saweiss/Phase1Contest2020.dyalog

## Phase1Contest2020.dyalog
P1←(1≠(×⊣))⌽↑{⊆⍺⍵}↓
P2←(128∘>∨191∘<)⊂⊢
P3←26⊥⎕A∘⍳
P4←≠⌿0=400 100 4∘.|⊢
P5←⊢{⍵,⍵-(××⍳∘|)-/⍺}⊃
P6←(⊣(⌿⍨)(+⌿=))⍪~⍨
P7←{⍺=2⊥∧/(2∘⊥⍣¯1)⍺⍵}
P8←¯1∧.=2×/(×2-/10∘⊥⍣¯1)
P9←{1∧.=≢∘∪¨⊆⍨2@(¯1∘=)×0~⍨(+\⍣¯1)⍵}
P10←↑((⊢⍴⍨(×/⍴))~((⊂' '⍴⍨(⍴⊃))))∘(↓(↑⍕¨))

## Phase2Contest2020.dyalog
:Namespace Contest2020
⍝ === VARIABLES ===

    L←⎕av[3+⎕io]
    AboutMe←L,''

    FilePath←''

    Reaction←L,''

    ⎕ex 'L'

⍝ === End of variables definition ===

    (⎕IO ⎕ML ⎕WX)←1 1 3

    :Namespace Problems
        (⎕IO ⎕ML ⎕WX)←1 1 3

        ∇ parts←Balance nums;n;K;T;P;S;i;j;H
      ⍝ 2020 APL Problem Solving Competition Phase II
      ⍝ Stub function for Problem 8, Task 1 - Balance
      ⍝ Put your code and comments below here

      ⍝ NOTE: I wasn't sure if ⎕IO could be used in the competition, so the
      ⍝ comments use 0-based indexing and the code uses 1-based.

          T←+/nums
      ⍝ Return ⍬ if the sum of nums is odd; can't split evenly.
          :If 2∘|T
              parts←⍬
          :Else
              n←≢nums
              K←T÷2
          ⍝ Boolean table where each column, j, represents the first j
          ⍝ elements of nums, where j is in range [0,n] (empty set is 0).
          ⍝ Each row, i, represents the ith partial sum in range [0,K].
          ⍝ Let P[i;j] be 1 if a subset of the jth subset sums to i.
          ⍝ Otherwise, P[i;j] is 0. Initialize the top row to 1 because
          ⍝ the null set is a subset of all sets, and it sums to 0.
              P←((1⍴⍨1∘+)⍪0⍴⍨(K,1∘+))n
          ⍝ Store the parent of P[i;j]'s row index, i-nums[j], in S[i;j] if
          ⍝ the last element of the jth subset was included in the sum to i.
              S←(1∘+K n)⍴⍬

              :For i j :In 1∘+⍳K n
              ⍝ A smaller subset that excludes j already sums to i.
                  :If P[i;j]←P[i;j-1]
              ⍝ Can't sum to i if j is larger.
                  :ElseIf i>nums[j-1]
              ⍝ Including nums[j] in the sum to i compares the same as
              ⍝ excluding nums[j] and summing to i-nums[j].
                  :AndIf P[i;j]←P[i-nums[j-1];j-1]
                      S[i;j]←(i-nums[j-1])
                  :EndIf
              :EndFor

              i←1+K
              H←⍬
          ⍝ From the last element of S, traverse backwards and collect the
          ⍝ columns that contain parents pointers which directly produced the
          ⍝ last element of S. Theses columns correspond to the indexes of
          ⍝ nums which make up one element of parts.
              :For j :In ⌽1+⍳n
                  :If (i∘≠∧0∘≠)S[i;j]
                      H,←j-1
                      i←S[i;j]
                  :EndIf
              :EndFor

          ⍝ If the last value of P is 1, then split nums by equal sums.
          ⍝ Otherwise, nums can't be split evenly, so return ⍬.
              parts←{P[1+K;1+n]:⊆nums[H](nums[H~⍨⍳n]) ⋄ ⍬}⍬
          :EndIf
        ∇

          CheckDigit←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 7, Tasl 1 - CheckDigit
          ⍝ Put your code and comments below here

