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7/25/2019 Chng 4 - Phn tch s nguyn.doc
1/13
Chng 4
PHN TCH S NGUYN THNH NHN T
4.1 Nhn t ha vi h!" t# $% h%& &'
4.1.1 () *+
Trong mc ny chng ta xem xt cc thut ton phn tch s t nhin n ra tha s, m
n thc hi!n "# cnO $!nh s h%c, c $ h&ng s, '(c()* ho+c thc hi!n "$og# ) nnO cc $!nh s
h%c -.i m/t s gi tr0 ),cc 1 2hng ta s3 gi.i h4n 5&ng cch t6m 7i8m s phn tch s ra
tha s9 n:a5, nba
7/25/2019 Chng 4 - Phn tch s nguyn.doc
2/13
]i tr0 5an >Su "',#",# '' nyx = 1 Y t^ng s 7 Li[n ra theo Xuy tGc sau1 ;8u nhiKu
7h{ng >0nh th_ nh=t >ng1 2|n n8u nh< L:7, th6 7jpP), c ngha $ "#moL) k# 1
4., Phn t"h L n/+On th%nh nhn t vi h!" t# $% h%& &' /iQ
4.,.1 () *+
W hi!u [ ]c)n * $ hm c >+c >iJm sau9 [ ]
+=
)"$og#$og"""#$og)##* xx0c
x 1c) , '")# 0 ,
7hi +x , ,c $ h&ng s1
Trong ch
7/25/2019 Chng 4 - Phn tch s nguyn.doc
6/13
;Inh $J 4.62ho n $ h?p s $, - gi tr0 cBa n 7hCng 5&ng gi tr0 cBa hm m cBa
m/t s nguyn t1 hi > >i -.i c+p ngku nhin ),),, nyxyx , tha mHn cc 5iJu
th_c
"#moL
)",#",#
nyx
ny(C)*nx(C)*
==
c su=t >J
nnyx(C)* J ~ tha mHn 5=t >{ng th_c ph
nn.(C)* y, s $
7/25/2019 Chng 4 - Phn tch s nguyn.doc
7/13
k''
k'
'
##m2
nm
,), 111"#
)
)
=
7/25/2019 Chng 4 - Phn tch s nguyn.doc
8/13
Ta th=y ))` $ m/t A thut ton 5an >Su sng 5c hai1 2hng ta xy Lng 5iJu th_c
"#moL
n43 - 7iJm tra 5=t >{ng th_c
nn43(C)*
7/25/2019 Chng 4 - Phn tch s nguyn.doc
9/13
q1 Trong mi phSn tE cBa ma trn -.i s th_ t x ta >+t gi tr0 "#$og x2 1 ;gha $
[ ] j"#j$og x2x- = 1
b1 Yau > >i -.i tng gi tr0 p t cD s@ nhn tE Y chng ta thc hi!n Xu tr6nh
sng nh< sau9 T mi phSn tE cBa ma trn Z, t_c $ [ ]x- , s th_ t cBa n n&m
trong c=p s c/ng "#moL"#) #rx # - "#moL"# #rx
# , chng ta tnh ton gi tr0
cBa #$og 1
@ >y $ -i!c tnh ton n&m @ ch, >i -.i phSn tE x trong c=p s nh< -y, gi tr0
cBa #x" s3 chia h8t cho p, nh gi tr0 cBa ma trn
c >/ $.n 7hCng Xu $.n1 Ii -.i cc -0 tr x nh< -y gi tr0 #x" phn tch nhanh hDn
trong cD s@ nhn tE cBa chng ta - chng ta phn tch s #x" 5&ng
7/25/2019 Chng 4 - Phn tch s nguyn.doc
10/13
g%i $ Xy >4o cBa phSn tE q",,# n&.yx , n >iJm n:28 , >
7/25/2019 Chng 4 - Phn tch s nguyn.doc
11/13
i -.i
s nguyn t 5=t 7v p, pjn1 hi > chng ta t6m "#moL"# )) nxx 5&ng thut ton m@
r/ng uc$iL1 Ti8p theo ta >+t
"#moL""## ))) nxxyy = , "#moL)) nxyv = , "#moL
)q nxxx += ,
"#moLqq nvxy = 1
hi > theo >0nh ngha tng cBa R - 5&ng ")99# qq yx28; =+= 1
Uy giN chng ta xem tr
7/25/2019 Chng 4 - Phn tch s nguyn.doc
12/13
]iF sE n:yx8 = ")99# 1 hi > R n&m trn >
7/25/2019 Chng 4 - Phn tch s nguyn.doc
13/13
{ }&vv##
8=
j"#'
'
2hng ta xem nh x4
'9 n8
&&f #nhm 7hF ngh0ch theo php nhn cc phSn tE trong -nh n& "
= ''"#moL""##
8#
v#8## navf
#
1
T*n/ ,1 T6m mi $in h!
>y chng ta t6m -ector K1rf v , t_c $ '"# 8##vv = , sao cho
'
"#moL)8#
v
# na #
2hng ta cSn t6m tp h?p >B $.n { }K1rfv: = cc -ector nh< th8, chnh xc hDn jj
cSn phFi $.n hDn jj '8 1T*n/ 61 T6m s ph thu/c
>y chng ta t6m s ph thu/c tuy8n tnh 7hCng tSm th