APL Practice Problems

1: What an Odd Bunch

Write a function that will return the first n odd natural numbers.

Examples:

      your_function 5
1 3 5 7 9
      your_function 1
1     
      your_function 0 ⍝ should return an empty vector

2: Good Evening

Write a function that takes an integer array and replaces all the odd numbers with the next greater even number.

Examples:

      your_function 1 2 3 4 5
2 2 4 4 6       
      your_function ⍬ ⍝ should return an empty vector      

      your_function 4 4⍴⍳16 ⍝ should work with arrays of any rank  
 2  2  4  4
 6  6  8  8
10 10 12 12
14 14 16 16

3: Miss Quoted

Write a function that will remove text found between pairs of double quotes (").

💡 Hint: One technique is to use ≠\, but there are many ways to solve this problem.

Examples:

      your_function 'this "is" a test'
this "" a test
      your_function 'this is a test'
this is a test
      your_function 'this "is" a "test"'
this "" a ""
      your_function ''  ⍝ should return an empty vector

4: Slice(s) of Pie(s)

Write a function that calculates and returns the areas of 0 or more pie slices. The left argument is 0 or more angles (in degrees). The right argument is 0 or more pie diameters. If the number of angles and diameters are not equal to each other (and neither is a single number), a LENGTH ERROR should be generated.

💡 Hint: If you use APL properly, you should not have to check for the length of either argument – it will just work.

Examples:

      60 your_function 12 
18.84955592 
      0 your_function 12  ⍝ 0 degree slice
0
      60 your_function 0  ⍝ 0 diameter pie
0
      60 your_function 9 12 15  ⍝ 60 degree slices of 3 different pies
10.60287521 18.84955592 29.45243113 
      60 90 120 your_function 12 ⍝ 3 different size slices of the same pie 
18.84955592 28.27433388 37.69911184
      60 90 120 your_function 9 12 15 ⍝ different sizes of different pies
10.60287521 28.27433388 58.90486225 
      60 90 120 your_function 9 12 ⍝ 3 slices, 2 pies? 
LENGTH ERROR

5: DNA?

Write a a function that takes a string representing a nucleotide and returns a 1 if it is a valid DNA string, 0 otherwise. In other words, are all the characters in the string in the set 'ACGT'?

Examples:

      your_function 'ATGCTTCAGAAAGGTCTTACG'
1
      your_function 'Dyalog'
0
      your_function ''       ⍝ an empty string is valid
1
      your_function 'T'      
1  

6: k-mers

The term k-mer typically refers to all the possible substrings of length k that are contained in a string. In computational genomics, k-mers refer to all the possible subsequences (of length k) from a read obtained through DNA Sequencing. Write a dfn that takes a character vector as its right argument and k (the substring length) as its left argument and returns a vector of the k-mers of the original string.

Examples:

      4 your_function 'ATCGAAGGTCGT'
┌────┬────┬────┬────┬────┬────┬────┬────┬────┐
│ATCG│TCGA│CGAA│GAAG│AAGG│AGGT│GGTC│GTCG│TCGT│
└────┴────┴────┴────┴────┴────┴────┴────┴────┘
      4 your_function 'AC'    ⍝  k>string length? Return an empty vector

7: Counting DNA Nucleotides

Write a function that takes a character vector representing a DNA string and returns 4 integers of the number of occurrences for each of the symbols ‘A’, ‘C’, ‘G’, and ‘T’ respectively.

Examples:

      your_function 'AGCTTTTCATTCTGACTGCTGTCTTTAAAAAAAGAGTGTCTGATAGCAG' 
14 8 10 17
      your_function 'CCAAATGGGG 
3 2 4 1
      your_function ''
0 0 0 0
      your_function ,'G'
0 0 1 0

8: Be the First 1

Write a dfn that takes a Boolean vector or scalar and “turns off” all the 1s after the first 1.

Examples:

      your_function 0 1 0 1 0 0 1
0 1 0 0 0 0 0
      your_function ⍬ ⍝ should return an empty vector      

      your_function 0 0 0 0 ⍝ no 1's?  no problem!
0 0 0 0

9: Double Trouble

Write a function that takes a character vector or scalar and returns a Boolean vector indicating anywhere an element is followed by an element of the same value.

Examples:

      your_function 'bookkeeper'
0 1 0 1 0 1 0 0 0 0  
      your_function ''  ⍝ should return an empty vector      

      your_function 'aaaaaa'
1 1 1 1 1 0
      your_function 'd'
0 

10: Squaring Off

Write a function that will reshape a given array into the smallest square matrix that will contain all the elements of the argument, padding with additional elements if necessary. The pad element should be 0 if the array is numeric and space ' ' if the array is character.

Examples:

      your_function 1 2 3 4
1 2 
3 4
      your_function 1 2 3 4 5
1 2 3 
4 5 0 
0 0 0
      your_function 'Dyalog APL'       ⍝ should work with any data
Dyal  
og A  
PL     
      ' '=your_function 'Dyalog APL'   ⍝ show where the spaces are
0 0 0 0
0 0 1 0
0 0 1 1 
1 1 1 1  
      your_function 100  ⍝ should return a 1×1 matrix 
100
      your_function ⍬    ⍝ should return a 0×0 matrix

      ⍴your_function ⍬   ⍝ should return a 0×0 matrix
0 0