• This quiz is SOLO.
• This portion is worth 50 pts.  A written portion (also optional) worth 50 points will be in class tomorrow.  It will emphasize strings, lists, sets, and maps.
• No notes, books, web sites (except reading this quiz and accessing Autolab).
• IDLE hint:  python -m idlelib.idle &
• Autolab hint (to submit):  http://autolab.cs.cmu.edu/
• You must submit your quizb.py file to Autolab before leaving the lab!  You will not have access to this file after you leave the lab!
• To start, download this one file: optional-quizB.py
• The private autograder you have is "very nearly" the final version.  We will keep the same tests worth the same points, but the constants will be changed when we autograde after the quiz so you cannot just hardcode the answers.
• You may use up to 5 submissions during the quiz, though (as always) your last submission is the only one that counts.  Obviously, you may not submit nor resubmit after you leave the lab (do not attempt to do so, even if Autolab for some reason allows it).
• Good luck! :-)

1. isPalindromicWing [10pts]
2. nthPalindromicWingPrime [15pts]
3. fasterNthPalindromicWingPrime [25pts]

1. isPalindromicWing [10pts]
   A number is a "palindromic wing" if it is of the form xxxxxYxxxxx, so the x's form the "wings" and the Y is the "body" (and where x and Y are single (non-negative) digits, and the two wings have the same non-zero length).  With this in mind, write the function isPalindromicWing(n), that takes an integer n and returns True if it is a palindromic wing and False otherwise.  Hint:  we found it useful to convert numbers to strings in part of our sample solution, though that certainly is not required here.  Here is a sample test function for you:

   def testIsPalindromicWing():
       print "Testing isPalindromicWing()...",
       assert(isPalindromicWing(2223222) == True)
       assert(isPalindromicWing(2232322) == False)
       assert(isPalindromicWing(2233322) == False)
       assert(isPalindromicWing(22) == False) # too small
       assert(isPalindromicWing(2222) == False) # must have odd # of digits (right?)
       print "Passed!"

2. nthPalindromicWingPrime [15pts]
   A number is a palindromic wing prime if it is both a palindromic wing and prime.  Here are the first several palindromic wing primes:
   101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777,...
   
   With this in mind, write nthPalindromicWingPrime the naive way -- that is, just as we wrote nthPrime in the course notes.  This should work just fine for small numbers n.  Here is a sample test function for you:

   def testNthPalindromicWingPrime():
       print "Testing nthPalindromicWingPrime()...",
       assert(nthPalindromicWingPrime(0) == 101)
       assert(nthPalindromicWingPrime(1) == 131)
       assert(nthPalindromicWingPrime(2) == 151)
       assert(nthPalindromicWingPrime(3) == 181)
       assert(nthPalindromicWingPrime(4) == 191)
       assert(nthPalindromicWingPrime(5) == 313)
       assert(nthPalindromicWingPrime(15) == 11311)
       print "Passed!"

3. fasterNthPalindromicWingPrime [25pts]
   Unfortunately, the naive algorithm in the previous solution does not run fast enough for anything but the smallest n.  And so here you must fix that and write fasterNthPalindromicWingPrime(n), that produces the same results as nthPalindromicWingPrime(n), only faster.  The key: do not check every possible integer to see if it is a palindromic wing and if it is prime.  Instead, think of a way to generate the palindromic wings in order...  Here is a sample test function for you (and this test function should run with nearly no delay):

   def testFasterNthPalindromicWingPrime():
       print "Testing fasterNthPalindromicWingPrime()...",
       assert(fasterNthPalindromicWingPrime(29) == 111191111)
       assert(fasterNthPalindromicWingPrime(30) == 777767777)
       assert(fasterNthPalindromicWingPrime(31) == 77777677777)
       print "Passed!"

carpe diem   -   carpe diem   -   carpe diem   -   carpe diem   -   carpe diem   -   carpe diem   -   carpe diem   -   carpe diem   -   carpe diem