Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura

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1 Moul grph.py CS 231 Nomi Nishimur 1 Introution Just lik th Python list n th Python itionry provi wys of storing, ssing, n moifying t, grph n viw s wy of storing, ssing, n moifying t. Bus Python os not hv uilt-in support for grphs, I hv suppli moul for us in th ours. This oumnt provis kgroun on th typs of grphs support y th moul s wll s spifis of th funtions provi. Th moul is not intn to ovr ll kins of grphs nor to provi ll possil funtions. Dtils of th implmnttion of th funtions r not isuss hr; to lrn mor out suh implmnttions, onsir tking CS 234. At tims you my writing psuoo tht uss grph oprtions. To us grph funtion, simply trnslt from ot nottion n put th nm in ll pitl lttrs. For xmpl, inst of grph.g ll(on, two), writ Eg Ll(grph, on, two). 2 Grph sis A grph onsists of st of vrtis n st of gs, whr h g is pir of vrtis, ll th npoints of th g. W llow t most on g twn pir of vrtis, so th gs must ll istint. You n think of gs s rprsnting onntions twn vrtis. If two vrtis r npoints of n g, thy r nighours. Th st of nighours of prtiulr vrtx is its nighourhoo. Th numr of nighours of vrtx is th gr of th vrtx, not g(v) for vrtx v. W will rquir tht h g hv two iffrnt vrtis s its npoints, so vrtx will nvr its own nighour. Two vrtis r jnt if thy r npoints of n g, n two gs r inint if thy shr n npoint. Th trm inint is lso us to sri th rltionship twn n g n its npoints. A squn of vrtis forms pth if thr is n g twn h onsutiv pir of vrtis in th squn, n yl if thr is lso n g twn th first n lst vrtis in th squn. At tims w might tlk out grph rprsnting nothr grph. In tht s, w my us th trm no s synonym for vrtx. Typilly w will rfr to vrtis in th originl grph n nos in th rprsnttion grph. 3 Moul grph.py 3.1 Ojts Th grph moul mks us of thr iffrnt typs of ojts: Vrtx, Eg, n Grph. In th grphs us in th ours, h Vrtx ojt hs n ID, ll, wight, n olour,

2 CS 231: Moul grph.py 2 whr th wight is n intgr n ll othr ttriuts r strings; th fult vlus of th ll, wight, n olour r "non", 0, n "whit". Th ID of h Vrtx must uniqu. Eh Eg ojt onsists of th IDs of two Vrtx ojts, ll, wight, n olour. Noti tht gs o not hv IDs; h g n uniquly intifi y th IDs of its two npoints. 3.2 Crting grph from fil Th moul grph.py ontins th funtion mk grph, whih onsums string (th nm of fil) n prous n ojt of typ Grph. A fil ontining grph t shoul ontin th following informtion, in this orr: th numr of vrtis in th grph (on on lin), ID, ll, wight, n olour of vrtx (four vlus pr lin, whr wight is n intgr n th othr vlus r strings), n IDs of oth npoints, ll, wight, n olour of n g (fiv vlus pr lin, whr wight is n intgr n othr vlus r strings). For grph with n vrtis n m gs, thr will totl of 1 + n + m lins in th fil. Pls not tht whn rting grph from fil, you n to spify lls, wights, n olours, vn if you wish to us th fults. 3.3 Mthos Th tl low lists th mthos tht n us on ojts of th lss Grph. Py los ttntion to th typs onsum n prou y h mtho; somtims you will hnling ojts n somtims you will hnling string IDs. Th fil grphus.py givs n xmpl of th mthos ing us. You n us print to print singl Vrtx, Eg, or Grph. If you wish to print list of gs, rt for loop n print h g in th list. Du to th wy tht grph is implmnt, list prou y mtho my not hv th itms ppr in pritl orr. Pls s informtion on th moul quiv.py for funtions to us in suh situtions. You n to nsur tht IDs r istint for ll vrtis; th o will not hk for you. Similrly, you shoul nsur tht whn you supply th npoints of n Eg, suh n Eg xists. Th orr in whih th npoints r suppli is not importnt. Tht is, th Eg with npoints with IDs "" n "" is intil to th Eg with npoints with IDs "" n ""; th two orrs of npoints r two wys of rfrring to th sm Eg. Bus th moul is sign to llow you to implmnt o with grphs without onsiring th tils of how th grph is implmnt, th worst-s osts list in th tl r not intn to rflt th tul osts of this prtiulr implmnttion. Whn writing n lgorithm for grphs, on oftn hooss mong vrious options with iffring osts for oprtions. Th osts list hr r not th st possil, ut rsonl hoi tht you n us for nlysis. Hr w us n to not th numr of vrtis in grph, m to not th numr of gs in grph, n to not th gr of th vrtx with ID on; not tht O(n). In