          ⍝ Given an array of 11 UPC-A digits, compute the check digit.
          ⍝
          ⍝ Starting at the right, label digits alternately odd and even.
          ⍝ multiply odd digits by 3 and even digits by 1. Sum all resulting
          ⍝ numbers. The distance from this sum to the next highest multiple
          ⍝ of 10 is the check digit. If the sum is a multiple of 10, then
          ⍝ the check digit is 0, i.e., 0 numbers away from a multiple of 10.
              10|10-10|⍵+.×11⍴3 1
          }

          DiveScore←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 1, Task 1 - DiveScore
          ⍝ Put your code and comments below here

          ⍝ ⍺: Single degree of dificulty (⍺ > 1).
          ⍝ ⍵: Two or more judges' scores, each in range [0,10].
          ⍝ Calculate the diving score to at most 2 decimal places.
          ⍝
          ⍝ Throw out all but the three median judges' scores. The remaining
          ⍝ scores are summed and multiplied by the degree of dificultly.
              ⍎2⍕⍺×+/(¯1+⌊2÷⍨≢⍵){(-⍺)↓⍺↓⍵[⍋⍵]}⍵
          }

        ∇ text←templateFile Merge jsonFile;t;m;n;v;z;s;q;i;j
      ⍝ 2020 APL Problem Solving Competition Phase II
      ⍝ Stub function for Problem 6, Task 1 - Merge
      ⍝ Put your code and comments below here

      ⍝ Read in the template and json files.
          (t m)←⊃∘⎕NGET¨templateFile jsonFile
      ⍝ Convert the JSON into a namespace.
          n←⎕JSON m
      ⍝ Get the variable names in the namespace.
          v←n.⎕NL ¯2
      ⍝ Get the corresponding namespace variable values, prepend @.
          z←(⊂'@'),n⍎¨v
      ⍝ Prepend a blank corresponding to @, then surround each with @.
          v←(1⌽'@@'∘,)¨(⊂''),v
      ⍝ Partition the template so merge areas are in their own boxes.
          s←t⊆⍨{(⍳≢⍵)/⍨⍵+1 ¯1⍴⍨≢⍵}≢¨⊂⍨'@'=t
      ⍝ Find merge areas that are missing from the JSON file.
          q←v~⍨{⍵/⍨'@'∊¨⍵}∪s
      ⍝ Prepend the missing merge area names to the existing ones.
          v,⍨←q
      ⍝ For each missing merge area, prepend ??? to the replacements.
          z,⍨←(≢q)⍴⊂'???'
      ⍝ Replace each merge area with its corresponding replacement.
          :For i j :InEach v z
              s←((⊂j)@{(⊂i)⍷s})s
          :EndFor
      ⍝ Reassemble into a single character vector.
          text←⊃,/s
        ∇

          PastTasks←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 3, Task 1 - PastTasks
          ⍝ Put your code and comments below here

          ⍝ Get the HTML from the given URL and convert to matrix form.
              w←⎕XML(#.HttpCommand.Get ⍵).Data
          ⍝ Find the indexes of the ⍺ string in the ⍵ list of strings.
              f←{(⊂,⍺)⍸⍤⍷⍵}
          ⍝ Filter the attributes column by the 'a' and 'base' elements.
              (a b)←{⍵[⍺ f ⍵[;2];4]}∘w¨'a' 'base'
          ⍝ Filter the value column by 'href' for all attributes.
              (h j)←{⊃¨'href'∘{⍵[⍺ f ⍵[;1];2]}¨⍵}¨a b
          ⍝ Filter 'a' element attribute values by the PDF file ending.
              p←h[1+('.pdf'⎕S 2)h]
          ⍝ Attach the URL base to each relative URL.
              j,¨p
          }

          ReadUPC←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 7, Task 3 - ReadUPC
          ⍝ Put your code and comments below here

          ⍝ Ensure the input contains 95 bits
              95≠≢⍵:¯1
          ⍝ Split up the 7 bit arrays by left and right sides (drop padding).
              B←{⍉6 7⍴⍵[⍺+⍳42]}
              U←B∘⍵¨3 50
          ⍝ Ensure one side has even parity and the other has odd.
              D←∧/¨2|¨+⌿¨U
              ⍲/0 1∊D:¯1
          ⍝ Put odd parity matrix on left side and match the parities.
              U←↑,/(~@1)(⌽∘(⌽∘⊖¨)⍣(¯1=×-/D))U
          ⍝ Even parity barcode digits 0-9 converted to decimal then ASCII.
              DG←'rflB\NPDHt'
          ⍝ Convert from binary to decimal according to conversion table.
              R←¯1+DG⍳⎕UCS 2⊥U
          ⍝ Ensure the check digit is valid.
              (¯1↑R)≠CheckDigit ¯1↓R:¯1
              R
          }

