Cosom Lab File

8/16/2019 Cosom Lab File

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AMITY UNIVERSITY

Computer Oriented Statistical andOptimization Methods

Submitted to

Submitted b!:

Ms. upasana Sharma

Jasdeep Singh

BCA (III-A)

A1004814024


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IN"E#

S.N. !"perimen#s Signa#ure

1. $ri#e a prgram # %nd mean& median and

mde.2. $ri#e a prgram # e'aua#e measure

dispersin.

*. $ri#e a prgram # %nd s+e,ness.

4. $ri#e a prgram # %nd ur#sis.

. $ri#e a prgram # %nd regressin ine / n

" rm an/ gi'en se# pin#s.. $ri#e a prgram # %nd regressin ine " n

/ rm an/ gi'en se# pin#s.

. $ri#e a prgram # %nd #he su#in inear

eua#ins using Simpe" Me#hd.8. $ri#e a prgram # %nd #he su#in inear

eua#ins using Big M Me#hd.

3. $ri#e a prgram # %nd #he su#in ranspr#a#in pr5em using Nr#h-$es#

6rner Me#hd.10. $ri#e a prgram # %nd #he su#in

ranspr#a#in pr5em using 7eas# Cs#

Me#hd.

11. $ri#e a prgram # %nd #he su#in

ranspr#a#in pr5em using ge9s Me#hd.


3/37

$ro%ram &' (rite a pro%ram to )nd mean* median and mode'

Su#in:-

in6ude ;is#ream<

using namespa6e s#d='id mde(in#> ?& in#)='id mean(in#> ?& in#)='id sr#(in#> ?& in#)='id median(in#> ?& in#)=in# main( )@ in# arra/>1?= a# ##a& mde= in# n 1=num5er eemen#s in arra/ % in #he 'aue arra/

r(in# i0= i;n= iDD)@ 6u# ;; E% in #he E;; iD1 ;; E num5er. :E= 6in i?= F sr#(arra/& n)= re#urn 0=F'id mean(in# ne,Garra/>?& in# num)@ H! A7 CA7CK7A! M!AN a# ##a= r(in# i0=i;num= iDD)@

##a D ne,Garra/>i?= F 6u# ;; Ehe mean is E ;; ##anum ;; end= mde(ne,Garra/& num)= F'id median(in# ne,Garra/>?& in# num)@ CA7CK7A! L! M!IAN (midde num5er) i(num 2 O 0)@ is #he eemen#s ddP in# #emp ((numD1)2)-1= 6u# ;; Ehe median is E ;; ne,Garra/>#emp? ;; end= F

ese@ #hen i#Qs e'enO :) 6u# ;; Ehe median is E;; ne,Garra/>(num2)-1? ;; Eand E ;; ne,Garra/>num2? ;; end= F mean(ne,Garra/& num)=F'id mde(in# ne,Garra/>?& in# num) @ in#R ipepe#i#in ne, in#>num?=


4/37

a6a#e a ne, arra/ in memr/ #he same siTe (runda5u# ,a/ de%ning num5er eemen#s 5/ a 'aria5e) r (in# i 0= i ; num= iDD) @ ipepe#i#in>i? 0=ini#iaiTe ea6h eemen# # 0 in# U 0=

,hie ((U ; i) (ne,Garra/>i? O ne,Garra/>U?)) @ i (ne,Garra/>i? O ne,Garra/>U?) @ UDD= F F (ipepe#i#in>U?)DD= F in# iMa"epea# 0= r (in# i 1= i ; num= iDD) @ i (ipepe#i#in>i? < ipepe#i#in>iMa"epea#?) @ iMa"epea# i=

F F 6u#;; Ehe mde is E ;; ne,Garra/>iMa"epea#? ;; end=

F'id sr#(in# ne,Garra/>?& in# num)@ AANH! A7K!S r(in# "0= ";num= "DD)@ r(in# /0= /;num-1= /DD)@ i(ne,Garra/>/?/D1?)@ in# #emp ne,Garra/>/D1?=

ne,Garra/>/D1? ne,Garra/>/?= ne,Garra/>/? #emp= F F F 6u# ;; E7is#: E= r(in# i 0= i;num= iDD)@ 6u# ;; ne,Garra/>i? ;; E E= F 6u# ;; EVnE= median(ne,Garra/& num)=

