Programming Praxis

I’ll be taking a break until the new year, as my daughter is visiting from out-of-town and daily hits are cut about in half at the end of the academic year. I wish a Merry Christmas and Happy New Year to my readers and their families.

Today’s exercise provides simple finger exercise for a Friday morning:

A palindrome is a string that reads the same forward and backward; for instance “abcdedcba” is a palindrome. A rotated palindrome is a string that reads the same forward and backward, either directly or in any rotation of the string; for instance, “dedcbaabc” is a rotated palindrome, because if the last three letters at the end of the string are rotated to the beginning of the string, it becomes “abcdedcba” which is a palindrome.

Your task is to write a program to determine if a string is a rotated palindrome. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Today’s exercise is from user Jane, who needs homework help:

Consider all partitionings of a list of positive integers into two partitions. For each partitioning, compute the sums of the two partitions, then compute the least common multiple of the two sums. Report the maximum of all possible least common multiples. For example, given the list (2 3 4 6), the possible partitionings, the associated sums, and the least common multiples, are:

    () (2 3 4 6) -  0 15 -  0
    (2)  (3 4 6) -  2 13 - 26
    (3)  (2 4 6) -  3 12 - 12
    (2 3)  (4 6) -  5 10 - 10
    (4)  (2 3 6) -  4 11 - 44
    (2 4)  (3 6) -  6  9 - 18
    (3 4)  (2 6) -  7  8 - 56
    (2 3 4)  (6) -  9  6 - 18
    (6)  (2 3 4) -  6  9 - 18
    (2 6)  (3 4) -  8  7 - 56
    (3 6)  (2 4) -  9  6 - 18
    (2 3 6)  (4) - 11  4 - 44
    (4 6)  (2 3) - 10  5 - 10
    (2 4 6)  (3) - 12  3 - 12
    (3 4 6)  (2) - 13  2 - 26
    (2 3 4 6) () - 15  0 -  0

Thus, the maximum least common multiple is 56.

Jane writes that she wants to be able to recursively find all partitions given a list, and she thinks she will have to use lambda in her program.

Your task is to write a program that finds the maximum least common multiple of the part-sums of all possible 2-partitionings of a list of positive integers. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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A cyclical list has no beginning and no end; Chez Scheme writes it like this:

#0=(1 2 3 . #0#)

Your task is to write a program that removes an item from a cyclical list; if the item is not present in the cyclical list, it should remain unchanged. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Today’s exercise is about basic programming techniques.

Your task is to pick a function and write two versions of it, one recursive, the other iterative; compare the two versions on readability, programming ease, speed, and any other criteria that are important to you. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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All programming languages provide ways to handle exceptions, and all programs should be careful to handle exceptions properly; it’s good programming practice to keep exceptions from interfering with the normal conduct of your program, and courteous to your users. A good way to handle exceptions is to replace them with default values. Consider this:

> (car '())
Exception in car: () is not a pair
> (try (car '()) #f)
#f

The first exception is unhandled, and displays an error to the user. The second exception is handled, and converts the error to a default value. Replacing exceptions with defaults makes programs more robust.

Your task is to devise a simple system of replacing exceptions with defaults in your favorite programming language. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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