          Steps←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 2, Task 1 - Steps
          ⍝ Put your code and comments below here

          ⍝ No ⍺ is the same as a step size of 1.
              ⍺←1
          ⍝ The first endpoint.
              f←⊃⍵
          ⍝ No steps is just the first endpoint because no steps were made.
              0≡⍺:f
          ⍝ Indexes from 1 to |∘⊢ all times the sign of ⊢.
              j←(××⍳∘|)⊢
          ⍝ Positive ⍺ gives the step size from ⍵[1] to ⍵[2], the endpoints.
          ⍝ Truncate the last step size if ⍺ doesn't divided evenly into the
          ⍝ the absolute diffence between the endpoints.
              1≡×⍺:∪1⌽(⌽⍵),f-⍺×j⌊-/⍵÷⍺
          ⍝ Negative ⍺'s floor magnitude gives the number of equally sized
          ⍝ steps to take between the endpoints.
              f,f-⍵((-/÷)×j)|⌊⍺
          }

        ∇ weights←Weights filename;m;k;x;y;v;a;q;b;j;e;c;l;u;d;p;t;n;o;f;s;i;r;h
      ⍝ 2020 APL Problem Solving Competition Phase II
      ⍝ Stub function for Problem 9, Task 1 - Weights
      ⍝ Put your code and comments below here

      ⍝ Read the mobile diagram into a character matrix.
          m←↑⊃⎕NGET filename 1
      ⍝ Sort ascending.
          k←{⍵[⍋⍵]}
      ⍝ Sort ascending by columns.
          x←{⌽¨k⌽¨⍵}
      ⍝ Append the first of ⍺ to the difference between the last ⍺ and ⍵.
          y←{(⊃⍺),⍵-⍥(1∘↓)⍺}
      ⍝ Get the indexes of each vector of ⍺ in vector of vectors ⍵.
          v←{⍵∘{⊃(⊂⍵)⍸⍤⍷⍺}¨⍺}
      ⍝ Get the indexes of each letter in alphabetical order.
          a←⍸27≠⎕A∘⍳m
      ⍝ Get the indexes of all turning points.
          q←⍸('┐'∘=∨'┌'∘=)m
      ⍝ Get the indexes of all fulcrums.
          b←'┴'⍸⍤=m
      ⍝ Reshape 'a' so a single row can be taken from it.
          a←{(1,⍴⍵)⍴⍵}a

          :Repeat
          ⍝ Get the last row of 'a'.
              e←{(¯1↑⍴⍵)⍴⍵}¯1↑[1]a
          ⍝ Place turning point indexes next to fulcrums/letters below them.
              c←x∪q,e
          ⍝ Check for any that reached the parent fulcrum.
              u←b[1]≡¨e
          ⍝ Climb the tree if not already at the top.
              d←c[¯1+u+e v c]
              a⍪←d
          ⍝ Place fulcrum indexes next to their related turning points.
              p←k∪b,d
          ⍝ Get each turning point direction; ¯1 for left and 1 for right.
              t←¯2+'┐ ┌'⍳m[d]
          ⍝ Traverse the tree from the turning points to fulcrums.
              n←p[(t×~u)+d v p]
              a⍪←n
          ⍝ Stop when the last row of 'a' contains only the parent fulcrum.
          :Until b[1]∧.≡n