F


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KWK:


6/37

$ro%ram +' (rite a pro%ram to e,aluate measure o- dispersion'

Su#in:-in6ude ;s#di.h<in6ude ;ma#h.h<

de%ne MAXSIY! 10 'id main()@ a# ">MAXSIY!?= in# i& n= a# a'erage& 'arian6e& s#dGde'ia#in& sum 0& sum1 0=

prin#(E!n#er #he 'aue N VnE)= s6an(EdE& n)= prin#(E!n#er d rea num5ers VnE& n)=

r (i 0= i ; n= iDD) @ s6an(EE& ">i?)= F R Cmpu#e #he sum a eemen#s R r (i 0= i ; n= iDD) @ sum sum D ">i?= F a'erage sum (a#)n= R Cmpu#e 'arian6e and s#andard de'ia#in R

r (i 0= i ; n= iDD) @ sum1 sum1 D p,((">i? - a'erage)& 2)= F 'arian6e sum1 (a#)n= s#dGde'ia#in sr#('arian6e)= prin#(EA'erage a eemen#s .2VnE& a'erage)= prin#(E'arian6e a eemen#s .2VnE& 'arian6e)= prin#(ES#andard de'ia#in .2VnE& s#dGde'ia#in)=F


7/37

KWK:


8/37

$ro%ram .' (rite a pro%ram to )nd s/e0ness.

Su#in:in6ude ;6s#di5<in6ude ;is#ream<

in6ude ;agri#hm<in6ude ;numeri6<in6ude ;'e6#r<in6ude ;ma#h.h<using namespa6e s#d=in# main()@ 6u# ;; E!n#er num5er eemen#s.E ;; end= in# n& i& "= du5e a'g& 'ar 0& s+e,ness 0& S& + 0= 6in ? @2& 11& 8& 10& 1& 1*& 3& & 3& 2& 10& *& 8& & 1& 2& 10&1& 14& F= r (i 0= i ; n= iDD) @ " a>i?= '.pushG5a6+(")= F sr#('.5egin()& '.end())= r (i 0= i ; n= iDD) 6u# ;; '>i? ;; E E=

in# sum a66umua#e('.5egin()& '.end()& 0)= a'g (du5e)sumn= 6u# ;; EVnMean E ;; a'g ;; end= 'e6#r;in#


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r (i 0= i ; n= iDD) @ 'ar D ('>i? - a'g)R('>i? - a'g)= F 'ar (du5e)('ar)(n - 1)=

6u# ;; Earian6e E ;; 'ar ;; end= S (du5e)sr#('ar)= r (i 0= i ; n= iDD) s+e,ness D ('>i? - a'g)R('>i? - a'g)R('>i? - a'g)= s+e,ness s+e,ness(n R S R S R S)= 6u# ;; ES+e,ness E ;; s+e,ness ;; end= s/s#em(EWAKS!E)= re#urn !XIGSKCC!SS=F

u#pu#:


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$ro%ram 1' (rite a pro%ram to )nd 2urtosis'

Su#in:-in6ude ;6s#di5<

in6ude ;is#ream<in6ude ;agri#hm<in6ude ;numeri6<in6ude ;'e6#r<in6ude ;ma#h.h<using namespa6e s#d=in# main()@ 6u# ;; E!n#er num5er eemen#s.E ;; end= in# n& i& "= du5e a'g& 'ar 0& s+e,ness 0& S& + 0= 6in ? @2& 11& 8& 10& 1& 1*& 3& & 3& 2& 10& *& 8& & 1& 2& 10&1& 14& F=

r (i 0= i ; n= iDD) @ " a>i?= '.pushG5a6+(")= F

sr#('.5egin()& '.end())= r (i 0= i ; n= iDD) 6u# ;; '>i? ;; E E= in# sum a66umua#e('.5egin()& '.end()& 0)= a'g (du5e)sumn= 6u# ;; EVnMean E ;; a'g ;; end= 'e6#r;in#


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i# '.5egin() D "= m (R('.5egin()D " - 1) D (R('.5egin() D " - 2 )))2= 6u# ;; EMedian E ;; m ;; end= F r (i 0= i ; n= iDD)

