Fall 2018 Midterm 2 November 15, 2018

Transcription

1 Nme: Fll 2018 Midterm 2 November 15, 2018 Andrew ID: Recittion Section: ˆ You my not use ny books, notes, extr pper, or electronic devices during this exm. There should be nothing on your desk or chir side from this exm nd ny writing implements. ˆ You my not sk questions bout the exm except for lnguge clrifictions. ˆ Show your work on the exm to receive credit. ˆ You my use the bcks of pges s scrtch pper. Nothing written on the bck of ny pges will be grded. ˆ You my complete the problems in ny order you d like; you my wish to strt with the free response problems, which re worth most of the credit. ˆ All code smples run without crshing unless we stte otherwise. ˆ You my ssume tht os, mth, string, tkinter, rndom, nd copy re imported; do not import ny other modules. Don t write nything in the tble below. Question Points Score Totl: 102

2 Fll 2018 Midterm 2 November 15, Short Answer Answer ech of the following questions. Red the instructions crefully! For multiple choice questions, you MUST fill in the bubbles ENTIRELY. () (1 point) A filesystem is nturlly recursive dt structure, nd therefore hs bse cse nd recursive cse in the dt representtion. Using only one word in ech nswer, wht is filesystem s: Bse cse? Recursive cse? (b) (2 points) Fill in the circles for ll of the following sttements which re correct ccording to our definitions of inheritnce, clsses, nd instnces. A clss is like templte, while n instnce is like specific object. Dog could be superclss of Animl. Different instnces of clss hve different methods. Shirt could be subclss of Clothing. (c) (1 point) Assume tht you re implementing side-scrolling s shown on the course website, with scrollx nd scrolly (bbrevited here s sx nd sy). If circle is t position x,y with rdius 5 in the min world mp, how should it be drwn in redrwall? Choose only one response. cnvs.crete_ovl(x-5, y-5, x+5, y+5) cnvs.crete_ovl(x-5 - sx, y-5 - sy, x+5 - sx, y+5 - sy) cnvs.crete_ovl(x-5 + sx, y-5 + sy, x+5 + sx, y+5 + sy) cnvs.crete_ovl(sx - (x-5), sy - (y-5), sx - (x+5), sy - (y+5)) (d) (2 points) Select ll the vlid resons why you my wnt to use wrpper function for recursive problem: Seprte out the recursive logic from ny other logic to improve clrity of code It elimintes the need for recursion entirely It cn llow you to initilize extr vribles you might wnt to use for the recursive logic You shouldn t use wrpper functions - it is lwys better style to use defult prmeters insted Pge 1 of 17

3 Fll 2018 Midterm 2 November 15, 2018 (e) (3 points) Consider the H-Frctl shown below. The leftmost figure is the frctl t depth 0. Assume tht the bse cse of its recursive function drws one H shpe. (i) How mny recursive clls to hfrctl() re mde in the recursive cse? Choose only one response None of the bove (ii) Select ll the necessry inputs to the recursive function, bsed on our frctl demonstrtions. Assume you my not use ny input not on this list. X nd Y coordintes for the center of the H Height of the H Number of H shpes tht lredy exist Depth (or level) (f) (3 points) The following three questions hve to do with hsh functions nd sets. Choose only one nswer for ech. (i) Wht is hsh function? A function tht turns mutble dt type into n immutble dt type A function tht turns n immutble vlue into n integer A function tht plces n object into set or dictionry A function tht finds vlue in list in constnt time (ii) How is hshed item put into set? The hsh vlue is used to crete n index into list, nd the item is plced in n inner list t tht index The hsh vlue is plced into the set insted of the item The hsh vlue is stored s key nd the item is stored s vlue, just like in dictionry The hsh vlue nd item re ppended to the end of the set in tuple (iii) How is it possible to see if n item is in set in O(1) time? Since set hs constnt size, we cn scn the entire set in O(1) time We cn hsh the item gin, nd it s fster to look up the hsh vlue thn the originl item, llowing us to serch the set in O(1) time Hshing the item will tell us which index to look into, nd we cn serch the inner list in O(1) time We cn t see if n item is in set in O(1) time Pge 2 of 17

4 Fll 2018 Midterm 2 November 15, Code Trcing Indicte wht ech piece of code will print. Plce your nswer (nd nothing else) in the box below ech piece of code. () (4 points) CT 1 def ct1(s, lst): if s in lst: print(s, "repet!") return else: lst.ppend(s) if len(s) == 1: print(s) else: if len(s) == 3: print("\n3:", s) ct1(s[1:], lst) ct1(s[:-1], lst) ct1("woh", []) Pge 3 of 17