      ⍝ Drop the locations of the letters.
          a←1↓[1]a
      ⍝ Get the signs of the last turns made by each letter.
          j←1,⍨¨{1=≢b:1 1 ⋄ ⊃-/{∨⌿b[⍺]⍷⍵}∘⍵¨2 3}a
      ⍝ Apply the signs in 'j' to the rows of 'a' except ¯1 stays 1.
          a←1@{0,⍨¯1=⊃⍵}¨↑(⊂j)×↓a
      ⍝ Substract pairs of tree rows, keeping the first values the same.
          a←{,⌿y/¨⍵⊆[1]⍨2/⍳2÷⍨≢⍵}a
      ⍝ Get the unique tree row numbers.
          o←∪⊃¨⊃,/a
      ⍝ Group each column by tree row numbers, then get just the columns.
      ⍝ The result is a matrix for of the needed system of equations.
          f←↑{2⊃¨⊃¨(~∘(⊃⍵,./⍨⍺{⍺≠⊃⍵}¨¨⍵))¨⍵}∘a¨o
      ⍝ Scale a vector by its GCD.
          s←⊢÷∨/
      ⍝ Generate an identity matrix of the given size.
          i←∘.=⍨⍳
      ⍝ Compute a right inverse of the given non-square matrix.
          r←⍉+.×(⌹⊢+.×⍉)
      ⍝ Compute the smallest nontrivial integer solution to the given
      ⍝ singular homogeneous integer coefficient system.
          h←s(+/i∘(1↓⍴)-r+.×⊢)
          weights←h f
        ∇

          WriteUPC←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 7, Task 2 - WriteUPC
          ⍝ Put your code and comments below here

          ⍝ Ensure input length is exactly 11.
              11≠≢⍵:¯1
          ⍝ Ensure input contains only single digits.
              ~∧/⍵∊¯1+⍳10:¯1
          ⍝ Convert decimal to binary.
              DB←2∘⊥⍣¯1
          ⍝ Beginning and ending digits.
              BE←DB 5
          ⍝ Middle digits.
              MD←0,BE,0
          ⍝ Even parity barcode digits 0-9 converted to decimal then ASCII.
              DG←'rflB\NPDHt'
          ⍝ Convert input to bit array (tacking the check digit on the end).
              TD←,⍉DB ⎕UCS DG[1+⍵,CheckDigit ⍵]
          ⍝ Negate left bits for parity, and insert start, middle, end bits.
              42{↑,/BE(~⍺↑⍵)MD(⍺↓⍵)BE}TD
          }

          pv←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 5, Task 2 - pv
          ⍝ Put your code and comments below here

          ⍝ Given an ⍺ of cash flows and an ⍵ of corresponding interest
          ⍝ rates, compute the present value.
          ⍝
          ⍝ The present value is the dot product between the current values
          ⍝ and the reciprocal of 1 + the cumulative interest rates.
              ⍺+.÷×\1+⍵
          }

          revp←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 4, Task 1 - revp
          ⍝ Put your code and comments below here

          ⍝ Complement pairs AT and CG are equidistant from the space.
              d←'AC GT'
          ⍝ Replace complements by equal and opposite integers.
              e←¯3+d⍳⍵
          ⍝ Table of indexes up to ⍺ with a sliding ⍵-width window.
              i←{↑⍵,/⍳⍺}
          ⍝ Moving width index tables for widths in range [4,12].
              m←(≢⍵)i¨2+2×⍳5
          ⍝ Tables of complement numbers for each window width.
              n←e∘(⊣⌷⍨∘⊂)¨m
          ⍝ Location and length pairs for each reverse palindrome.
              ↑↑,/(((⍸(∧/0∘=)),¨¯1∘↑∘⍴)(⊢+⌽))¨n
          }

          rr←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 5, Task 1 - rr
          ⍝ Put your code and comments below here

          ⍝ Given an ⍺ of cash flows and an ⍵ of corresponding interest
          ⍝ rates, compute the future values for each (⍺[i],⍵[i]) pair.
          ⍝
          ⍝ The previous results are appended to the current result
          ⍝ at each step of the reduction.
              1↓⌽⊃{⍵,⍨⊃⍺+⊃⍵×1+1↓⍺}/⌽⍺,¨⍵
          }

          sset←{
          ⍝ 2020 APL Problem Solving Competition Phase II
          ⍝ Stub function for Problem 4, Task 2 - sset
          ⍝ Put your code and comments below here