@ 'ar D ('>i? - a'g)R('>i? - a'g)= F 'ar (du5e)('ar)(n - 1)= 6u# ;; Earian6e E ;; 'ar ;; end= S (du5e)sr#('ar)= r (i 0= i ; n= iDD) s+e,ness D ('>i? - a'g)R('>i? - a'g)R('>i? - a'g)= s+e,ness s+e,ness(n R S R S R S)= 6u# ;; ES+e,ness E ;; s+e,ness ;; end= r (i 0= i ; n= iDD)

+ D ('>i? - a'g)R('>i? - a'g)R('>i? - a'g)R('>i? - a'g)= + +(nRSRSRSRS)= + - *=

6u# ;; Eur#sis E ;; + ;; end= s/s#em(EWAKS!E)= re#urn !XIGSKCC!SS=F

upu#:


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$ro%ram 3' (rite a pro%ram to )nd re%ression line o- ! on 4-rom an! %i,en set o- points'

Su#in:

in6ude;is#ream<Ksing namespa6e s#d=a# mean(a# Ra& in# n)='id de'ia#in(a# Ra& a# mean& in# n& a# Rd& a# RS)=

'id main()@a# a>20?&5>20?&d">20?&d/>20?=a# s/0&s"0&meanG"0&meanG/0&sumG"/0=a# 6rrG6Z0&regG6ZG"/0& regG6ZG/"0=6har #/peG6Z>?=

in# n0&i0=

6rs6r()=

prin#(E!n#er #he 'aue n: E)=s6an(EdE&n)=prin#(E!n#er #he 'aues " and /:VnE)=r(i0=i s6an(EE&a>i?&5>i?)=meanG"mean(a&n)=meanG/mean(5&n)=de'ia#in(a&meanG"&n&d"&s")=

de'ia#in(5&meanG/&n&d/&s/)=

r(i0=i sumG"/sumG"/Dd">i?Rd/>i?=6rrG6ZsumG"/(nRs"Rs/)=prin#(E!n#er #he #/pe regressin 6e[6ien# as Q" n /Q rQ/ n "Q: E)=\ush(s#din)=ge#s(#/peG6Z)=

i(s#r6mp(#/peG6Z&E" n /E)1)@

regG6ZG"/6rrG6ZR(s"s/)=prin#(EVnhe 'aue inear regressin 6e[6ien# isE&regG6ZG"/)=Fese i(s#r6mp(#/peG6Z&E/ n "E)1)@regG6ZG/"6rrG6ZR(s/s")=


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prin#(EVnhe 'aue inear regressin 6e[6ien# isE&regG6ZG/")=Feseprin#(EVn!n#er #he 6rre6# #/pe regressin 6e[6ien#.E)=

ge#6h()=F

a# mean(a# Ra& in# n)@a# sum0& i0=r(i0=i sumsumDa>i?=sumsumn=re#urn (sum)=F

'id de'ia#in(a# Ra& a# mean& in# n& a# Rd& a# Rs)@a# sum00=in# i0=r(i0=i @d>i?a>i?-mean=#d>i?Rd>i?=sumsumD#=Fsumsumn=

Rssr#(sum)=F

KWK:


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$ro%ram 5' (rite a pro%ram to )nd re%ression line o- 4 on !-rom an! %i,en set o- points'Su#in:

in6ude ;is#ream<in6ude ;imanip<using namespa6e s#d= in# main()@ du5e ">? @ 1.& 2.4& *.2& 4.8& .0& .0& 8.4* F= du5e />? @ *.& .*& .& .2& 11.0& 3.& 10.2 F=

Ma#hs::egressin::7inear A(& "& /)=

6u# ;; E Spe E ;; A.ge#Spe() ;; end=

6u# ;; EIn#er6ep# E ;; A.ge#In#er6ep#() ;; end ;; end=

6u# ;; Eegressin 6e[6ien# E ;; A.ge#Ce[6ien#() ;;end=

6u# ;; end ;; Eegressin ine 'auesE ;; end ;; end= r (du5e i 0.0= i ; *= i D 0.)

