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Ljts Ljdrn fn Njw L``h

O(( fs d afgglj!ljvjl pr`krdaafnkldnkudkj gjvjl`pjg my Mcdrnj _tr`ustrup

stdrtfnk fn 46;6 dt Mjll Ldms. Ft runs `n dvdrfjty `b pldtb`ras, suoe ds [fng`ws,Ado @_, dng tej vdrf`us vjrsf`ns `b ZNFU.

_EDFH MFLDL DEAJG

4;!Ady!4?

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O(( Wut`rfdl

O(( fs d stdtfodlly typjg, o`apfljg, kjnjrdl purp`sj, odsj!sjnsftfvj, brjj!b`ra pr`krdaafnkldnkudkj tedt supp`rts pr`ojgurdl, `mcjot!`rfjntjg, dng kjnjrfo pr`krdaafnk.

O(( fs rjkdrgjg ds d afgglj!ljvjl ldnkudkj, ds ft o`aprfsjs d o`amfndtf`n `b m`te efke!ljvjldng l`w!ljvjl ldnkudkj bjdturjs.

O(( wds gjvjl`pjg my Mcdrnj _tr`ustrup stdrtfnk fn 46;6 dt Mjll Ldms fn Aurrdy Efll, NjwCjrsjy ds dn jnednojajnt t` tej O ldnkudkj dng `rfkfndlly ndajg O wfte Oldssjs mut ldtjr ft

wds rjndajg O(( fn 465?.

O(( fs d supjrsjt `b O, dng tedt vfrtudlly dny ljkdl O pr`krda fs d ljkdl O(( pr`krda.

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O(( O`apfljr3Wefs fs dotudl O(( o`apfljr wefoe wfll mj usjg t` o`apflj y`ur s`uroj o`gj fnt` bfndl jxjoutdmljpr`krda. A`st O(( o`apfljrs g`n+t odrj wedt jxtjnsf`n y`u kfvj y`ur s`uroj o`gj, mut fb

y`u g`n+t spjofby `tejrwfsj, adny wfll usj .opp my gjbdult A`st brjqujntly usjg dng brjjdvdfldmlj o`apfljr fs KNZ O/O(( o`apfljr, `tejrwfsj y`u odn edvj o`apfljrs jftejr br`a EY

`r _`ldrfs fb y`u edvj rjspjotfvj @pjrdtfnk _ystjas.

O(( Yr`krda _truoturj3Ljt us l``h dt d sfaplj o`gj tedt w`ulg prfnt tej w`rgs Ejll` [`rlg.

/fnolugj usfnk ndajspdoj stg8

adfn%& fs wejrj pr`krda jxjoutf`n mjkfns.

fnt adfn%&{

o`ut

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O(( Yrfaftfvj Muflt!fn Wypjs3O(( `bbjr tej pr`krdaajr d rfoe dss`rtajnt `b muflt!fn ds wjll ds usjr gjbfnjg gdtd typjs.

B`ll`wfnk tdmlj lfst g`wn sjvjn mdsfo O (( gdtd typjs3

Wypj Hjyw`rgM``ljdn m``lOedrdotjr oedrFntjkjr fntBl`dtfnk p`fnt bl`dtG`umlj bl`dtfnk p`fnt g`umljRdlujljss v`fg[fgj oedrdotjr woedrPt

Rdrfdmlj Gjoldrdtf`n " Fnftfdlfzdtf`n fn O((3_`aj jxdapljs drj3

fnt g 1 ?, b 1 :8 fnftfdlfzfnk g dng b.mytj z 1 ==8 fnftfdlfzjs z.

g`umlj pf 1 ?.474:68 gjoldrjs dn dppr`xfadtf`n b pf.oedr x 1 +x+8 tej vdrfdmlj x eds tej vdluj +x+.

O(( Rdrfdmlj _o`pj3D so`pj fs d rjkf`n `b tej pr`krda dng mr`dgly spjdhfnk tejrj drj terjj pldojs wejrj vdrfdmljsodn mj gjoldrjg3

4. Fnsfgj d bunotf n `r d ml`oh wefoe fs odlljg l`odl vdrfdmljs,

=. Fn tej gjbfnftf`n `b bunotf`n pdrdajtjrs wefoe fs odlljg b`radl pdrdajtjrs.?. @utsfgj `b dll bunotf`ns wefoe fs odlljg kl`mdl vdrfdmljs.