              ⍺←2
              m←1000000∘|
          ⍝ Compute 2*⍵ (mod 1e6) using the right-to-left binary method.
          ⍝ NOTE: Conversion of ⍵ to binary is implicit. Normally, one
          ⍝ would expect that ⍵ must be converted with (2∘⊥⍣¯1), but
          ⍝ in this specific case, it works without it. Bug or feature?
              (≢⍵)=≢⍺:m⍤×/⍵/⍺ ⋄ (⍺,⍨m2*⍨1↑⍺)∇ ⍵
          }

        u←(⊂¯1 0)∘+

    :EndNamespace
:EndNamespace
	P1←(1≠(×⊣))⌽↑{⊆⍺⍵}↓
	P2←(128∘>∨191∘<)⊂⊢
	P3←26⊥⎕A∘⍳
	P4←≠⌿0=400 100 4∘.\|⊢
	P5←⊢{⍵,⍵-(××⍳∘\|)-/⍺}⊃
	P6←(⊣(⌿⍨)(+⌿=))⍪~⍨
	P7←{⍺=2⊥∧/(2∘⊥⍣¯1)⍺⍵}
	P8←¯1∧.=2×/(×2-/10∘⊥⍣¯1)
	P9←{1∧.=≢∘∪¨⊆⍨2@(¯1∘=)×0~⍨(+\⍣¯1)⍵}
	P10←↑((⊢⍴⍨(×/⍴))~((⊂' '⍴⍨(⍴⊃))))∘(↓(↑⍕¨))
	:Namespace Contest2020
	⍝ === VARIABLES ===

	L←⎕av[3+⎕io]
	AboutMe←L,''

	FilePath←''

	Reaction←L,''

	⎕ex 'L'

	⍝ === End of variables definition ===

	(⎕IO ⎕ML ⎕WX)←1 1 3

	:Namespace Problems
	(⎕IO ⎕ML ⎕WX)←1 1 3

	∇ parts←Balance nums;n;K;T;P;S;i;j;H
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 8, Task 1 - Balance
	⍝ Put your code and comments below here

	⍝ NOTE: I wasn't sure if ⎕IO could be used in the competition, so the
	⍝ comments use 0-based indexing and the code uses 1-based.

	T←+/nums
	⍝ Return ⍬ if the sum of nums is odd; can't split evenly.
	:If 2∘\|T
	parts←⍬
	:Else
	n←≢nums
	K←T÷2
	⍝ Boolean table where each column, j, represents the first j
	⍝ elements of nums, where j is in range [0,n] (empty set is 0).
	⍝ Each row, i, represents the ith partial sum in range [0,K].
	⍝ Let P[i;j] be 1 if a subset of the jth subset sums to i.
	⍝ Otherwise, P[i;j] is 0. Initialize the top row to 1 because
	⍝ the null set is a subset of all sets, and it sums to 0.
	P←((1⍴⍨1∘+)⍪0⍴⍨(K,1∘+))n
	⍝ Store the parent of P[i;j]'s row index, i-nums[j], in S[i;j] if
	⍝ the last element of the jth subset was included in the sum to i.
	S←(1∘+K n)⍴⍬

	:For i j :In 1∘+⍳K n
	⍝ A smaller subset that excludes j already sums to i.
	:If P[i;j]←P[i;j-1]
	⍝ Can't sum to i if j is larger.
	:ElseIf i>nums[j-1]
	⍝ Including nums[j] in the sum to i compares the same as
	⍝ excluding nums[j] and summing to i-nums[j].
	:AndIf P[i;j]←P[i-nums[j-1];j-1]
	S[i;j]←(i-nums[j-1])
	:EndIf
	:EndFor

	i←1+K
	H←⍬
	⍝ From the last element of S, traverse backwards and collect the
	⍝ columns that contain parents pointers which directly produced the
	⍝ last element of S. Theses columns correspond to the indexes of
	⍝ nums which make up one element of parts.
	:For j :In ⌽1+⍳n
	:If (i∘≠∧0∘≠)S[i;j]
	H,←j-1
	i←S[i;j]
	:EndIf
	:EndFor

	⍝ If the last value of P is 1, then split nums by equal sums.
	⍝ Otherwise, nums can't be split evenly, so return ⍬.
	parts←{P[1+K;1+n]:⊆nums[H](nums[H~⍨⍳n]) ⋄ ⍬}⍬
	:EndIf
	∇

	CheckDigit←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 7, Tasl 1 - CheckDigit
	⍝ Put your code and comments below here

