazi kuchukua pembejeo,
hoja, na kurudi thamani kama zao

10
00:00:31,160 --> 00:00:34,480
pato kuwakilishwa na
mchoro huu hapa.

11
00:00:34,480 --> 00:00:38,060
Tutaweza kufikiria sanduku kama mwili wa
kazi, zenye seti ya

12
00:00:38,060 --> 00:00:42,340
maelekezo ya kwamba kutafsiri
pembejeo na kutoa pato.

13
00:00:42,340 --> 00:00:45,660
Kuchukua kuangalia kwa karibu ndani ya mwili wa
kazi inaweza kufunua wito kwa

14
00:00:45,660 --> 00:00:47,430
majukumu mengine kama vizuri.

15
00:00:47,430 --> 00:00:51,300
Kuchukua kazi hii rahisi, foo, kwamba
inachukua kamba moja kama mchango na

16
00:00:51,300 --> 00:00:54,630
prints wangapi barua
kamba ambayo ina.

17
00:00:54,630 --> 00:00:58,490
kazi strlen, kwa kamba urefu,
inaitwa, ambaye pato ni

18
00:00:58,490 --> 00:01:01,890
inahitajika kwa ajili ya wito wa printf.

19
00:01:01,890 --> 00:01:05,770
>> Sasa, nini hufanya kazi ya kujirudia
maalum ni kwamba wito yenyewe.

20
00:01:05,770 --> 00:01:09,610
Tunaweza kuwakilisha kujirudia hii
wito kwa hii machungwa arrow

21
00:01:09,610 --> 00:01:11,360
wanaoendesha nyuma yenyewe.

22
00:01:11,360 --> 00:01:15,630
Lakini utekelezaji yenyewe tena mapenzi tu
kufanya wito mwingine kujirudia, na

23
00:01:15,630 --> 00:01:17,150
mwingine na mwingine.

24
00:01:17,150 --> 00:01:19,100
Lakini kazi ya kujirudia
hawezi kuwa kubwa.

25
00:01:19,100 --> 00:01:23,490
Wanapaswa mwisho kwa kiasi fulani, au yako
mpango wa kukimbia milele.

26
00:01:23,490 --> 00:01:27,680
>> Kwa hiyo, tunahitaji kutafuta njia ya kuvunja
nje ya simu ya kujirudia.

27
00:01:27,680 --> 00:01:29,900
Sisi wito huu kesi ya msingi.

28
00:01:29,900 --> 00:01:33,570
Wakati hali kesi ya msingi ni alikutana,
kazi anarudi bila kufanya

29
00:01:33,570 --> 00:01:34,950
mwingine wito kujirudia.

30
00:01:34,950 --> 00:01:39,610
Kuchukua kazi hii, hi, utupu kazi
kwamba inachukua int n kama pembejeo.

31
00:01:39,610 --> 00:01:41,260
kesi ya msingi anakuja kwanza.

32
00:01:41,260 --> 00:01:46,220
Kama n ni chini ya sifuri, magazeti bye na
kurudi kwa ajili ya kesi nyingine zote,

33
00:01:46,220 --> 00:01:49,400
kazi magazeti hi na kutekeleza
wito kujirudia.

34
00:01:49,400 --> 00:01:53,600
Mwingine wito kwa kazi hi na
decremented pembejeo thamani.

35
00:01:53,600 --> 00:01:56,790
>> Sasa, hata kama sisi magazeti hi,
kazi si kusitisha mpaka sisi

36
00:01:56,790 --> 00:02:00,370
kurudi kurudi aina yake,
katika hii utupu kesi.

37
00:02:00,370 --> 00:02:04,830
Hivyo kwa kila n kingine chochote zaidi ya kesi ya msingi,
hii hi kazi atarudi hi

38
00:02:04,830 --> 00:02:06,890
ya n minus 1.

39
00:02:06,890 --> 00:02:10,050
Tangu kazi hii ni batili ingawa, sisi
si wazi aina ya kurudi hapa.

40
00:02:10,050 --> 00:02:12,000
Tutaweza tu kutekeleza kazi.

