## Happy Thanksgiving

### November 27, 2015

There will be no exercise today. To all my readers in the United States: Happy Thanksgiving!

## Reversible Random Number Generator

### November 24, 2015

Some applications of random number generators. games, for instance, require that the random sequence be available to run in reverse.

This is easy to do with a simple linear congruential random number generator, which is characterized by the formula `next = a * prev + c (mod m)`

. With a little bit of algebra, that formula can be written `prev = a`

, where a^{−1} * (next - c) (mod m)^{−1} is the inverse of `a (mod m)`

; that modular inverse always exists because the linear congruential generator requires that *a* and *m* are coprime.

Your task is to write a reversible random number generator. 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.

## External Sorting

### November 20, 2015

Sorting the lines of a file that fits in memory is a simple matter of loading the file and calling the sort function. When the file doesn’t fit in memory, however, it must be sorted in pieces, then combined into a single output, which is harder.

Your task is to write a program that sorts the lines of a file that is too large to fit into memory into ascending ascii order. 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.

## File Reversal

### November 17, 2015

Given a file containing lines of text that fits into memory, it is easy to write the file with lines in reverse order: read the lines of text into memory, then write them in reverse. It is harder to reverse the lines of a file if the file is too big to fit into memory.

Your task is to write a program that reverses the lines of a text file that is too big to fit in memory. 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.

## Head And Tail

### November 13, 2015

Today’s exercise is a simple file-handling task for beginning programmers: take the name of a text file as input and write as output the first and last lines of the file.

Your task is to write the file-handling program described 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.

## Triangle Of The Gods

### November 10, 2015

The *n*th element of the Smarandache consecutive number sequence (A007908) is the sequence of the numbers from 1 to *n* concatenated in order:

1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910, 1234567891011, 123456789101112, …

The sequence is sometimes called the “Triangle of the Gods,” and the story goes that anyone who can specify the smallest prime number in the sequence is admitted to heaven.

Your task is to find the smallest prime number in the sequence. 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.

## Self-Organizing Lists

### November 6, 2015

There are many applications where you need to keep a small number of items, a set, and check for membership in the set, and there are many algorithms for doing that: a linked list keeps the items in random order to be retrieved by linear search, an ordered array keeps the items in sequence to be retrieved by binary search, a hash table performs some kind of math on the item, various kinds of trees can store and search the items, and so on.

Today’s exercise looks at a simple algorithm that is appropriate for search in a set that isn’t too big, doesn’t change too often, and isn’t searched too many times, where the definition of “too” depends on the needs of the user. The idea is to store the items of the set in a linked list, search the list on request, and each time an item is found, move it to the front of the list. The hope is that frequently-accessed items will stay near the front of the list, so that instead of an average search that requires inspection of half the list, frequently-accessed items are found much more quickly.

Your task is to write functions that maintain a set as a self-organizing list: you should provide functions to insert and delete items from the set as well as to search within the set. 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.

## School Awards

### November 3, 2015

This counting problem appears from time to time:

There is a school that awards students who, during a given period, are never late more than once and who are never absent for three or more consecutive days. How many permutations of on-time, late and absent, with repetition, are possible for a given timeframe that will result in an award being given to a particular student. For instance, for a three-day timeframe there are 19 ways in which a student can win an award.

Your task is to solve the counting problem given 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.

## Reverse String Ignoring Special Characters

### October 30, 2015

Today’s exercise solves a homework problem for some lucky reader:

Given an input string that contains both alphabetic characters and non-alphabetic characters, reverse the alphabetic characters while leaving the non-alphabetic characters in place. For instance, given the input string

`a!b3c`

, return the output string`c!b3a`

, where the non-alphabetic characters`!`

and`3`

are in their original positions.

Your task is to write a program that reverses a string while leaving non-alphabetic characters in place. 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.

## Strangers On A Train

### October 27, 2015

In Sloane’s Encyclopedia, sequence A247665 is defined as

a(1) = 2; thereafter a(

n) is the smallest number not yet used which is compatible with the condition that a(n) is relatively prime to the nextnterms. The sequence begins 2, 3, 4, 5, 7, 9, 8, 11, 13, 17, 19, 23, 15, 29, 14, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, …

The sequence was submitted by Amarnath Murthy and given to Neil Sloane as a birthday present. Sloane calls the sequence “Strangers on a Train” after the psychological thriller novel by Patricia Highsmith and subsequent film by Alfred Hitchcock, because the *n*th element of the sequence has no factors in common with the next *n* elements (they are “strangers”).

Your task is to write a program that generates the sequence. 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.