Perfect Shuffle
March 13, 2020
A perfect shuffle, also known as a faro shuffle, splits a deck of cards into equal halves (there must be an even number of cards), then perfectly interleaves them. Eventually a series of perfect shuffles returns a deck to its original order. For instance, with a deck of 8 cards named (1 2 3 4 5 6 7 8), the first shuffle rearranges the cards to (1 5 2 6 3 7 4 8), the second shuffle rearranges the cards to (1 3 5 7 2 4 6 8), and the third shuffle restores the original order (1 2 3 4 5 6 7 8).
Your task is to write a program that performs a perfect shuffle and use it to determine how many perfect shuffles are required to return an n-card deck to its original order; how many perfect shuffles are required for a standard 52-card deck? 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.
2SUM
March 10, 2020
We’ve done this in a previous exercise, but it’s a common problem both as an interview question and in programming classes, and I’ve seen in it several times in the last week, so now is a good time to do it again:
Given a list of integers and a target integer, find all the pairs of integers in the list that sum to the target integer, or report that there are no such pairs.
Your task is to write a program to find pairs of integers that sum to a target; you should write three programs, with time complexities of O(n²), O(n log n), and O(n). When you are finished, you are welcome to read a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Squares Of A Sorted Array
March 6, 2020
This problem has been going around the internet the last few days. I’ve seen it on several message boards, though I don’t know the original source:
Given an array of integers sorted in non-decreasing order, return an array of the squares of each number, also sorted in non-decreasing order. For instance, given (-4 -1 0 3 10), the desired output is (0 1 9 16 100).
Your task is to write a program to compute the sorted squares of a sorted 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.
Two Easy Tasks
March 3, 2020
Many of the tasks I publish on this blog come from beginning-programmer forums. Here is a task taken from some sort of entrance examination:
Jason rings every multiple of 13 less than 500. He then crosses every multiple of 17 less than 500. How many numbers get both ringed and crossed?
The test is a multiple-choice examination with possible selections 10, 0, 1 and 4. The solution sheet shows the correct answer is 4. The questioner who posted this question was asking how to calculate the answer given on the solution sheet.
And here is another simple task:
Given positive integer n < 1018, find the sum of the integers from 1 to n, mod 109 + 7. Assume you are using a language that provides 64-bit arithmetic, so no intermediate results can be larger than 264.
Your task is to write a program to solve these two tasks. 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.
String Rotations
February 28, 2020
Pythagorean Quadruple
February 25, 2020
A Pythagorean quadruple consists of four positive integers a, b, c and d such that a ≤ b ≤ c ≤ d and a² + b² + c² = d². For instance, (2 3 6 7) is a Pythagorean quadruple because 2² + 3² + 6² = 4 + 9 + 36 = 49 = 7².
Your task is to write a program that counts the Pythagorian quadruples with a, b, c less than or equal to some given N, and compute the number of Pythagorian quadruples with N = 1000. 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.
Formatted Dates
February 21, 2020
Regular readers of this blog know that I work with a team of programmers, sysadmins and database administrators to maintain a large legacy database application, running on Oracle and HP-UX, and Scheme is nowhere in sight. Lately I have been “stealth programming” by writing awk programs in shell wrappers, because shell programming is a normal part of our environment. One thing I have been doing is formatting reports with awk. That frequently requires a formatted date string, either for today or some other day; gawk provides the strftime function to format dates, but Posix awk, which is what HP-UX provides, doesn’t. So I wrote my own.
Your task is to write a function that formats dates; use any convention you like to determine how the date is formatted. 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.
Square Triple
February 14, 2020
We have a simple homework problem today:
Given a list of distinct integers, find all triples (x y z) where x, y and z are in the list and x * y = z².
Your task is to find the list of triples. 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.
Removing Spaces
February 11, 2020
We have a simple task today, with dozens of potential solutions:
Write a program to remove all spaces from a string.
Your task is to write a program to remove all spaces from a string. 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.
My Mailbag
February 7, 2020
I had two interesting emails from readers this week. I’ll discuss both of them, but suppress the names of the writers; they can identify themselves in the comments below if they wish.
One writer saw Johnny Ball’s video about Russian Multiplication on Numberphile and suggested it would make a good exercise. Indeed it would; in fact, we have already done it twice ([1] [2]).
Another writer suggested that the compose function in the Standard Prelude should return the identity function if called with no arguments, rather than reporting an error. That is, of course, correct; my apologies for the bug.
Your task is to write programs to perform russian multiplication and compose functions, as suggested above. 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 