@ 6u# ;; E" E ;; se#,(*) ;; i ;; E / E ;;A.ge#aue(i)= 6u# ;; end= F re#urn 0= F


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KWK: -R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-

L, man/ 'aues ]u are !n#ering

-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-

!n#er 6resspnding !emen#s X ]

1 0. 2 2. * 2 4 4 *. .8


]-0.*1423D0.81423X


$ro%ram 6' (rite a pro%ram to )nd the solution o- lineare7uations usin% Simple4 Method'

Su#in:in6ude ;s#di.h<in6ude ;ma#h.h<de%ne CMAX 10de%ne MAX 10in# NC& N& NWIMA7&W1&W2&X!=du5e S>CMAX?>MAX?='id a#a() @du5e 1&2=6har =in# I&J=prin#(EVn SIMW7!X M!LVnVnE)=prin#(E MAXIMIY! (]N) P E)= s6an(E6E& )=prin#(EVn NKMB! ^ AIAB7!S ^ L! ^KNCIN P E)=s6an(EdE& N)=

prin#(EVn NKMB! ^ CNSAINS P E)= s6an(EdE& NC)=i ( Q]Q __ Q/Q)1 1.0=ese1 -1.0=prin#(EVn INWK C!^^ICI!NS ^ L! ^KNCIN:VnE)=r (J 1= J;N= JDD) @prin#(E d P E& J)= s6an(EE& 2)=


16/37

S>1?>JD1? 2 R 1=Fprin#(E igh# hand side P E)= s6an(EE& 2)= S>1?>1? 2 R 1=r (I 1= I;NC= IDD) @

prin#(EVn CNSAIN d:VnE& I)=r (J 1= J;N= JDD) @prin#(E d P E& J)= s6an(EE& 2)= S>I D 1?>J D 1? -2=Fprin#(E igh# hand side P E)= s6an(EE& S>ID1?>1?)=Fprin#(EVnVn !SK7S:VnVnE)=r(J1= J;N= JDD) S>0?>JD1? J=r(IND1= I;NDNC= IDD) S>I-ND1?>0? I=F

'id Wi'#()='id ^rmua()='id p#imiTe()='id Simpe"() @e10: Wi'#()=^rmua()=p#imiTe()=i (NWIMA7 1) g# e10=F'id Wi'#() @du5e AW&&XMAX=

in# I&J=XMAX 0.0=r(J2= J;ND1= JDD) @i (S>1?>J? < 0.0 S>1?>J? < XMAX) @XMAX S>1?>J?=W2 J=FFAW 333333.0=r (I2= I;NCD1= IDD) @i (S>I?>W2? I?>1? S>I?>W2?)=i ( ; AW) @AW =W1 I=Fe10:=F S>0?>W2?= S>0?>W2? S>W1?>0?= S>W1?>0? =F


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'id ^rmua() @=in# I&J=r (I1= I;NCD1= IDD) @i (I W1) g# e0=r (J1= J;ND1= JDD) @

i (J W2) g# e0= S>I?>J? - S>W1?>J? R S>I?>W2? S>W1?>W2?=e0:=Fe0:=F S>W1?>W2? 1.0 S>W1?>W2?=r (J1= J;ND1= JDD) @i (J W2) g# e100= S>W1?>J? R a5s(S>W1?>W2?)=e100:=Fr (I1= I;NCD1= IDD) @i (I W1) g# e110=

S>I?>W2? R S>W1?>W2?=e110:=FF'id p#imiTe() @in# I&J=r (I2= I;NCD1= IDD)i (S>I?>1? ; 0.0) X! 1=NWIMA7 0=i (X! 1) re#urn=r (J2= J;ND1= JDD)i (S>1?>J? < 0.0) NWIMA7 1=

F'id esu#s() @in# I&J=i (X! 0) g# e*0=prin#(E N S7KIN.VnE)= g# e100=e*0:r (I1= I;N= IDD)r (J2= J;NCD1= JDD) @i (S>J?>0? O 1.0RI) g# e0=prin#(E AIAB7! d: VnE& I& S>J?>1?)=e0: =Fprin#(EVn !CNMIC ̂ KNCIN: VnE& S>1?>1?)=

e100:prin#(EVnE)=F'id main() @a#a()=Simpe"()=esu#s()=F


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KWK:

MAXIMIY! (]N) P /

NKMB! ^ AIAB7!S ^ L! ^KNCIN P 2

NKMB! ^ CNSAINS P *

INWK C!^^ICI!NS ^ L! ^KNCIN: 1 P 4 2 P 10 igh# hand side P

0

CNSAIN 1:

1 P 2 2 P 1 igh# hand side P 0

CNSAIN 2: 1 P 2 2 P igh# hand side P 100

CNSAIN *: 1 P 2

2 P * igh# hand side P 30

!SK7S:

AIAB7! 2: 20.000000

!CNMIC ̂ KNCIN: 200.0000008


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$ro%ram 8' (rite a pro%ram to )nd the solution o- lineare7uations usin% 9i% M Method'

Su#in:in6ude ;s#di.h<in# 5+1&g&='id ma"()='id min()=in# main()

@in# i=prin#(EVnN!: S7AC AIAB7!S L!7W IN ^MINH L! KNIMA`IX. BKBJ!CI!VnE)=prin#(E^KNCINS $IL ; $I77 WI! S7AC AIAB7!SBK LS!$IL


20/37

esere#urn 0=F'id min()@

in# i&U&r,&6&+6&+r&su5&'ar&ag-1&+=du5e sum&ma"&5a&+n=du5e 6U>20?&5asis>20?&6>20?&6ma#>20?a5>20?>20?=5+0=prin#(EVnVnA! VEMVE AS A BI 7AH! LAN AN] 7AH!SNKMB! IN L!prin#(EVnA7 NKMB! ^ i?)=F

prin#(EVn!N! A7 NKMB! ^ SKBJ!CI! ^KNCINS:VnE)=s6an(EdE& su5)=!CIINH AB7! IM!NSIN6'arD4=r,su5D2=r(i1=i;r,-1=iDD)@prin#(EVn!N! !7!M!NS IN d-#h $:VnE&i)=r(U4=U;6=UDD) @s6an(EE&#a5>i?>U?)= FFprin#(EVn!N! L! BASIS:VnE)=

r(i0=i;su5=iDD)s6an(EE& 5asis>i?)=prin#(EVn!N! L! A7K!S ^ VECVE ̂ M BJ!CI!^KNCINVnE)=r(i0=i;su5=iDD)s6an(EE& 6>i?)=prin#(EVn!N! L! C7KMN MAIX:VnE)=r(i0=i;su5=iDD)


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s6an(EE& 6ma#>i?)=INIIA7IYINH L! AB7!r(i1=i;r,-1=iDD)#a5>i?>0?i=r(i1=i;r,-1=iDD)

@#a5>i?>1?5asis>i-1?=#a5>i?>2?6>i-1?=#a5>i?>*?6ma#>i-1?=Fprin#(EVnWININH L! MAIX ]K LA! INS!!:VnE)=prin#(E---------------------------------------VnE)=r(i1=i;r,-1=iDD)@r(U0=U;6=UDD)@

prin#(E.*V#Ea5>i?>U?)=Fprin#(EVnE)=Fprin#(E---------------------------------------VnE)=r(i4=i;6=iDD)#a5>r,-1?>i?0=#a5>r,-1?>*?0=SAINH L! I!AINr(+0=+;10=+DD)@

INIIA7IAYINH ̂ 7AHag-1.00=Y0r(i1=i;r,-1=iDD)#a5>r,-1?>*?#a5>r,-1?>*?D#a5>i?>*?R#a5>i?>2?=YU-CUr(i4=i;6=iDD)@sum0=r(U1=U;r,-1=UDD)sum#a5>U?>i?R#a5>U?>2?Dsum=

#a5>r,-1?>i?sum-6U>i-4?=F^ININH MAXIMKM IN YU-CUma"#a5>r,-1?>4?=+64=r(i4=i;6=iDD)@i(ma";#a5>r,-1?>i?)


22/37

@ma"#a5>r,-1?>i?=+6i=FF

^ININH 5a AIr(U1=U;r,-1=UDD)@i(#a5>U?>+6?U-1?#a5>U?>+6?)=g# pp=FFpp:+rU=

r(=U;r,-1=UDD)@i((#a5>U?>+6?U-1?#a5>U?>+6?);5a))+rU=FS$AWWINH !] C7KMN $IL BASIS#a5>+r?>1?+6-*=+n#a5>+r?>+6?=#a5>+r?>2?6U>+6-4?=IIINH L! $S B] L! ^MK7Ar(i1=i;r,-1=iDD)

