# QUESTIONS BEGIN HERE!

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1 Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt of Computr n Informtion Sins CSCI 710 (Trnoff) Disrt Struturs TEST for Fll Smstr, 00 R this for strtin! This tst is los ook n los nots You my NOT us lultor All nswrs must hv ox rwn roun thm. This is to i th rr (who miht not m!) Filur to o so miht rsult in no rit for nswr. If you prform work on th k of p in this tst, init tht you hv on so in s th n riss for prtil rit to trmin. Sttmnt rrin mi misonut from Stion.7 of th Est Tnnss Stt Univrsity Fulty Hnook, Jun 1, 001: "Ami misonut will sujt to isiplinry tion. Any t of ishonsty in mi work onstituts mi misonut. This inlus plirism, th hnin of flsifyin of ny mi oumnts or mtrils, htin, n th ivin or rivin of unuthoriz i in tsts, xmintions, or othr ssin shool work. Pnltis for mi misonut will vry with th sriousnss of th offns n my inlu, ut r not limit to: r of 'F' on th work in qustion, r of 'F' of th ours, rprimn, protion, suspnsion, n xpulsion. For son mi offns th pnlty is prmnnt xpulsion." QUESTIONS BEGIN HERE! For prolms 1 thouh, lt A = {1,,,, } n B = {,, }. Dtrmin whthr th h of th rltions R from A to B in ths prolms is funtion. ( points h) 1. R = {(1, ), (, ), (1, ), (, ), (, )} Funtion Not funtion Sin 1 is pir with n, it osn t hv rltion with uniqu vlu in B.. R = {(1, ), (, ), (, )} Funtion Not funtion. R = {(, ), (, ), (, ), (, ), (1, )} Funtion Not funtion For prolms throuh 6, trmin th rn of th funtion ivn th omin A. In othr wors, if f() =, thn wht is th st of ll vlus of tht f prous from A? ( points h). A = Rl numrs; f() = Rn of f() = _Positiv Rl vlus. A = Positiv intrs; f() = (mo ) Rn of f() = _{0, 1,,, } 6. A = Intrs; f() = + 1 Rn of f() = _O Intrs For prolms 7 thouh 9, lt th univrsl st U = {,,,,, x, y, z}. Givn th sust A, trmin th output of th ivn hrtristi or mmrship funtion f A. (1 point h) 7. A = {t, h, o, m,, s} f A () = 0 8. A = {,, i, o, u} f A (y) = 0

2 9. A = {, o, r, i, n, } f A () = 1 For prolms 10 throuh 1, lt f th mo-0 funtion. Comput th output for h of th prolms. ( points h) 10. f(6) = 11. f() = _1 1. f(0) = 0 1. Assum tht hshin funtion h is us to stor ustomr rors to on of n link lists. If h ustomr is ssin uniqu 6-iit ount numr n th hshin funtion h is th mo 101 funtion, thn how mny link lists will n? ( points) Sin thr r 101 possil outoms from th mo 101 funtion, {0, 1,,,, 99, 100}, thn thr r 101 lists uniquly intifi y th hshin funtion h..) 1.) 6.) 6 1.) 99.) 100 f.) 101.) 10 6 h.) For prolms 1 throuh 17, h rltion R is fin on th st A. In h s, trmin if R is root tr, n if it is, wht is th root? If thr is no root, lv tht sp lnk. ( points h) 1. A = {,,,, } R is root tr R is not root tr R = {(, ), (, ), (, ), (, )} If R is root tr, th root is: 1. A = {q, r, s, t, u, v} R is root tr R is not root tr R = {(t, r), (u, s), (u, v), (s, q), (q, r), (s, t)} If R is root tr, th root is: u v s Thr s yl (s, t, r, q) whih is not llow in tr. q t r

3 16. A = {1,,,, } R is root tr R is not root tr R = {(1, ), (1, ), (, ), (, )} If R is root tr, th root is: 1 Tr hs two roots, n 1, whih is not llow with root tr. 17. A = {1,,,, } R is root tr R is not root tr R = {(, ), (1, ), (, ), (, )} If R is root tr, th root is: _1 1 For prolms 18 throuh, us th root tr T shown in th fiur to th riht. ( points h) 18. Wht is th hiht of T? 19. T is n n-tr. Wht is th vlu of n? 0. List ll of th lvs of T.,, f,, i, j, k f h 1. List ll of th silins of.,. List ll of th offsprin of. h i j k. List ll of th snnts of. h, i, j, k. Wht is th minimum numr of vrtis tht woul n to to T for it to omplt -tr? 6 To mk -tr, h non-lf vrtx must hv four offsprin. Th non-lf vrtis r:,,, n h. Vrtx lry hs thr offsprin, so it only ns 1 mor. Vrtx lso lry hs thr offsprin, so it only ns 1 mor rinin our totl to. Vrtx C only hs on offsprin, so it ns mor rinin our totl to. Lst of ll, h hs thr offsprin n ns on mor. Thrfor, our minimum numr of itionl vrtis is 6.. Construt th tr of th lri xprssion (( ) + ( )). ( points) +

4 6. Th followin is th oulin link list rprsnttion of inry positionl ll tr. Construt th irph of this tr with h vrtx ll s init. (6 points) inx lft t riht A 0 9 H 7 0 I T 6 0 Y E S S 0 T H I S E A S Y 7. Fill in th LEFT n RIGHT rrys in th tl to th lft for th tr shown low. Not tht I wnt you to put th root vrtx strtin t inx 7. (6 points) x m i s f u n inx lft t riht m 0 i 0 x 0 f s u n Us th Huffmn o tr shown to th riht to fin th strin of 0's n 1's tht rprsnts th wor SAY. ( points) I E 9. Us th Huffmn o tr shown to th riht to o th mss ( points) S Y A ISEASY 0. Th xprssion shown low is writtn in Polish (prfix) nottion. Evlut it to th finl intr rsult. Not tht ll of th numrs r sinl iit intrs. ( points) + 6 = = = 1

5 1. Th xprssion shown low is writtn in rvrs Polish (postfix) nottion. Evlut it to th finl intr rsult. Not tht ll of th numrs r sinl iit intrs. ( points) = = 1 + = 1 =. Tru or Fls: Prnthss r not n in orr to sussfully vlut xprssions riv in ny of th followin nottions: Polish (prfix), inorr (infix), or rvrs-polish (postfix). ( points) Tru for ll ut inorr (infix). Thrfor, ovrll sttmnt is fls.. List th vrtis in th orr tht thy r visit in prorr srh of th tr shown to th riht. ( points) f h i. List th vrtis in th orr tht thy r visit in n inorr srh of th sm tr from prolm. ( points) f f h i h i. In th sp to th riht, onvrt th tr shown low to inry positionl tr. ( points) f Usin th pross shown on p 69 of our txtook, th oriinl tr is onvrt into th inry tr to th riht. First silin to riht os to riht whil first hil os to lft. 6. Us ny mtho you wish to trmin th miniml spnnin tr for th onnt rph shown low n to th lft. Drw th onntions of th miniml spnnin tr usin th vrtis shown to th riht. ( points) 9 f 7. Tru or Fls: Thr is mor thn on possil miniml spnnin tr for th rph in prolm. ( points) 8. Mk sur your nm is on th front p. (1 point) Ovious, I hop.

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