41
00:02:12,000 --> 00:02:16,960
Hivyo wito hi (3) magazeti hi na
kutekeleza hi (2) ambayo inatimiza hi (1) moja

42
00:02:16,960 --> 00:02:20,560
ambayo inatimiza hi (0), ambapo
hali kesi ya msingi ni alikutana.

43
00:02:20,560 --> 00:02:24,100
Hivyo hi (0) Prints bye na kurudi.

44
00:02:24,100 --> 00:02:24,990
>> OK.

45
00:02:24,990 --> 00:02:28,690
Hivyo sasa kwamba sisi kuelewa misingi ya
kazi ya kujirudia, kwamba wanahitaji

46
00:02:28,690 --> 00:02:32,730
kesi angalau moja ya msingi ikiwa ni pamoja na
wito kujirudia, basi hoja juu ya

47
00:02:32,730 --> 00:02:34,120
maana zaidi mfano.

48
00:02:34,120 --> 00:02:37,830
Moja ambayo haina kurudi tu
utupu bila kujali.

49
00:02:37,830 --> 00:02:41,340
>> Hebu tuangalie factorial
operesheni kutumika kawaida katika

50
00:02:41,340 --> 00:02:43,660
uwezekano mahesabu.

51
00:02:43,660 --> 00:02:48,120
Factorial ya n ni bidhaa ya kila
integer chanya chini ya

52
00:02:48,120 --> 00:02:49,400
na sawa na n.

53
00:02:49,400 --> 00:02:56,731
Hivyo factorial tano ni mara 5 mara 4
Mara 3 2 mara 1 kwa kutoa 120.

54
00:02:56,731 --> 00:03:01,400
Nne factorial ni mara 4 mara 3
2 mara 1 kwa kutoa 24.

55
00:03:01,400 --> 00:03:04,910
Na utawala hiyo inatumika
kwa integer yoyote mazuri.

56
00:03:04,910 --> 00:03:08,670
>> Hivyo jinsi gani sisi kuandika kujirudia
kazi kwamba mahesabu ya factorial

57
00:03:08,670 --> 00:03:09,960
ya namba?

58
00:03:09,960 --> 00:03:14,700
Naam, tutaweza haja ya kutambua wote
kesi ya msingi na wito kujirudia.

59
00:03:14,700 --> 00:03:18,250
wito kujirudia itakuwa sawa
ajili ya matukio yote ila kwa msingi

60
00:03:18,250 --> 00:03:21,420
kesi, ambayo ina maana kwamba sisi itabidi
kupata mfano kwamba atatupa wetu

61
00:03:21,420 --> 00:03:23,350
taka matokeo.

62
00:03:23,350 --> 00:03:30,270
>> Kwa mfano huu, kuona jinsi 5 factorial
inahusisha kuzidisha 4 na 3 na 2 na 1

63
00:03:30,270 --> 00:03:33,010
Na kwamba kuzidisha sawa sana
ni kupatikana hapa,

64
00:03:33,010 --> 00:03:35,430
ufafanuzi wa 4 factorial.

65
00:03:35,430 --> 00:03:39,810
Hivyo tunaona kwamba 5 factorial ni
tu mara 5 4 factorial.

66
00:03:39,810 --> 00:03:43,360
Sasa haina muundo huu kuomba
4 Factorial vile vile?

67
00:03:43,360 --> 00:03:44,280
Ndiyo.

68
00:03:44,280 --> 00:03:49,120
Tunaona kwamba 4 factorial ina
kuzidisha mara 3 2 mara 1,

69
00:03:49,120 --> 00:03:51,590
ufafanuzi huo sana kama 3 factorial.

70
00:03:51,590 --> 00:03:56,950
Hivyo 4 factorial ni sawa na 4 mara 3
factorial, na kadhalika na kadhalika wetu

71
00:03:56,950 --> 00:04:02,170
mfano vijiti mpaka 1 factorial, ambayo
kwa ufafanuzi ni sawa na 1.

72
00:04:02,170 --> 00:04:04,950
>> Hakuna mengine chanya
integers wa kushoto.

