Description
1 A triangle of characters
Write a program that gets a strictly positive integer n as input and outputs a triangle of height n, following this kind of interaction:
Enter strictly positive number: 13 A BCB DEFED GHIJIHG KLMNONMLK PQRSTUTSRQP VWXYZABAZYXWV CDEFGHIJIHGFEDC KLMNOPQRSRQPONMLK TUVWXYZABCBAZYXWVUT DEFGHIJKLMNMLKJIHGFED OPQRSTUVWXYZYXWVUTSRQPO ABCDEFGHIJKLMLKJIHGFEDCBA
Two built-in functions are useful for this exercise:
• ord() returns the integer that encodes the character provided as argument; • chr() returns the character encoded by the integer provided as argument.
For instance: ord(’A’) 65 chr(65) ’A’
Consecutive uppercase letters are encoded by consecutive integers. For instance: ord(’A’) , ord(’B’) , ord(’C’) (65, 66, 67)
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2 R Computing statistics on the characters in a text
Write a program that prompts the user for the name of a file that outputs how many times each digit occurs in this file, provided it does occur, following this kind of interaction:
$ cat test_1.txt The Kiwis were the tournaments gallants, but this day were overwhelmed, perhaps by the occasion, certainly by Australia’s brand of cricket forte. Plan B ? sans McCullum’s salvo ? had worked against other attacks, but not the Australians’ lair of limber lefties.
Beforehand, speculation centred on how the Kiwis, playing away from their compact homelands for the first time in the tournament, would deal with the vastness of the MCG. Now, though, the problem was not that the boundaries were too far away, but the bowlers too close. Starc, and after him Mitch Johnson, and must have looked like fishtailing trucks coming towards them, with Josh Hazlewood swerving from the other direction in the next lane. “Our bowlers won us the World Cup,” Clarke would aver later. After six weeks of batting hit-and-giggle, bowlers had the last laugh. They always do.
$ python question_2.py Enter the name of a file: test_1.txt There is no digit in this file. $ cat test_2.txt Chevron’s decision to sell its 50 per cent stake in Caltex Australia will make it easier for the local fuel supplier to release franking credits to shareholders, Caltex chief financial officer Simon Hepworth says.
Speaking after the $4.6 billion block sale, Caltex management sought to assure investors that the company’s broader business strategy would be unchanged, despite the departure of its US-domiciled major shareholder, which has held its stake for 40 years.
But Mr Hepworth conceded the deployment of the company’s $1.1 billion franking credit balance could be made easier by the transaction, given that as a US-based shareholder, the return of franking credits was not available to Chevron. $ python question_2.py Enter the name of a file: test_2.txt Digits: 0 1 4 5 6 Count: 2 2 2 1 1
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3 The Gale Shapley algorithm
Read the AMS Feature column on the stable marriage problem and the Gale Shapley algorithm. Write a program that
• lets the user input the number n of couples, • eitherletstheuserinputnamesorusesthedefaultnamesM_1, …, M_nformenandW_1, …, W_n for women, • either lets the user define preferences or randomly generates preferences.
If the preferences have been randomly generated then they are output. Finally, the Gale Shapley algorithm is applied and the matches are displayed. Here is a possible interaction (the ordering of the matches is arbitrary and could be different):
run_algorithm() Enter a strictly positive number for the number of couples: 4
Enter 4 names for the men, all on one line and separated by spaces, or just press Enter for the default “names” M_1, …, M_4:
Enter 4 names for the women, all on one line and separated by spaces, or just press Enter for the default “names” W_1, …, W_4:
Press Enter to get a default preference for all men or women. Otherwise, input one or more nonspace characters before Enter to be prompted and enter the preferences of your choice:
Preferences for M_3: W_2 W_1 W_3 W_4 Preferences for M_2: W_3 W_1 W_4 W_2 Preferences for M_1: W_4 W_1 W_3 W_2 Preferences for M_4: W_4 W_1 W_3 W_2
Preferences for W_1: M_2 M_3 M_4 M_1 Preferences for W_2: M_1 M_3 M_4 M_2 Preferences for W_3: M_3 M_2 M_1 M_4 Preferences for W_4: M_3 M_2 M_1 M_4
The matches are: W_4 — M_3 W_2 — M_4 W_3 — M_1 W_1 — M_2
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run_algorithm() Enter a strictly positive number for the number of couples: 4
Enter 4 names for the men, all on one line and separated by spaces, or just press Enter for the default “names” M_1, …, M_4:
Enter 4 names for the women, all on one line and separated by spaces, or just press Enter for the default “names” W_1, …, W_4:
Press Enter to get a default preference for all men or women. Otherwise, input one or more nonspace characters before Enter to be prompted and enter the preferences of your choice: add
List preferences for M_1, in decreasing order: W_1 W_2 W_3 W_4 List preferences for M_2, in decreasing order: W_1 W_4 W_3 W_2 List preferences for M_3, in decreasing order: W_2 W_1 W_3 W_4 List preferences for M_4, in decreasing order: W_4 W_2 W_3 W_1
List preferences for W_1, in decreasing order: M_4 M_3 M_1 M_2 List preferences for W_2, in decreasing order: M_2 M_4 M_1 M_3 List preferences for W_3, in decreasing order: M_4 M_1 M_2 M_3 List preferences for W_4, in decreasing order: M_3 M_2 M_1 M_4
The matches are: W_1 — M_3 W_2 — M_4 W_3 — M_1 W_4 — M_2
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run_algorithm() Enter a strictly positive number for the number of couples: 2
Enter 2 names for the men, all on one line and separated by spaces, or just press Enter for the default “names” M_1, …, M_2: paul john
Enter 2 names for the women, all on one line and separated by spaces, or just press Enter for the default “names” W_1, …, W_2: kim lucy
Press Enter to get a default preference for all men or women. Otherwise, input one or more nonspace characters before Enter to be prompted and enter the preferences of your choice: y
List preferences for paul, in decreasing order: kim lucy List preferences for john, in decreasing order: lucy kim
List preferences for kim, in decreasing order: paul john List preferences for lucy, in decreasing order: paul john
The matches are: kim — paul lucy — john