@i(i+r)6n#inue=ese@r(U*=U;+6=UDD)#a5>i?>U?#a5>i?>U?-((#a5>i?>+6?R#a5>+r?>U?)+n)=FFprin#(EVnVnE)=r(i1=i;r,-1=iDD)

@i(i+r)6n#inue=ese@r(U+6D1=U;6=UDD)#a5>i?>U?#a5>i?>U?-((#a5>i?>+6?R#a5>+r?>U?)+n)=F


23/37

Fr(i1=i;r,-1=iDD)@i(i+r)6n#inue=

ese#a5>i?>+6?#a5>i?>+6?-((#a5>i?>+6?R#a5>+r?>+6?)+n)=FIIINH !] $ B] !] NKMB!r(i*=i;6=iDD)#a5>+r?>i?#a5>+r?>i?+n=CL!CINH I^ YU-CU A! A77 N!HAI!r(i4=i;6=iDD)@i(#a5>r,-1?>i?i?>1?a5>i?>*?)=

F'id ma"()@in# i&U&r,&6&+6&+r&su5&'ar&ag-1&+=du5e sum&ma"&5a&+n=du5e 6U>20?&5asis>20?&6>20?&6ma#>20?a5>20?>20?=5+0=prin#(EVnVnA! VEMVE AS A BI SMA77! LAN AN] SMA77!SNKMB! IN L! !`KAINS...VnVnVnE)=prin#(EVnA7 NKMB! ^


24/37

s6an(EdE& 'ar)=prin#(EVnSA !N!INH L! C!^^ICI!NS ^ L! BJ!CI!^KNCIN:VnE)=r(i0=i;'ar=iDD)

@s6an(EE& 6U>i?)=Fprin#(EVn!N! A7 NKMB! ^ SKBJ!CI! ^KNCINS:VnE)=s6an(EdE& su5)=!CIINH AB7! IM!NSIN6'arD4=r,su5D2=r(i1=i;r,-1=iDD)@prin#(EVn!N! !7!M!NS IN d-#h $:VnE&i)=

r(U4=U;6=UDD)@s6an(EE&#a5>i?>U?)=FFprin#(EVn!N! L! BASIS:VnE)=r(i0=i;su5=iDD)s6an(EE& 5asis>i?)=prin#(EVn!N! L! A7K!S ^ VECVE ̂ M BJ!CI!^KNCINVnE)=r(i0=i;su5=iDD)

s6an(EE& 6>i?)=prin#(EVn!N! L! C7KMN MAIX:VnE)=r(i0=i;su5=iDD)s6an(EE& 6ma#>i?)=INIIA7IYINH L! AB7!r(i1=i;r,-1=iDD)#a5>i?>0?i=r(i1=i;r,-1=iDD)@#a5>i?>1?5asis>i-1?=#a5>i?>2?6>i-1?=

#a5>i?>*?6ma#>i-1?=Fprin#(EVnWININH L! MAIX ]K LA! INS!!:VnE)=prin#(E---------------------------------------VnE)=r(i1=i;r,-1=iDD)@r(U0=U;6=UDD)@


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prin#(E.*V#Ea5>i?>U?)=Fprin#(EVnE)=Fprin#(E---------------------------------------VnE)=

r(i4=i;6=iDD)#a5>r,-1?>i?0=#a5>r,-1?>*?0=SAINH L! I!AINr(+0=+;10=+DD)@INIIA7IAYINH ̂ 7AHag-1.00=Y0r(i1=i;r,-1=iDD)#a5>r,-1?>*?#a5>r,-1?>*?D#a5>i?>*?R#a5>i?>2?=

YU-CUr(i4=i;6=iDD)@sum0=r(U1=U;r,-1=UDD)sum#a5>U?>i?R#a5>U?>2?Dsum=#a5>r,-1?>i?sum-6U>i-4?=F^ININH MAXIMKM IN YU-CUma"#a5>r,-1?>4?=+64=

r(i4=i;6=iDD)@i(ma";#a5>r,-1?>i?)@ma"#a5>r,-1?>i?=+6i=FF^ININH 5a AIr(U1=U;r,-1=UDD)@

i(#a5>U?>+6?U-1?#a5>U?>+6?)=g# pp=FFpp:+rU=


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r(=U;r,-1=UDD)@i((#a5>U?>+6?U-1?#a5>U?>+6?);5a))+rU=F

