rodrigogiraoserrao

⍝ PROBLEM 9.1, array-oriented solution, faster for the 3 examples provided.
Weights ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Reads the mobile data from the file ⍵ and returns its weights.
    ⍝ Monadic function expecting a character vector and returning an integer vector.
    ⍝ Returns the weights ordered from left to right, top to bottom.

    ⍝ How it works:
    ⍝ We will build a square coefficient matrix where each variable is the weight of a left (┌) or right (┐) corner.
    ⍝ Let's say n is the number of leafs in the mobile; then n is also the number of pivots and by the lengths of the arms

rodrigogiraoserrao

:Namespace Mobiles
    ⍝ This namespace defines a set of helper functions for the recursive solution of the last problem.
    (⎕IO ⎕ML ⎕WX) ← 0 1 3 

    ⍝ Monadic function to take a path to a mobile.txt file and return a character matrix.
    OpenToMatrix ← {↑⊃⎕nget ⍵ 1}

    Parse ← {
        (⎕IO ⎕ML ⎕WX) ← 0 1 3 
        ⍝ Monadic function to parse (recursively) a mobile in matrix form.

rodrigogiraoserrao

⍝ PROBLEM 8.1
Balance ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Given an integer vector ⍵, find a 2-partition with equal sums.
    ⍝ Monadic function expecting an integer vector.
    ⍝ This algorithm is O(2*≢⍵); we compute possible partitions of ⍵ and check
    ⍝  if their sums satisfy the requirement.
    ⍝ Return a 2-element vector of integer vectors.
    S ← 1⊥⍵     ⍝ Check simple necessary properties:
    2|S: ⍬      ⍝ odd sum can't be evenly split 

rodrigogiraoserrao

⍝ PROBLEM 7.1
⍝ Computes the check digit for a UPC-A barcode.
⍝ Monadic function expecting an 11-element integer vector.
⍝ Returns an integer. 
CheckDigit ← (10|∘-+.×∘(11⍴3 1))

⍝ Decimal repr of the right digits of a UPC-A barcode.
UPCRD ← 114 102 108 66 92 78 80 68 72 116            
⍝ Bit matrix with one right digit per row.
bUPCRD ← ⍉2∘⊥⍣¯1⊢ UPCRD

rodrigogiraoserrao

⍝ PROBLEM 6.1
Merge ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Merges JSON data from a file named ⍵ into a template file named ⍺.
    ⍝ Dyadic function expecting a character vector on the left (template path) and a character vector on the right (data path).
    ⍝ Returns a character vector.
    t ← ⊃⎕NGET ⍺
    G ← (⎕JSON⊃⎕NGET ⍵)_SafeGet
    R ← {
        ⍝ Convert matched regex patterns into the appropriate replacements.

rodrigogiraoserrao

⍝ PROBLEM 5.1 
rr ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Computes how much your investment is worth after cash flows and rate calculations.
    ⍝ Dyadic function expecting number vector on the left (deposits/withdrawals) and number vector on the right (corresponding rates).
    ⍝ At moment 1 you have r[1] ← ⍺[0] and at the subsequent moments you have r[n] ← ⍺[n-1] + r[n-1]×⍵[n-1].
    ⍝ Expanding the recurrence relation we can determine beforehand all expressions.
    ⍝ Assuming ⎕IO←0 and traditional mathematical notation,
    ⍝ r[1]←⍺[0], r[2]←⍺[1]+⍺[0]⍵[1], r[3]←⍺[2]+⍺[1]⍵[2]+⍺[0]⍵[2]⍵[1], r[4]←⍺[3]+⍺[2]⍵[3]+⍺[1]⍵[3]⍵[2]+⍺[0]⍵[3]⍵[2]⍵[1]
    ⍝ Returns a number.

rodrigogiraoserrao

⍝ PROBLEM 4.1
revp ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Find reverse palindromes of lengths between 4 and 12 in a DNA character vector.
    ⍝ Monadic function expecting a character vector.
    ⍝ A substring is a reverse palindrome if the substring is equal to its reverse complement.
    ⍝ The complement of a DNA string changes these pairs: 'A'←→'T', 'C'←→'G'.
    ⍝ Returns a 2 column integer matrix as if ⎕IO←1
    (⊢+⍴∘1 0∘⍴) 4 12 _revp ⍵
}

rodrigogiraoserrao

PastTasksBlast ← {
    ⍝ Function to scrape Dyalog's webpage for the URLs of past year's competition problem statements.
    ⍝ Monadic function expecting a character vector. 
    ⍝ Assumes HttpCommand is loaded.
    ⍝ Returns a vector of character vectors.
    r ← #.HttpCommand.Get ⍵
    r.HttpStatus≠200: 0⍴⊂,' '
    base ← ⊃('<base +href="(.*?)"' ⎕S '\1') r.Data
    ('href="(.*?[.]pdf)"' ⎕S (base,'\1')) r.Data
}

rodrigogiraoserrao

Steps ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Utility function to generate ranges of numbers.
    ⍝ Dyadic function expecting a number on the left (mode) and a 2-element number vector (s f) on the right (steps start and end points).  
    ⍝  - if ⍺ is negative, return vector with |⌊⍺ equally-sized steps from s to f.
    ⍝  - if ⍺ is positive, ⍺ represents the step size.
    ⍝  - if ⍺ is 0, return s
    ⍝ Returns a vector of numbers between s and f.
    ⍺ ← 1
    (s f) ← ⍵

rodrigogiraoserrao

DiveScore ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Computes the olympic dive score up to two decimal places.
    ⍝ Dyadic function expecting a number (dive difficulty) on the left and a vector of numbers on the right (judge scores).
    ⍝ ⍵ is assumed to have odd length ≥ 3.
    ⍝ Returns a number with, at most, 2 decimal places. 
    ⍎2⍕⍺×1⊥ (⊂⊃⍨¨3↑(÷∘2-∘3∘≢)⌽⍋) ⍵
}