73
00:04:04,950 --> 00:04:07,870
Hivyo tuna mfano kwa
wito wetu kujirudia.

74
00:04:07,870 --> 00:04:13,260
n factorial ni sawa na mara n
factorial ya n minus 1.

75
00:04:13,260 --> 00:04:14,370
Na kesi yetu ya msingi?

76
00:04:14,370 --> 00:04:17,370
Kwamba itabidi kuwa na tafsiri yetu
ya 1 factorial.

77
00:04:17,370 --> 00:04:19,995
>> Hivyo sasa tunaweza kuendelea na kuandika
kanuni kwa ajili ya kazi.

78
00:04:19,995 --> 00:04:24,110
Kwa kesi ya msingi, tutaweza kuwa
hali n sawa na usawa 1, ambapo

79
00:04:24,110 --> 00:04:25,780
tutaweza kurudi 1.

80
00:04:25,780 --> 00:04:29,280
Kisha kuhamia kwenye wito kujirudia,
sisi itabidi kurudi mara n

81
00:04:29,280 --> 00:04:32,180
factorial ya n minus 1.

82
00:04:32,180 --> 00:04:33,590
>> Sasa hebu mtihani yetu hii.

83
00:04:33,590 --> 00:04:35,900
Hebu jaribu factorial 4.

84
00:04:35,900 --> 00:04:39,420
Kwa kazi yetu ni sawa
kwa mara 4 factorial (3).

85
00:04:39,420 --> 00:04:43,040
Factorial (3) ni sawa na
Mara 3 factorial (2).

86
00:04:43,040 --> 00:04:48,700
Factorial (2) ni sawa na mara 2
factorial (1), ambayo anarudi 1.

87
00:04:48,700 --> 00:04:52,490
Factorial (2) sasa anarudi 2 mara 1, 2.

88
00:04:52,490 --> 00:04:55,960
Factorial (3) sasa wanaweza kurudi
Mara 3 2, 6.

89
00:04:55,960 --> 00:05:02,490
Na hatimaye, factorial (4)
anarudi 4 mara 6, 24.

90
00:05:02,490 --> 00:05:06,780
>> Kama wewe ni kukutana na shida
pamoja na simu ya kujirudia, kujifanya kuwa

91
00:05:06,780 --> 00:05:09,660
kazi kazi tayari.

92
00:05:09,660 --> 00:05:13,450
Nini maana na hii ni kwamba ni lazima
imani wito wako kujirudia kurudi

93
00:05:13,450 --> 00:05:15,100
maadili ya haki.

94
00:05:15,100 --> 00:05:18,960
Kwa mfano, kama mimi kujua kwamba
factorial (5) sawa na mara 5

95
00:05:18,960 --> 00:05:24,870
factorial (4), mimi nina kwenda kuamini kwamba
factorial (4) atanipa 24.

96
00:05:24,870 --> 00:05:28,510
Fikiria kama variable, kama wewe
mapenzi, kama ikiwa tayari inavyoelezwa

97
00:05:28,510 --> 00:05:30,070
factorial (4).

98
00:05:30,070 --> 00:05:33,850
Hivyo kwa factorial yoyote (n), ni
bidhaa ya n na

99
00:05:33,850 --> 00:05:35,360
factorial uliopita.

100
00:05:35,360 --> 00:05:38,130
Na factorial hii ya awali
ni kupatikana kwa kupiga

101
00:05:38,130 --> 00:05:41,330
factorial ya n minus 1.

102
00:05:41,330 --> 00:05:45,130
>> Sasa, kuona kama unaweza kutekeleza
kujirudia kazi mwenyewe.

103
00:05:45,130 --> 00:05:50,490
Ujazo wa juu terminal yako, au run.cs50.net,
na kuandika kazi Jumla

104
00:05:50,490 --> 00:05:54,770
kwamba inachukua integer n na anarudi
Jumla ya yote mfululizo chanya

105
00:05:54,770 --> 00:05:57,490
integers kutoka n 1.