	⍝ Given an array of 11 UPC-A digits, compute the check digit.
	⍝
	⍝ Starting at the right, label digits alternately odd and even.
	⍝ multiply odd digits by 3 and even digits by 1. Sum all resulting
	⍝ numbers. The distance from this sum to the next highest multiple
	⍝ of 10 is the check digit. If the sum is a multiple of 10, then
	⍝ the check digit is 0, i.e., 0 numbers away from a multiple of 10.
	10\|10-10\|⍵+.×11⍴3 1
	}

	DiveScore←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 1, Task 1 - DiveScore
	⍝ Put your code and comments below here

	⍝ ⍺: Single degree of dificulty (⍺ > 1).
	⍝ ⍵: Two or more judges' scores, each in range [0,10].
	⍝ Calculate the diving score to at most 2 decimal places.
	⍝
	⍝ Throw out all but the three median judges' scores. The remaining
	⍝ scores are summed and multiplied by the degree of dificultly.
	⍎2⍕⍺×+/(¯1+⌊2÷⍨≢⍵){(-⍺)↓⍺↓⍵[⍋⍵]}⍵
	}

	∇ text←templateFile Merge jsonFile;t;m;n;v;z;s;q;i;j
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 6, Task 1 - Merge
	⍝ Put your code and comments below here

	⍝ Read in the template and json files.
	(t m)←⊃∘⎕NGET¨templateFile jsonFile
	⍝ Convert the JSON into a namespace.
	n←⎕JSON m
	⍝ Get the variable names in the namespace.
	v←n.⎕NL ¯2
	⍝ Get the corresponding namespace variable values, prepend @.
	z←(⊂'@'),n⍎¨v
	⍝ Prepend a blank corresponding to @, then surround each with @.
	v←(1⌽'@@'∘,)¨(⊂''),v
	⍝ Partition the template so merge areas are in their own boxes.
	s←t⊆⍨{(⍳≢⍵)/⍨⍵+1 ¯1⍴⍨≢⍵}≢¨⊂⍨'@'=t
	⍝ Find merge areas that are missing from the JSON file.
	q←v~⍨{⍵/⍨'@'∊¨⍵}∪s
	⍝ Prepend the missing merge area names to the existing ones.
	v,⍨←q
	⍝ For each missing merge area, prepend ??? to the replacements.
	z,⍨←(≢q)⍴⊂'???'
	⍝ Replace each merge area with its corresponding replacement.
	:For i j :InEach v z
	s←((⊂j)@{(⊂i)⍷s})s
	:EndFor
	⍝ Reassemble into a single character vector.
	text←⊃,/s
	∇

	PastTasks←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 3, Task 1 - PastTasks
	⍝ Put your code and comments below here

	⍝ Get the HTML from the given URL and convert to matrix form.
	w←⎕XML(#.HttpCommand.Get ⍵).Data
	⍝ Find the indexes of the ⍺ string in the ⍵ list of strings.
	f←{(⊂,⍺)⍸⍤⍷⍵}
	⍝ Filter the attributes column by the 'a' and 'base' elements.
	(a b)←{⍵[⍺ f ⍵[;2];4]}∘w¨'a' 'base'
	⍝ Filter the value column by 'href' for all attributes.
	(h j)←{⊃¨'href'∘{⍵[⍺ f ⍵[;1];2]}¨⍵}¨a b
	⍝ Filter 'a' element attribute values by the PDF file ending.
	p←h[1+('.pdf'⎕S 2)h]
	⍝ Attach the URL base to each relative URL.
	j,¨p
	}

	ReadUPC←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 7, Task 3 - ReadUPC
	⍝ Put your code and comments below here

	⍝ Ensure the input contains 95 bits
	95≠≢⍵:¯1
	⍝ Split up the 7 bit arrays by left and right sides (drop padding).
	B←{⍉6 7⍴⍵[⍺+⍳42]}
	U←B∘⍵¨3 50
	⍝ Ensure one side has even parity and the other has odd.
	D←∧/¨2\|¨+⌿¨U
	⍲/0 1∊D:¯1
	⍝ Put odd parity matrix on left side and match the parities.
	U←↑,/(~@1)(⌽∘(⌽∘⊖¨)⍣(¯1=×-/D))U
	⍝ Even parity barcode digits 0-9 converted to decimal then ASCII.
	DG←'rflB\NPDHt'
	⍝ Convert from binary to decimal according to conversion table.
	R←¯1+DG⍳⎕UCS 2⊥U
	⍝ Ensure the check digit is valid.
	(¯1↑R)≠CheckDigit ¯1↓R:¯1
	R
	}