O(( O`nstdnts/Lftjrdls3O`nstdnts rjbjr t` bfxjg vdlujs tedt tej pr`krda ady n`t dltjr dng tejy drj odlljg lftjrdls.

O`nstdnts odn mj `b dny `b tej mdsfo gdtd typjs dng odn mj gfvfgjg fn Fntjkjr Nuajrdls,

Bl`dtfnk!Y`fnt Nuajrdls, Oedrdotjrs, _trfnks dng M``ljdn Rdlujs.

Dkdfn, o`nstdnts drj trjdtjg cust lfhj rjkuldr vdrfdmljs jxojpt tedt tejfr vdlujs odnn`t mj

a`gfbfjg dbtjr tejfr gjbfnftf n.

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O(( A`gfbfjr Wypjs3O(( dll`ws tej oedr, fnt, dng g`umlj gdtd typjs t` edvj a`gfbfjrs prjojgfnk teja. D a`gfbfjr

fs usjg t` dltjr tej ajdnfnk `b tej mdsj typj s` tedt ft a`rj prjofsjly bfts tej njjgs `b vdrf`ussftudtf`ns.

Wej gdtd typj a`gfbfjrs drj lfstjg ejrj3

sfknjg unsfknjg l`nk se`rt

Wej a`gfbfjrs sfknjg, unsfknjg, l`nk, dng se`rt odn mj dpplfjg t` fntjkjr mdsj typjs. Fn

dggftf`n, sfknjg dng unsfknjg odn mj dpplfjg t` oedr, dng l`nk odn mj dpplfjg t` g`umlj.

Wej a`gfbfjrs sfknjg dng unsfknjg odn dls` mj usjg ds prjbfx t` l`nk `r se`rt a`gfbfjrs. B`r

jxdaplj unsfknjg l`nk fnt.

O(( dll`ws d se`rtedng n`tdtf`n b`r gjoldrfnk unsfknjg, se`rt, `r l`nk fntjkjrs. V`u odn

sfaply usj tej w`rg unsfknjg, se`rt, `r l`nk, wfte`ut tej fnt. Wej fnt fs faplfjg. B`r jxdaplj,tej b`ll`wfnk tw` s tdtjajnts m`te gjoldrj unsfknjg fntjkjr vdr fdmljs.

unsfknjg x8unsfknjg fnt y8

_t`rdkj Oldssjs fn O((3D st`rdkj oldss gjbfnjs tej so`pj %vfsfmflfty& dng lfbj tfaj `b vdrfdmljs dng/`r bunotf`ns wftefn d

O(( Yr`krda. Wejsj spjofbfjrs prjojgj tej typj tedt tejy a`gfby. Wejrj drj b`ll`wfnk st`rdkjoldssjs wefoe odn mj usjg fn d O(( Yr`krda

dut` rjkfstjr stdtfo jxtjrn autdmlj

O(( @pjrdt`rs3Dn `pjrdt`r fs d syam`l tedt tjlls tej o`apfljr t` pjrb`ra spjofbfo adtejadtfodl `r l`kfodl

adnfpuldtf`ns. O(( fs rfoe fn muflt!fn `pjrdt`rs dng pr`vfgjs b`ll`wfnk typj `b `pjrdt`rs3

Drfteajtfo @pjrdt`rs % (, !, \, #, ((, !!& ]jldtf`ndl @pjrdt`rs %11, $1, >. 1,

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O(( L``p Wypjs3O(( pr`krdaafnk ldnkudkj pr`vfgjs b`ll`wfnk typjs `b l``p t` ednglj l``pfnk rjqufrjajnts.Olfoh tej b`ll`wfnk lfnhs t` oejoh tejfr gjtdfl.

L``p Wypj Gjsorfptf`nweflj l``p ]jpjdts d stdtjajnt `r kr`up `b stdtjajnts untfl d kfvjn o`ngftf`n

fs truj. Ft tjsts tej o`ngftf n mjb`rj jxjoutfnk tej l``p m`gy.b`r l``p Jxjoutj d sjqujnoj `b stdtjajnts aultfplj tfajs dng dmmrjvfdtjs

tej o`gj tedt adndkjs tej l``p vdrfdmlj.g`...weflj l``p Lfhj d weflj stdtjajnt, jxojpt tedt ft tjsts tej o`ngftf`n dt tej

jng `b tej l``p m`gynjstjg l``ps V`u odn usj `nj `r a`rj l``p fnsfgj dny dn`tejr weflj, b`r `r

g`..weflj l``p.