106
00:05:57,490 --> 00:06:01,000
Nimeandika nje kiasi ya baadhi ya
maadili kukusaidia yetu.

107
00:06:01,000 --> 00:06:04,030
Kwanza, kufikiri
kesi ya msingi hali hiyo.

108
00:06:04,030 --> 00:06:06,170
Basi, kuangalia Jumla (5).

109
00:06:06,170 --> 00:06:09,270
Je, unaweza kueleza kuwa katika suala
Jumla ya mwingine?

110
00:06:09,270 --> 00:06:11,290
Sasa, nini kuhusu Jumla (4)?

111
00:06:11,290 --> 00:06:15,630
Jinsi gani unaweza kueleza Jumla (4)
katika suala la Jumla mwingine?

112
00:06:15,630 --> 00:06:19,655
>> Mara baada ya kuwa na kiasi (5) na jumla (4)
walionyesha katika suala la kiasi mengine, tazama

113
00:06:19,655 --> 00:06:22,970
kama unaweza kutambua
mfano kwa Jumla (n).

114
00:06:22,970 --> 00:06:26,190
Kama siyo, kujaribu chache idadi nyingine
na kueleza kiasi yao katika

115
00:06:26,190 --> 00:06:28,410
suala la idadi mwingine.

116
00:06:28,410 --> 00:06:31,930
Kwa kutambua chati kwa discrete
idadi, wewe ni vizuri njia yako ya

117
00:06:31,930 --> 00:06:34,320
kutambua mfano kwa n yoyote.

118
00:06:34,320 --> 00:06:38,040
>> Recursion kweli zana yenye nguvu,
hivyo bila shaka ni si mdogo

119
00:06:38,040 --> 00:06:39,820
kazi hisabati.

120
00:06:39,820 --> 00:06:44,040
Recursion inaweza kutumika kwa ufanisi sana
wakati wa kushughulika na miti kwa mfano.

121
00:06:44,040 --> 00:06:47,210
Angalia short juu ya miti kwa ajili ya
mapitio ya kina zaidi, lakini kwa sasa

122
00:06:47,210 --> 00:06:51,140
kukumbuka kwamba binary miti search, katika
hasa, ni kufanywa juu ya nodes, kila

123
00:06:51,140 --> 00:06:53,820
na thamani na kuyatumia node mbili.

124
00:06:53,820 --> 00:06:57,270
Kwa kawaida, hii ni kuwakilishwa na
mzazi node kuwa moja line akizungumzia

125
00:06:57,270 --> 00:07:01,870
upande wa kushoto mtoto node na moja
kwa haki ya mtoto nodi.

126
00:07:01,870 --> 00:07:04,510
muundo wa search binary
mti imejikita vizuri

127
00:07:04,510 --> 00:07:05,940
ya kutafuta kujirudia.

128
00:07:05,940 --> 00:07:09,730
wito kujirudia ama hupita katika
upande wa kushoto au node haki, lakini zaidi

129
00:07:09,730 --> 00:07:10,950
ya kwamba katika mti mfupi.

130
00:07:10,950 --> 00:07:15,690
>> Sema unataka kufanya operesheni juu ya
kila nodi moja katika mti binary.

131
00:07:15,690 --> 00:07:17,410
Jinsi gani kwenda kuhusu hilo?

132
00:07:17,410 --> 00:07:20,600
Naam, unaweza kuandika kujirudia
kazi ambayo hufanya kazi

133
00:07:20,600 --> 00:07:24,450
juu ya mzazi node na hufanya kujirudia
kuwaita kazi moja,

134
00:07:24,450 --> 00:07:27,630
kupita katika upande wa kushoto na
haki ya mtoto nodes.

135
00:07:27,630 --> 00:07:31,650
Kwa mfano, kazi hii, foo, kwamba
mabadiliko thamani ya node aliyopewa na

136
00:07:31,650 --> 00:07:33,830
yote ya watoto wake kwa 1.

137
00:07:33,830 --> 00:07:37,400
kesi ya msingi ya sababu null node
kazi kurudi, kuonyesha

138
00:07:37,400 --> 00:07:41,290
kwamba kuna nodes yoyote
kushoto kwa kuwa ndogo ya mti.