3 CS 231: Moul grph.py 3 ition, you n ssum tht ss to ny of th ttriuts n omplish in onstnt tim. Mtho Wht it os Cost Grph() rts nw mpty grph print(grph) lists informtion out vrtis n gs in grph Θ(nm) grph.vrtis() prous list of IDs of vrtis in grph Θ(n) grph.gs() prous list of Eg ojts in grph Θ(m) grph.nighours(on) prous list of IDs of nighours of th vrtx with ID on Θ() grph.r jnt(on, two) prous Tru if vrtis with IDs on n two r jnt n Fls othrwis Θ() grph.vrtx ll(on) prous th ll of th vrtx with ID on grph.vrtx wight(on) prous th wight of th vrtx with ID on grph.vrtx olour(on) prous th olour of th vrtx with ID on grph.g ll(on, two) prous th ll of th g twn vrtis with IDs on n two Θ() grph.g wight(on, two) prous th wight of th g twn vrtis with IDs on n two Θ() grph.g olour(on, two) prous th olour of th g twn vrtis with IDs on n two Θ() grph. vrtx(on) s nw vrtx with ID on grph.l vrtx(on) lts th vrtx with ID on n ll gs with th vrtx s n npoint Θ(m) grph. g(on, two) s nw g twn vrtis with IDs on n two grph.l g(on, two) lts th g twn vrtis with IDS on n two Θ(m) grph.st vrtx ll(on, nw) upts th ll of th vrtx with ID on to nw grph.st vrtx wight(on, nw) upts th wight of th vrtx with ID on to nw grph.st vrtx olour(on, nw) upts th olour of th vrtx with ID on to nw grph.st g ll(on, two, nw) upts th ll of th g twn vrtis with IDs on n two to nw Θ() grph.st g wight(on, two, nw) upts th wight of th g twn vrtis with IDs on n two to nw Θ() grph.st g olour(on, two, nw) upts th olour of th g twn vrtis with IDs on n two to nw Θ() grph == grph prous Tru if grph n grph hv vrtis with th sm IDs n th sm s gs (ut lls, wights, n olours n not iffr) low

4 CS 231: Moul grph.py 4 For your onvnin, th moul lso llows you to hk for qulity of grphs (us this only for tsts, pls), whr vrtx IDs n gs muh mth ut lls, wights, n olours n iffr. Not: Mor pris nlysis my possil y using th osrvtion tht th sum of th grs of th vrtis in grph is qul to twi th numr of gs. (To s why this is tru, osrv tht th gr of vrtx is th numr of nighours it hs, whih is qul to th numr of gs for whih it is n npoint. Sin h g hs two npoints, summing ovr th grs ounts h g twi.) For ssignmnt n xm qustions in this ours, unlss stt othrwis, you my us th lss pris oun otin y using th ft tht O(n). 4 Using th moul to writ o 4.1 Writing your own grph funtions You n lso writ your own grph funtions y irtly ssing th ttriuts in th lsss Vrtx n Eg. In lulting osts, you n ssum tht ss ny of th ttriuts n omplish in onstnt tim. A Vrtx ojt hs th following ttriuts: i ( string) ll ( string) wight (n intgr) olour ( string) An Eg ojt hs th following ttriuts: vrtx u ( Vrtx ojt) vrtx v ( Vrtx ojt) ll ( string) wight (n intgr) olour ( string) It is not rommn tht you irtly ss th ttriuts of th lss Grph, s trmining th osts rquirs knowlg xtrnous to this ours. 4.2 Copying grphs If you wish to mk opy of grph, import th opy moul n us opy.popy.

5 CS 231: Moul grph.py 5 g f j h i Figur 1: Smpl grph 1 Figur 2: Smpl grph 2 5 Smpl grphs Smpl grphs hv n provi for you in th fils smplgrph1.txt, smplgrph2.txt, smplgrph3.txt, smplgrph4.txt, n smplgrph5.txt. For your onvnin, thy hv n illustrt hr. Co tht you writ for ssignmnts shoul work for ny grph, not just th smpls provi. Th vrtis r ll with th vrtx IDs. Th lls on th gs of th lst two smpl grphs r th wights of th gs.

6 CS 231: Moul grph.py 6 Figur 3: Smpl grph Figur 4: Smpl grph f g 9 Figur 5: Smpl grph 5