5 Fll 2018 Midterm 2 November 15, 2018 (b) (4 points) CT 2 import copy def ct2(lst): d={} for i in rnge(len(lst)//2): d[lst[i]]=lst[i*2] print(d) d[none]={0} for i in lst: if i not in d: d[none].dd(i) print(d[none]) b=copy.deepcopy(d) for i in b: if type(d[i]) not in {set, list, tuple}: if d[i] in d: del d[i] del d[none] print(d) return len(d) lst=['x','x','y','z',4,5,6,6] print(ct2(lst)) Pge 4 of 17

6 Fll 2018 Midterm 2 November 15, 2018 (c) (4 points) CT 3 def ct3(lst,x): L=0 R=len(lst)-1 while L<=R: i=(l+r)//2 if lst[i]==x: return i elif lst[i]<x: L=i+1 else: R=i-1 print(lst[l:r+1]) return -1 lst=[0,2,3,3,6,7,9,13,14,17,18] print(ct3(lst,5)) Pge 5 of 17

7 Fll 2018 Midterm 2 November 15, Resoning Over Code For ech function, find prmeter vlues tht will mke the function return True. Plce your nswer (nd nothing else) in the box below ech block of code. () (4 points) ROC 1: Find prmeter vlues tht will mke the function roc1 return True. Plce your nswer (nd nothing else) in the box below. def roc1(lst): ssert(isinstnce(lst,list) nd len(lst)==8) s=set() i=0 while len(lst)>i: if lst[i] in s: i+=1 else: s.dd(lst.pop(i)) ssert(len(s)-len(lst)==2) for i in s: if i in lst: lst.remove(i) return(lst==["z"]) Pge 6 of 17

8 Fll 2018 Midterm 2 November 15, 2018 (b) (4 points) ROC 2: Find prmeter vlues tht will mke the function roc2 return True. Plce your nswer (nd nothing else) in the box below. def r1(x, y): if x<10: return [x,y] else: return r1(x%10,y+1)+r2(x//10,y+1) def r2(x, y): if x<10: return [x,y] else: return r1(x//10,y+1)+r2(x%10,y+1) def roc2(x): ssert(isinstnce(x,int)) ssert(100<x<999) return r1(x,x%10)==[5,6,3,7,1,7] Pge 7 of 17

9 Fll 2018 Midterm 2 November 15, (10 points) Big-O: For ech function shown below, write next to ech line of the function either the Big-O runtime of the line or the number of times the line loops. Then write the totl Big-O runtime of the function in terms of N in the box to the right of the code. All nswers must be simplified- do not include lower-order terms! For full credit, you must include line-by-line Big-O. Built-in Big-O Runtimes Generl Strings len(item) O(1) chr(s) / ord(s) O(1) item[i] O(1) s.count(c) O(N) c in item (for strings nd lists) O(N) s.find(c) O(N) 1: def bigo1(l): # L is list of length N # Big-O 2: x = y = z = 0 # 3: for i in rnge(len(l)//2): # 4: x += L[i] # 5: for j in rnge(0, len(l), len(l)//2): # 6: y += L[j] # 7: k = len(l) - 1 # 8: while k > 0: # 9: z += L[k] # 10: k = k // 2 # 11: return (x - y) / z # 1: import string 2: def bigo2(s): # s is string of length N # Big-O 3: x = 0 # 4: for c in s: # 5: nextc = chr(ord(c) + 1) # 6: if c in string.digits: # 7: x += s.count(c) # 8: elif nextc in s: # 9: x -= s.find(nextc) # 10: return x # 1: def bigoh3(l): # L is list of length N # Big-O 2: x = 0 # 3: n = len(l) # 4: for i in rnge(n): # 5: if i > n/2: # 6: for j in rnge(n**2): # 7: if i == j nd i in L: # 8: x += 1 # 9: return x # Pge 8 of 17

10 Fll 2018 Midterm 2 November 15, (8 points) Free Response: getitemcounts Write the function getitemcounts(lst) which tkes list of vlues nd returns dictionry mpping ech vlue in the list to the number of times it ppers. For exmple, getitemcounts(["", "b", "c", "", "", "c"]) would return {"" : 3, "b" : 1, "c" : 2} Your solution must use recursion. If you use ny loops, comprehensions, or itertive functions, you will receive no points on this problem. Pge 9 of 17

11 Fll 2018 Midterm 2 November 15, (10 points) Free Response: Circle Animtion Assuming the run() function is lredy written for you, write the timerfired(d) function for the following nimtion. init(d) nd redrwall(c, d) hve lredy been implemented for you; the code is included below. Do not modify these functions. 1. Every second, circle is dded to the screen. The circle should be plced in rndom loction on the screen nd should hve rdius of 20. The number 0 should be displyed in the middle of the circle. 2. All circles on the screen move to the right continuously. As soon s circle moves entirely off the screen, it reppers on the left side, still moving to the right. Every time circle wrps round the screen in this wy, the number in the middle of the circle should increse by one. Mke resonble ssumptions for nything not specified here. Do not hrdcode vlues for the width or height. We recommend tht, to sve time writing, you bbrevite cnvs, event, nd dt: use c, e nd d, respectively. You should use short vrible nmes. # Strter code def init(d): d.timerdely = 100 d.timepssed = 0 d.circles = [ ] def redrwall(c, d): for circle in d.circles: x, y, count = circle c.crete_ovl(x - 20, y - 20, x + 20, y + 20) c.crete_text(x, y, text=str(count)) Pge 10 of 17

