Leap Year
October 5, 2018
Today’s exercise comes from a student who asked for homework help on the internet:
Write a program that determines whether or not a given year is a leap year. A year is a leap year if it is divisible by 4, except that it is not a leap year if it is divisible by 100, except that it is a leap year if it is divisible by 400.
Your task is to write a program to identify leap years. 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.
Palindrome List
October 2, 2018
Today’s exercise sounds like a homework problem:
Write a program that determines if a linked list of integers is palindromic — i.e., reads the same in both directions. Your solution must operate in O(1) space.
Your task is to write a program to determine if a list of integers is palindromic, in O(1) space. 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.
No Exercise Today
September 28, 2018
There was no exercise Monday, and there is no exercise today. I’ve been very busy at work on the implementation of a major upgrade to our primary application, with go-live scheduled for early December. I’m responsible for a major component of the system, which unfortunately hasn’t yet worked properly. I’ll be sure to write an exercise this weekend for next Tuesday.
The 37% Rule
September 21, 2018
You have to hire a new programmer from a pool of 100 applicants. One method is to interview all 100 and hire the best, but that takes a while. Mathematicians have developed the 37% rule:
Examine 37% of the candidates, knowing in advance you will not select any of them. Then examine the remaining candidates one-by-one, choosing the first of them that is better than any of the first 37%.
Your task is to simulate this process and determine how close you get to the optimal candidate. 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.
1-800-PPRAXIS
September 18, 2018
I hate businesses with telephone numbers that spell words; it’s awkward to type letters at a telephone, and often the words are abbreviated or spelled wrong so they are no longer mnemonic, which defeats the purpose. So this morning when I had to call one of those businesses, I wrote a program to translate letters to numbers after I had been waiting on hold long enough to get really annoyed.
Your task is to write a program to translate telephone numbers specified as words. 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.
Nth From The End
September 11, 2018
Counting from the end of the list, the third-last item in the list (1 2 3 4 5 6 7 8 9) is 7.
Your task is to write a program to find the nth-last item in a list; you must provide at least three fundamentally different solutions. 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.
List Homework
September 7, 2018
For many students, school started a few weeks ago, so today’s exercise is typical of homework:
- Write a program to determine the length of a linked list.
- Write a program to reverse a linked list.
Your task is to write the two list exercises described above; write them as if you are three weeks into your first data structures class. 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.
Mind-Boggling Card Trick
September 4, 2018
Today’s exercise is a mind-boggling card trick:
Create a pack of 52 cards, half red, half black, and shuffle them. With the cards face down, turn over the top card. If it is black, add the next card, unseen, to the black stack; if it is red, add the next card, unseen, to the red stack. Add the original top card to the discard stack. Repeat these steps for all the cards in the pack. Now, randomly choose a number less than the size of the smaller of the black and red stacks, choose that many cards randomly from each of the two stacks, and swap those randomly-chosen cards from one stack to the other. The number of black cards in the black stack will equal the number of red cards in the red stack.
Your taks is to write a program to simulate the card trick and confirm that the number of black cards in the black stack equals the number of red cards in the red stack. 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.
Sum Of Perfect Powers
August 31, 2018
I think this must be somebody’s homework:
Write a program to determine if a number x can be written as the sum of two perfect powers. This is, given x determine if there exist non-negative integers a, b, m and n such that am + bn = x where 1 ≤ x ≤ 106 and m > 1 and n > 1.
Your task is to write a program that determines if a number is a sum of two perfect powers. 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.
Array Of Integers
August 28, 2018
Today’s exercise is an interview question from Amazon:
You are given an array of integers, not necessarily unique. Your goal is to transform the array of integers so that the smallest number does not differ from the largest number by more than two times by removing integers from the array; thus, if x is the smallest element in the array, and y is the largest, then y ≤ 2x. You need only find the number of items to be removed from the array, not make a list of the items. As an example, given the array [4,5,3,8,3,7], you can remove the 2 smallest integers, leaving [4,5,7,8], so that 8 ≤ 2 × 4, or you can remove the 2 largest integers, leaving [3,4,5,6], so that 5 ≤ 2 × 3.
Your task is to write a function to determine how many items to remove from the array. 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.
Programming Praxis 