139
00:07:41,290 --> 00:07:42,620
>> Hebu kutembea kwa njia hiyo.

140
00:07:42,620 --> 00:07:44,340
mzazi kwanza ni 13.

141
00:07:44,340 --> 00:07:47,930
Sisi mabadiliko ya thamani ya 1, na kisha kuwaita
kazi yetu upande wa kushoto kama vizuri

142
00:07:47,930 --> 00:07:49,600
kama ni haki.

143
00:07:49,600 --> 00:07:53,910
kazi, foo, ni wito wa kushoto
ndogo ya mti wa kwanza, hivyo node kushoto

144
00:07:53,910 --> 00:07:57,730
itakuwa reassigned 1 na foo mapenzi
kuitwa juu ya watoto node ya,

145
00:07:57,730 --> 00:08:01,900
kwanza kushoto na kisha haki,
na kadhalika na kadhalika.

146
00:08:01,900 --> 00:08:05,630
Na kuwaambia kwamba matawi hawana
watoto zaidi ili mchakato huo

147
00:08:05,630 --> 00:08:09,700
itaendelea kwa watoto haki
mpaka nodes mti mzima ni

148
00:08:09,700 --> 00:08:11,430
reassigned 1.

149
00:08:11,430 --> 00:08:15,390
>> Kama unaweza kuona, wewe si mdogo
wito wa kujirudia moja tu.

150
00:08:15,390 --> 00:08:17,930
Tu kama wengi kama kupata kazi kufanyika.

151
00:08:17,930 --> 00:08:21,200
Nini kama alikuwa na mti ambapo kila
node na watoto watatu,

152
00:08:21,200 --> 00:08:23,100
Kushoto, katikati, na haki?

153
00:08:23,100 --> 00:08:24,886
Jinsi gani unaweza hariri foo?

154
00:08:24,886 --> 00:08:25,860
Naam, rahisi.

155
00:08:25,860 --> 00:08:30,250
Tu kuongeza mwingine wito kujirudia na
kupita katika pointer node katikati.

156
00:08:30,250 --> 00:08:34,549
>> Recursion ni wenye nguvu sana na si kwa
kutaja kifahari, lakini inaweza kuwa

157
00:08:34,549 --> 00:08:38,010
vigumu dhana kwa mara ya kwanza, hivyo kuwa na
mvumilivu na kuchukua muda wako.

158
00:08:38,010 --> 00:08:39,370
Kuanza na kesi ya msingi.

159
00:08:39,370 --> 00:08:42,650
Ni kawaida rahisi kutambua,
na kisha unaweza kufanya kazi

160
00:08:42,650 --> 00:08:43,830
nyuma kutoka huko.

161
00:08:43,830 --> 00:08:46,190
Unajua unahitaji kufikia yako
msingi kesi, hivyo nguvu kwamba

162
00:08:46,190 --> 00:08:47,760
kukupa mwanga chache.

163
00:08:47,760 --> 00:08:53,120
Jaribu kueleza kesi moja maalum katika
suala la kesi nyingine, au katika ndogo ya seti.

164
00:08:53,120 --> 00:08:54,700
>> Shukrani kwa ajili ya kuangalia hii fupi.

165
00:08:54,700 --> 00:08:58,920
Kwa uchache sana, sasa unaweza
kuelewa utani kama hii.

166
00:08:58,920 --> 00:09:01,250
Jina langu ni Zamyla, na hii ni cs50.

167
00:09:01,250 --> 00:09:04,306

168
00:09:04,306 --> 00:09:07,170
>> Kuchukua kazi hii, hi, a
utupu kazi ambayo inachukua

169
00:09:07,170 --> 00:09:09,212
int, n, kama pembejeo.

170
00:09:09,212 --> 00:09:11,020
kesi ya msingi anakuja kwanza.

171
00:09:11,020 --> 00:09:14,240
Kama n ni, magazeti chini ya 0
"Bye" na kurudi.

172
00:09:14,240 --> 00:09:15,490