12 Fll 2018 Midterm 2 November 15, 2018 Additionl Spce for Answer to Question 6 Pge 11 of 17

13 Fll 2018 Midterm 2 November 15, (20 points) Free Response: OOP Write set of clsses so tht they pss the following test cses. Your clsses should include Bird nd Chicken, but re not limited to these two. You my not hrdcode ny test cses. For full credit you must use inheritnce ppropritely. ###Mke bird nmed Steve b = Bird("Steve",5) ssert(b.nme=="steve") ssert(b.size==5) ssert(b.fly()=="cn fly") #Feed Steve b.feed(2) ssert(b.size==7) ssert(repr(b)=="steve weighs 7oz nd cn fly") #Birds cn't fly if their size is twice s big s their originl size! b.feed(4) ssert(b.size==11) ssert(b.fly()=="cn't fly") #Birds re equl if they hve the sme nme nd size b2=bird("steve",11) ssert(b==b2) ###Mke chicken nmed Betty c = Chicken("Betty") ssert(isinstnce(c,bird)) ssert(c.nme=="betty") ssert(c.size==20) #Chickens cn't fly ssert(c.fly()=="cn't fly") ssert(repr(c)=="betty weighs 20oz nd cn't fly") #You cn still feed chickens though c.feed(5) ssert(c.size==25) ###Chickens cn lso ly chicken eggs e=c.lychickenegg() ssert(type(e)==chickenegg) ssert(isinstnce(e,bird)==flse) ###Other birds cn't ly chicken eggs though try: b.lychickenegg() egglid=true except: egglid=flse ssert(not egglid) Pge 12 of 17

14 Fll 2018 Midterm 2 November 15, 2018 Additionl Spce for Answer to Question 7 Pge 13 of 17

15 Fll 2018 Midterm 2 November 15, 2018 Additionl Spce for Answer to Question 7 Pge 14 of 17

16 Fll 2018 Midterm 2 November 15, (20 points) Free Response: pckitems You re bout to trvel home for Thnksgiving, so you need to pck up your stuff! However, you hve so much stuff to bring home tht you ll need to use multiple bgs. This is mde more difficult by the fct tht ech item hs weight, nd ech bg hs mximum weight tht it cn hndle- if bg gets overloded, it will brek. Your tsk is to find wy to orgnize ll of your items into ll of your bgs such tht no item is left behind nd no bg contins hevier weight thn its limit. Solve this problem by writing the function pckitems(items, bgsizes). The function tkes two lists: items, which is list of the weights of ll the items, nd bgsizes, which is list of the weight limits of ll the bgs. It should return list of bgs, where bg is list of items (numbers). The bg list should be the sme length s bgsizes, nd ech bg should not weigh more thn the corresponding weight limit. For exmple, sy you hve two bgs with weight limits of 12 nd 9, nd the following list of item weights: [4, 8, 1, 4, 3]. The function cll for this would be pckitems([4, 8, 1, 4, 3], [12, 9]) nd it would return [ [4, 8], [1, 4, 3] ] Note tht the first bg sums to 12 (the first weight limit) while the second sums to 8 (less thn the second weight limit). There re other possible pckings for this set of items; ny vlid pcking is cceptble. If the provided bg sizes were insted [10, 10], there would be no vlid wy to pck the bgs; in tht cse, the function should return None insted of list of bgs. You re gurnteed tht item weights nd bg sizes will be non-negtive. Note: You must use recursion nd bcktrcking to solve the problem to receive credit, even if nother pproch would work. Pge 15 of 17

17 Fll 2018 Midterm 2 November 15, 2018 Additionl Spce for Answer to Question 8 Pge 16 of 17

18 Fll 2018 Midterm 2 November 15, 2018 Additionl Spce for Answer to Question 8 9. (2 points) Bonus CT: Only try this if you re done with the other questions nd re bored! Print wht the following code prints def bonusct(): def f(x,y=[]): return y if x < 2 else y.ppend(x % (x - 5)) or g(y) def g(z): return f(14-sum(z)*len(z)) if len(z) <= 2 \ else f(sum([bs(x) for x in z]) % 10) return evl("".join([str(x) for x in f(7)])) print(bonusct()) Pge 17 of 17