Write a dfn to produce a vector of the first n odd numbers.
{your_solution} 10
1 3 5 7 9 11 13 15 17 19
{your_solution} 1
1
{your_solution} 0 ⍝ this should return an empty vector
Write a dfn which returns the percent (from 0 to 100) of passing (65 or higher) grades in a vector of grades.
{your_solution} 25 90 100 64 65
60
{your_solution} 50
0
{your_solution} 80 90 100
100
{your_solution} ⍳0 ⍝ all grades in an empty vector are passing
100
Write a dfn which returns the number of words in the given character scalar or vector.
For simplicity’s sake, you can consider the space character ' ' to be the only word separator.
{your_solution} 'Testing one, two, three'
4
{your_solution} '' ⍝ empty vector has no words
0
{your_solution} ' this vector has extra blanks ' ⍝ just counting the blanks won't work
5
Write an APL dfn which returns a 1 if the opening and closing parentheses in a character vector are balanced, or a zero otherwise.
{your_solution} '((2×3)+4)'
1
{your_solution} ''
1
{your_solution} 'hello world!'
1
{your_solution} ')(2×3)+4('
0
{your_solution} '(()'
0
{your_solution} ')'
0
An identity matrix is a square matrix (table) of 0 with 1’s in the main diagonal.
Write an APL dfn which produces an n×n identity matrix.
{your_solution} 5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
{your_solution} 1 ⍝ should return a 1×1 matrix
1
{your_solution} 0 ⍝ should return a 0×0 matrix
Write a dfn which returns the magnitude of the range (i.e. the difference between the lowest and highest values) of a numeric array.
{your_solution} 19 ¯3 7.6 22
25
{your_solution} 101 ⍝ should work with a scalar argument
0
{your_solution} 2 3⍴10 20 30 40 50 60 ⍝ should work with arrays of any number of dimensions
50
{your_solution} ⍳0 ⍝ including empty arrays
0
Write a dfn which selects the floating point (non-integer) numbers from a numeric vector.
{your_solution} 14.2 9 ¯3 3.1 0 ¯1.1
14.2 3.1 ¯1.1
{your_solution} 1 3 5 ⍝ should return an empty vector
{your_solution} 3.1415
3.1415
Write a dfn which produces a multiplication table.
{your_solution} 5
1 2 3 4 5
2 4 6 8 10
3 6 9 12 15
4 8 12 16 20
5 10 15 20 25
{your_solution} 1 ⍝ should return a 1×1 matrix
1
{your_solution} 0 ⍝ should return a 0×0 matrix
Write a dfn which produces n month moving averages for a year’s worth of data.
sales←200 300 2700 3400 100 2000 400 2100 3500 3000 4700 4300
2 {your_solution} sales ⍝ produces 2 month moving averages
250 1500 3050 1750 1050 1200 1250 2800 3250 3850 4500
10 {your_solution} sales ⍝ 10 month moving average
1770 2220 2620
1 {your_solution} sales ⍝ 1 month moving average is the same as sales
200 300 2700 3400 100 2000 400 2100 3500 3000 4700 4300
Many people have taken some sort of algebra class where you are presented with a set of linear equations like:
3x + 2y = 13
x - y = 1
The answer in this case is x=3 and y=2
Write a dfn which solves this type of problem. Hint: this is the easiest of all of the problems presented here.
The left argument is a vector of the values for the equations and the right argument is a matrix of the coefficients.
13 1 {your_solution} 2 2⍴3 2 1 ¯1
3 2
2 6 4 {your_solution} 3 3⍴4 1 3 2 2 2 6 3 1
¯1 3 1