O(( Gjofsf`n Adhfnk3O(( pr`krdaafnk ldnkudkj pr`vfgjs b`ll`wfnk typjs `b gjofsf`n adhfnk stdtjajnts. Olfoh tej

b`ll`wfnk lfnhs t` oejoh tejfr gjtdfl.

http://www.tutorialspoint.com/cplusplus/cpp_while_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_while_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_for_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_for_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_do_while_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_do_while_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_nested_loops.htmhttp://www.tutorialspoint.com/cplusplus/cpp_nested_loops.htmhttp://www.tutorialspoint.com/cplusplus/cpp_nested_loops.htmhttp://www.tutorialspoint.com/cplusplus/cpp_do_while_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_for_loop.htmhttp://www.tutorialspoint.com/cplusplus/cpp_while_loop.htm

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O(( Bunotf`ns3Wej kjnjrdl b`ra `b d O(( bunotf`n gjbfnftf`n fs ds b`ll`ws3

rjturnPtypj bunotf`nPndaj% pdrdajtjr lfst &{

m`gy `b tej bunotf`n}

D O(( bunotf`n gjbfnftf`n o`nsfsts `b d bunotf`n ejdgjr dng d bunotf`n m`gy. Ejrj drj dll tej

pdrts `b d bunotf`n3

]jturn Wypj3 D bunotf`n ady rjturn d vdluj. Wej rjturnPtypj fs tej gdtd typj `b tejvdluj tej bunotf`n rjturns. _`aj bunotf`ns pjrb`ra tej gjsfrjg `pjrdtf`ns wfte`utrjturnfnk d vdluj. Fn tefs odsj, tej rjturnPtypj fs tej hjyw`rg v`fg.

Bunotf`n Ndaj3 Wefs fs tej dotudl ndaj `b tej bunotf`n. Wej bunotf`n ndaj dng tejpdrdajtjr lfst t`kjtejr o`nstftutj tej bunotf`n sfkndturj.

Ydrdajtjrs3 D pdrdajtjr fs lfhj d pldoje`lgjr. [ejn d bunotf`n fs fnv`hjg, y`u pdss dvdluj t` tej pdrdajtjr. Wefs vdluj fs rjbjrrjg t` ds dotudl pdrdajtjr `r drkuajnt. Wej

pdrdajtjr lfst rjbjrs t` tej typj, `rgjr, dng nuamjr `b tej pdrdajtjrs `b d bunotf`n.Ydrdajtjrs drj `ptf`ndl8 tedt fs, d bunotf`n ady o`ntdfn n` pdrdajtjrs.

Bunotf`n M`gy3 Wej bunotf n m`gy o`ntdfns d o`lljotf`n `b std tjajnts tedt gjbfnj wedttej bunotf`n g`js.

Nuamjrs fn O((3B`ll`wfnk d sfaplj jxdaplj t` se`w bjw `b tej adtejadtfodl `pjrdtf`ns `n O(( nuamjrs3

/fnolugj

/fnolugj usfnk ndajspdoj stg8

fnt adfn %&{

nuamjr gjbfnftf`n3se`rt s 1 498fnt f 1 !49998l`nk l 1 4999998bl`dt b 1 =?9.7;8g`umlj g 1 =99.?;78

adtejadtfodl pjrdtf ns8o`ut

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O(( Drrdys3B`ll`wfnk fs dn jxdaplj wefoe wfll se`w drrdy gjoldrdtf`n, dssfknajnt dng doojssfnk drrdys fn

O((3

/fnolugj usfnk ndajspdoj stg8

/fnolugj usfnk stg33sjtw8

fnt adfn %&{

fnt nX 49 Q8 n fs dn drrdy `b 49 fntjkjrs

fnftfdlfzj jljajnts b drrdy n t` 9b`r % fnt f 1 98 f < 498 f(( &{

nX f Q 1 f ( 4998 sjt jljajnt dt l`odtf`n f t` f ( 499}o`ut

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/fnolugj /fnolugj

usfnk ndajspdoj stg8

fnt adfn %&{

strfnk str4 1 -Ejll`-8strfnk str= 1 -[`rlg-8strfnk str?8

o`py str4 fnt` str?str? 1 str48o`ut

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49 | Y d k j

Gjbfnj O(( @mcjots3D oldss pr`vfgjs tej mlujprfnts b`r `mcjots, s` mdsfodlly dn `mcjot fs orjdtjg br`a d oldss. [j

gjoldrj `mcjots `b d oldss wfte jxdotly tej sdaj s`rt `b gjoldrdtf`n tedt wj gjoldrj vdrfdmljs `bmdsfo typjs. B`ll`wfnk stdtjajnts gjoldrj tw` `mcjots `b oldss M`x3

M`x M`x48 Gjoldrj M`x4 b typj M`xM`x M`x=8 Gjoldrj M`x= b typj M`x

M`te `b tej `mcjots M`x4 dng M`x= wfll edvj tejfr `wn o`py `b gdtd ajamjrs.