S$AWWINH !] C7KMN $IL BASIS#a5>+r?>1?+6-*=+n#a5>+r?>+6?=#a5>+r?>2?6U>+6-4?=IIINH L! $S B] L! ^MK7Ar(i1=i;r,-1=iDD)@i(i+r)6n#inue=ese@

r(U*=U;+6=UDD)#a5>i?>U?#a5>i?>U?-((#a5>i?>+6?R#a5>+r?>U?)+n)=FFprin#(EVnVnE)=r(i1=i;r,-1=iDD)@i(i+r)6n#inue=ese@

r(U+6D1=U;6=UDD)#a5>i?>U?#a5>i?>U?-((#a5>i?>+6?R#a5>+r?>U?)+n)=FFr(i1=i;r,-1=iDD)@i(i+r)6n#inue=ese#a5>i?>+6?#a5>i?>+6?-((#a5>i?>+6?R#a5>+r?>+6?)+n)=F

IIINH !] $ B] !] NKMB!r(i*=i;6=iDD)#a5>+r?>i?#a5>+r?>i?+n=CL!CINH I^ YU-CU A! A77 WSII!r(i4=i;6=iDD)@i(#a5>r,-1?>i?;0)ag1=


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FB!AINH L! 7Wi(ag-1)g# ss=F

ss:prin#(EVnL! S7KIN IS...VnE)=r(i1=i;r,-1=iDD)prin#(EXdVnE&(in#)#a5>i?>1?a5>i?>*?)=F

$ro%ram :' (rite a pro%ram to )nd the solution o-Transportation problem usin% North;(est corner Method'Su#in:

in6ude;s#di.h<

in6ude;is#ream.h<

'id main()@

in# a>10?>10?&m&n&sum0&0&e0&d&6=

6u#;;Een#er #he n. 6mpaniesE=

6in


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6u#;;Een#er 'aue supp/E=

6in


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$ro%ram &


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prin#(E d E&6>i?>U?)= prin#(EdE&sup>i?)= prin#(EVnE)= F r(U0=U;n=UDD)

prin#(Ed E&dem>U?)= r(i0=i;m=iDD) r>i?0= r(i0=i;n=iDD) 6>i?0= 5m=dn= ,hie(5U?O1) @ i(mini?>U?) @ min6>i?>U?= pi= U= F FF

F F i(sup>p?;dem>?)

61sup>p?= ese 61dem>?= r(i0=i;m=iDD) @ i(r>i?O1) @ r(U0=U;n=UDD)

@ i(6>U?O1) @ i(min6>i?>U?) @ i(sup>i?;dem>U?) 62sup>i?= ese

62dem>U?= i(62


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F F F prin#(EVn d d d E&min&p&)= i(sup>p?;dem>?)

@ sumsumD6>p?>?Rsup>p?= dem>?-sup>p?= r>p?1= 5--= F ese i(sup>p??) @ sumsumD6>p?>?Rdem>?= sup>p?-dem>?= 6>?1= d--=

F ese i(sup>p?dem>?) @ sumsumD6>p?>?Rsup>p?= r>p?1= 6>?1= 5--= d--= F prin#(EVn dE&sum)= F

prin#(EVnVn dE&sum)= ge#6h()=F

KWK:


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$ro%ram &&' (rite a pro%ram to )nd the solution o-Transportation problem usin% Vo%el>s Method'Su#in:

in6ude;s#di.h<in6ude;6ni.h<'id sr#(in# a>?&in# n)@ in# #emp&U&+= r(U0=U;n=UDD) @ r(+UD1=+;n=+DD) @ i(a>U?+?) @ #empa>U?=


