## Deblank

### June 28, 2019

Today’s task is easy. I expect to see lots of imaginative and over-the-top solutions:

Write a program that passes its input to its output, removing any lines that are either empty or contain only “white” characters like space and tab.

Your task is to write a program that removes blank lines from files. 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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## Dividing Without Divide

### June 25, 2019

Today’s task comes from a student programmer:

Given a numerator and divisor of unsigned integers, compute the quotient and remainder. You cannot use divide, cannot use mod, and you want to optimize for speed.

After a while, the student programmer looked up the official solution:

```def divide_problem(num, div):
quotient = 1
while num - (quotient * div) >= div:
print(num - (quotient * div), "loop")
quotient += 1
remainder = num - (quotient * div)
return quotient, remainder```

Your task is to comment on the official solution and write a better one. 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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## String Comparison

### June 21, 2019

A string is a sequence of characters, perhaps including a backspace character that renders both itself and the previous character as if they were not part of the string. For instance, if we make the backspace character visible using the `#` symbol, the two strings `abcx#de` and `abcde` are identical. Multiple successive backspaces remove multiple successive characters.

Your task is to write a program that compares two strings that may contain backspaces and reports if they are equal. 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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## Latin Squares

### June 18, 2019

A latin square of order n is a square matrix with n rows and n columns, with each entry in the matrix containing an integer from 0 to n − 1, arranged so that no row or column contains duplicate integers. Here is a sample latin square of order 10:

```8 3 7 1 5 6 4 2 0 9
4 5 6 2 0 9 3 7 8 1
9 2 3 8 7 5 1 4 6 0
2 6 0 3 9 8 7 5 1 4
0 4 2 9 3 7 8 1 5 6
6 1 4 0 2 3 9 8 7 5
1 7 5 4 6 0 2 3 9 8
3 0 9 7 8 1 5 6 4 2
5 8 1 6 4 2 0 9 3 7
7 9 8 5 1 4 6 0 2 3```

Your task is to write a program that generates latin squares of order n. 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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## Van Eck Sequence

### June 14, 2019

Neil Sloane is on Numberphile again, discussing the Van Eck sequence (A181391):

The first item in the sequence is 0. Compute the next item as follows: If the previous item has not previously appeared in the sequence, add 0 to the sequence, otherwise add to the sequence the number of steps back in the sequence the previous item previously appeared. For instance, the first item is 0. Since 0 has not previously appeared in the sequence, the next item is 0. Now 0 has previously appeared, and the previous 0 was one back in the sequence, so add 1 to the sequence. Since 1 has not previously appeared, add 0. But 0 appeared previously, two back in the sequence, so add 2. Since 2 has not previously appeared, add 0. But 0 appeared previously, two items back, so add 2 to the sequence. Since 2 previously appeared in the sequence, two terms back, add another 2 to the sequence. The next item in the sequence is 1, because 2 also appeared as the previous number. Since 1 appeared in the sequence, count back to the previous 1, and add 6 to the sequence. And so on. The sequence begins 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, ….

Your task is to write a program that generates the Van Eck sequence and investigate the properties of the sequence. When you are finished, you are welcome to ,a href=”https://programmingpraxis.com/2019/06/14/van-eck-sequence/2/”>read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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## Maximum Product

### June 11, 2019

I think today’s exercise comes from one of those hacker testing sites, but I’m not sure:

Given three arrays of integers, both positive and negative, find the maximum product that can be formed by taking one element from each array. For instance, if A = [10,-10,15,-2], B = [10,-12,13,-2], and C = [-11,-10,9,-12], the maximum product is 2160 using 15, -12 and -12.

Your task is to write a program that finds the maximum product of three integers, taking one each from three arrays. 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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## Primitive Roots

### June 7, 2019

In modular arithmetic, a number g is a primitive root of n if, for every a coprime to n, there exists some k such that gka (mod n). The concept of a primitive root was developed by Gauss and pops up from time to time in work on cryptography and number theory.

There is no formula for computing a primitive root, but they are common enough that it is easy to just randomly search for them; more commonly, people just start at 2 and work their way up. Once a primitive root has been found, the remaining primitive roots of n can be found by exponentiating mod n.

Your task is to write a program that computes the primitive roots of prime n. 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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## Reverse Vowels

### June 4, 2019

Now that school is finished for the year, I’m catching up on the homework questions that people have sent me over the last several months. This one is fun:

Given a string, write it with the vowels reversed, maintaining the original capitalization of the vowels. For instance, “HELLO world” becomes “HOLLO werld” and “Programming PRAXIS” becomes “Prigramming PRAXOS” (I kinda like that one).

Your task is to write a program that returns an input string with vowels in reverse order, respecting the original capitalization. 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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