Doojssfnk tej Gdtd Ajamjrs3Wej pumlfo gdtd ajamjrs `b `mcjots `b d oldss odn mj doojssjg usfnk tej gfrjot ajamjr doojss

`pjrdt`r %.&. Ljt us try b`ll`wfnk jxdaplj t` adhj tej tefnks oljdr3

/fnolugj

usfnk ndajspdoj stg8

oldss M`x{

pumlfo3g`umlj ljnkte8 Ljnkte b d m`xg`umlj mrjdgte8 Mrjdgte `b d m`xg`umlj ejfket8 Ejfket b d m`x

}8

fnt adfn% &{

M`x M`x48 Gjoldrj M`x4 `b typj M`xM`x M`x=8 Gjoldrj M`x= `b typj M`xg`umlj v`luaj 1 9.98 _t`rj tej v`luaj b d m`x ejrj

m`x 4 spjofbfodtf`nM`x4.ejfket 1 :.98M`x4.ljnkte 1 2.98M`x4.mrjdgte 1 ;.98

m`x = spjofbfodtf`nM`x=.ejfket 1 49.98M`x=.ljnkte 1 4=.98M`x=.mrjdgte 1 4?.98

v`luaj `b m`x 4v`luaj 1 M`x4.ejfket # M`x4.ljnkte # M`x4.mrjdgte8o`ut

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O(( Fnejrftdnoj3@nj `b tej a`st fap`rtdnt o`nojpts fn `mcjot!`rfjntjg pr`krdaafnk fs tedt `b fnejrftdnoj.Fnejrftdnoj dll`ws us t` gjbfnj d oldss fn tjras `b dn`tejr oldss, wefoe adhjs ft jdsfjr t` orjdtj

dng adfntdfn dn dpplfodtf`n. Wefs dls` pr`vfgjs dn `pp`rtunfty t` rjusj tej o`gj bunotf`ndlfty

dng bdst fapljajntdtf`n tfaj.

[ejn orjdtfnk d oldss, fnstjdg `b wrftfnk o`apljtjly njw gdtd ajamjrs dng ajamjr bunotf`ns,

tej pr`krdaajr odn gjsfkndtj tedt tej njw oldss se`ulg fnejrft tej ajamjrs `b dn jxfstfnk

oldss. Wefs jxfstfnk oldss fs odlljg tej mdsj oldss, dng tej njw oldss fs rjbjrrjg t` ds tej

gjrfvjg oldss.

D oldss odn mj gjrfvjg br`a a`rj tedn `nj oldssjs, wefoe ajdns ft odn fnejrft gdtd dng

bunotf`ns br`a aultfplj mdsj oldssjs. W` gjbfnj d gjrfvjg oldss, wj usj d oldss gjrfvdtf`n lfst t`spjofby tej mdsj oldss%js&. D oldss gjrfvdtf`n lfst ndajs `nj `r a`rj mdsj oldssjs dng eds tej

b`ra3

oldss gjrfvjg!oldss3 doojss!spjofbfjr mdsj!oldss

[ejrj doojss!spjofbfjr fs `nj `bpumlfo, pr`tjotjg, `r prfvdtj, dng mdsj!oldss fs tej ndaj `b d

prjvf`usly gjbfnjg oldss. Fb tej doojss!spjofbfjr fs n`t usjg, tejn ft fs prfvdtj my gjbdult.