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a>U?a>+?=a>+?#emp=

F FFF'id main()@ in# i&U&5&p&d&+&m&n&6>20?>20?&6>20?&r>20?&a>20?&6p>20?&rp>20?=

in# sup>20?&dem>20?&ma"&min&s&sum0= 6rs6r()= prin#(EVn!n#er #he r, 6umn:E)= s6an(EddE&m&n)= prin#(EVn!n#er #he 6s#:E)= r(i0=i;m=iDD) @ r(U0=U;n=UDD) s6an(EdE&6>i?>U?)= F prin#(EVn!n#er #he demand:E)= r(i0=i;n=iDD)

s6an(EdE&dem>i?)= prin#(EVn!n#er #he supp/:E)= r(i0=i;m=iDD) s6an(EdE&sup>i?)= prin#(EVnMa#ri":VnE)= r(i0=i;m=iDD) @ r(U0=U;n=UDD) prin#(E d E&6>i?>U?)= prin#(EdE&sup>i?)= prin#(EVnE)= F

r(U0=U;n=UDD) prin#(Ed E&dem>U?)= r(i0=i;m=iDD) r>i?0= r(i0=i;n=iDD) 6>i?0= 5m&dn= ,hie(5i?-1= r(i0=i;m=iDD) @ +0= i(r>i?O1) @ r(U0=U;n=UDD)

@ i(6>U?O1) a>+DD?6>i?>U?=F


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i(+1) rp>i?a>0?=ese@ sr#(a&+)= rp>i?a>1?-a>0?=

FF F r(i0=i;n=iDD) @ +0= i(6>i?O1) @ r(U0=U;m=UDD)

@ i(r>U?O1) a>+DD?6>U?>i?=F

i(+1) 6p>i?a>0?=ese

@ sr#(a&+)= 6p>i?a>1?-a>0?=

FF r(i0=i;m=iDD) a>i?rp>i?= r(U0=U;n=UDD) a>iDU?6p>U?= ma"a>0?= p0= r(i1=i;mDn=iDD) @ i(ma";a>i?)

@ ma"a>i?=pi=

FF prin#(EVnVn d dE&ma"&p)= min1000= i(pp?O1) @ r(i0=i;m=iDD)

@ i(r>i?O1) @ i(mini?>p?)

@ min6>i?>p?= si= #p= FFFF F

ese @ i(r>p?O1) @ r(i0=i;n=iDD)

@ i(6>i?O1)


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@ i(minp?>i?) @ min6>p?>i?= sp= #i= FFFF F

prin#(EVnVn d d dE&min&s)= i(sup>s?;dem>#?) @ sumD6>s?>#?Rsup>s?= dem>#?-sup>s?= r>s?1= 5--= F ese i(sup>s?#?) @ sumD6>s?>#?Rdem>#?= sup>s?-dem>#?=

6>#?1= d--= F ese i(sup>s?dem>#?) @ sumD6>s?>#?Rdem>#?= 6>#?1= r>s?1= 5--= d--= F

F prin#(EVnVn d E&sum)= ge#6h()=F

KWK:

u#pu#: u#pu# ge Appr"ima#in Me#hd------------------------------------

* 2 13 (1)

4 3 1 * (*)

* 4 *4 (1)

1 18 *1 2


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(1) (1) (1) (1)

----------------------------------------------------

* 1111 13 (2)

4 3 1111 12 (*)

* 4 1111 *4 (1)

1 18 *1 0

(1) (1) (1) (0)

----------------------------------------------------

* 1111 13 (2)

1111 1111 1111 1111 0 (0)

* 4 1111 *4 (1)

4 18 *1 0

(2) (1) (1) (0)

----------------------------------------------------

1111 1111 1 (1)

1111 1111 1111 1111 0 (0)

* 1111 1111 *4 (4)

4 0 *1 0

(2) (0) (1) (0)

---------------------------------------------------

1111 1111 1111 1 (110)

1111 1111 1111 1111 0 (0)

1111 1111 1111 *0 (1104)

0 0 *1 0

(0) (0) (1) (0)

---------------------------------------------------

1111 1111 1111 1111 0 (0)

1111 1111 1111 1111 0 (0)

1111 1111 1111 *0 (1104)

0 0 *0 0

(0) (0) (1104) (0)

---------------------------------------------------

1111 1111 1111 1111 0 (0)

1111 1111 1111 1111 0 (0)

1111 1111 1111 1111 0 (0)

0 0 0 0


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(0) (0) (0) (0)

---------------------------------------------------

---------------------------------------------------

*_18 _1 2

4_12 3 1_2*_4 4 _*0

1111 1111 1111 *0 (1104)

X>1?>2? 18

X>1?>*? 1

X>2?>1? 12

X>2?>4? 2

X>*?>1? 4

X>*?>*? *0

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