Problems (John Earnest)

Pascal’s Triangle
A classic exercise demonstrating “for-scan”.

(1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1)

Dereplicated Map
Map a function x over y without recomputing duplicate values.

  f[{`0:,"f of ",$x;x+2};3 10 9 3 5 10]
f of 3
f of 10
f of 9
f of 5
5 12 11 5 7 12

2x2 Matrix Determinant
A nice use of dot-apply.

  f (3 8;4 6)
-14

Longest Cycle Count
Iterating on a permutation vector, how many steps is the longest cycle?

  f 1 2 3 0
4
  f 1 0 3 4 2
3
  f 0 1 2 3 4
1

Rising Edge
“Number go up! Number good.” -business man

  f 3 3 4 5 4 6 9
0 0 1 1 0 1 1

Sign
Iverson’s convention.

  f 34 -99 0
1 -1 0

Find a Function’s Name
An everyday convenience function.

  boop: {x+1}
  f {x+1}
"boop"

Is Inverleave?
Can you interleave x and y (merge without altering element orders) to arrive at z?

  f["don";"dogo";"dodongo"]
1
  f["don";"dogo";"gododon"]
0

Merge Dictionaries
Turn a list of dictionaries into a dictionary of lists.

  f (.,(`a;1);.,(`b;2);.((`a;3);(`b;4)))
.((`a
   1 3)
  (`b
   2 4))

Distinct Names
Tag duplicates by order of appearance.

  f ("foo";"bar";"foo";"quux";"zami";"bar")
("foo0"
 "bar0"
 "foo1"
 "quux0"
 "zami0"
 "bar1")

Limit Run Length
Cap runs of char z in y to length x.

  f[2;"xxxxOOxOOxxxOOx";"x"]
"xxOOxOOxxOOx"