O`nsfgjr d mdsj oldss _edpj dng fts gjrfvjg oldss ]jotdnklj ds b`ll`ws3

/fnolugj

usfnk ndajspdoj stg8

Mdsj oldssoldss _edpj{

pumlfo3v`fg sjt[fgte%fnt w&{

wfgte 1 w8}v`fg sjtEjfket%fnt e&{

ejfket 1 e8}

pr`tjotjg3

fnt wfgte8fnt ejfket8

}8

Gjrfvjg oldssoldss ]jotdnklj3 pumlfo _edpj{

pumlfo3fnt kjtDrjd%&{

rjturn %wfgte # ejfket&8}

}8

fnt adfn%v`fg&{

]jotdnklj ]jot8

]jot.sjt[fgte%:&8]jot.sjtEjfket%;&8

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4= | Y d k j

Yrfnt tej drjd `b tej `mcjot.o`ut

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4? | Y d k j

Y`lya`rpefsa fn O((O(( p`lya`rpefsa ajdns tedt d odll t` d ajamjr bunotf`n wfll odusj d gfbbjrjnt bunotf`n t` mj

jxjoutjg gjpjngfnk `n tej typj `b `mcjot tedt fnv`hjs tej bunotf`n.

O`nsfgjr tej b`ll`wfnk jxdaplj wejrj d mdsj oldss eds mjjn gjrfvjg my `tejr tw` oldssjs dng

drjd%& ajte`g eds mjjn fapljajntjg my tej tw` sum!oldssjs wfte gfbbjrjnt fapljajntdtf`n.

/fnolugj

usfnk ndajspdoj stg8

oldss _edpj {pr`tjotjg3

fnt wfgte, ejfket8

pumlfo3_edpj% fnt d19, fnt m19&

{ wfgte 1 d8ejfket 1 m8

}fnt drjd%&{

o`ut

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Gdtd Dmstrdotf`n fn O((3Gdtd dmstrdotf`n rjbjrs t`, pr`vfgfnk `nly jssjntfdl fnb`radtf`n t` tej `utsfgj w`rg dng efgfnk

tejfr mdohkr`ung gjtdfls fj. t` rjprjsjnt tej njjgjg fnb`radtf`n fn pr`krda wfte`ut prjsjntfnk

tej gjtdfls.

Gdtd dmstrdotf`n fs d pr`krdaafnk %dng gjsfkn& tjoenfquj tedt rjlfjs `n tej sjpdrdtf`n `b

fntjrbdoj dng fapljajntdtf n.

B`r jxdaplj, fn O(( wj usj oldssjs t` gjbfnj `ur `wn dmstrdot gdtd typjs %DGW&. V`u odn usjtej o`ut `mcjot `b oldss `strjda t` strjda gdtd t` stdngdrg `utput lfhj tefs3

/fnolugj usfnk ndajspdoj stg8

fnt adfn% &{

o`ut

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O(( Bfljs dng _trjdas3Wej f`strjda stdngdrg lfmrdry ofn dng o`ut ajte`gs b`r rjdgfnk br`a stdngdrg fnput dngwrftfnk t` stdngdrg `utput rjspjotfvjly.

W` rjdg dng wrftj br`a d bflj rjqufrjs dn`tejr stdngdrg O(( lfmrdry odlljg bstrjda wefoegjbfnjs terjj njw gdtd typjs3

Gdtd Wypj Gjsorfptf`n`bstrjda Wefs gdtd typj rjprjsjnts tej `utput bflj strjda dng fs usjg t`

orjdtj bfljs dng t` wrftj fnb`radtf`n t` bfljs.fbstrjda Wefs gdtd typj rjprjsjnts tej fnput bflj strjda dng fs usjg t` rjdg

fnb`radtf`n br`a bfljs.bstrjda Wefs gdtd typj rjprjsjnts tej bflj strjda kjnjrdlly, dng eds tej

odpdmflftfjs `b m`te `bstrjda dng fbstrjda wefoe ajdns ft odn

orjdtj bfljs, wrftj fnb`radtf`n t` bfljs, dng rjdg fnb`radtf`n br`a

bfljs.B`ll`wfnk fs tej O(( pr`krda wefoe `pjns d bflj fn rjdgfnk dng wrftfnk a`gj. Dbtjr wrftfnk

fnb`radtf`n fnputtjg my tej usjr t` d bflj ndajg dbflj.gdt, tej pr`krda rjdgs fnb`radtf`n br`atej bflj dng `utputs f t `nt` tej sorjjn3

/fnolugj /fnolugj

usfnk ndajspdoj stg8

fnt adfn %&{

oedr gdtdX499Q8

`pjn d bflj fn wrftj a`gj.`bstrjda utbflj8`utbflj.`pjn%-dbflj.gdt-&8

o`ut

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o`ut gdtd8

wrftj tej gdtd dt tej sorjjn. o`ut gdtd8o`ut