	Steps←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 2, Task 1 - Steps
	⍝ Put your code and comments below here

	⍝ No ⍺ is the same as a step size of 1.
	⍺←1
	⍝ The first endpoint.
	f←⊃⍵
	⍝ No steps is just the first endpoint because no steps were made.
	0≡⍺:f
	⍝ Indexes from 1 to \|∘⊢ all times the sign of ⊢.
	j←(××⍳∘\|)⊢
	⍝ Positive ⍺ gives the step size from ⍵[1] to ⍵[2], the endpoints.
	⍝ Truncate the last step size if ⍺ doesn't divided evenly into the
	⍝ the absolute diffence between the endpoints.
	1≡×⍺:∪1⌽(⌽⍵),f-⍺×j⌊-/⍵÷⍺
	⍝ Negative ⍺'s floor magnitude gives the number of equally sized
	⍝ steps to take between the endpoints.
	f,f-⍵((-/÷)×j)\|⌊⍺
	}

	∇ weights←Weights filename;m;k;x;y;v;a;q;b;j;e;c;l;u;d;p;t;n;o;f;s;i;r;h
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 9, Task 1 - Weights
	⍝ Put your code and comments below here

	⍝ Read the mobile diagram into a character matrix.
	m←↑⊃⎕NGET filename 1
	⍝ Sort ascending.
	k←{⍵[⍋⍵]}
	⍝ Sort ascending by columns.
	x←{⌽¨k⌽¨⍵}
	⍝ Append the first of ⍺ to the difference between the last ⍺ and ⍵.
	y←{(⊃⍺),⍵-⍥(1∘↓)⍺}
	⍝ Get the indexes of each vector of ⍺ in vector of vectors ⍵.
	v←{⍵∘{⊃(⊂⍵)⍸⍤⍷⍺}¨⍺}
	⍝ Get the indexes of each letter in alphabetical order.
	a←⍸27≠⎕A∘⍳m
	⍝ Get the indexes of all turning points.
	q←⍸('┐'∘=∨'┌'∘=)m
	⍝ Get the indexes of all fulcrums.
	b←'┴'⍸⍤=m
	⍝ Reshape 'a' so a single row can be taken from it.
	a←{(1,⍴⍵)⍴⍵}a

	:Repeat
	⍝ Get the last row of 'a'.
	e←{(¯1↑⍴⍵)⍴⍵}¯1↑[1]a
	⍝ Place turning point indexes next to fulcrums/letters below them.
	c←x∪q,e
	⍝ Check for any that reached the parent fulcrum.
	u←b[1]≡¨e
	⍝ Climb the tree if not already at the top.
	d←c[¯1+u+e v c]
	a⍪←d
	⍝ Place fulcrum indexes next to their related turning points.
	p←k∪b,d
	⍝ Get each turning point direction; ¯1 for left and 1 for right.
	t←¯2+'┐ ┌'⍳m[d]
	⍝ Traverse the tree from the turning points to fulcrums.
	n←p[(t×~u)+d v p]
	a⍪←n
	⍝ Stop when the last row of 'a' contains only the parent fulcrum.
	:Until b[1]∧.≡n

	⍝ Drop the locations of the letters.
	a←1↓[1]a
	⍝ Get the signs of the last turns made by each letter.
	j←1,⍨¨{1=≢b:1 1 ⋄ ⊃-/{∨⌿b[⍺]⍷⍵}∘⍵¨2 3}a
	⍝ Apply the signs in 'j' to the rows of 'a' except ¯1 stays 1.
	a←1@{0,⍨¯1=⊃⍵}¨↑(⊂j)×↓a
	⍝ Substract pairs of tree rows, keeping the first values the same.
	a←{,⌿y/¨⍵⊆[1]⍨2/⍳2÷⍨≢⍵}a
	⍝ Get the unique tree row numbers.
	o←∪⊃¨⊃,/a
	⍝ Group each column by tree row numbers, then get just the columns.
	⍝ The result is a matrix for of the needed system of equations.
	f←↑{2⊃¨⊃¨(~∘(⊃⍵,./⍨⍺{⍺≠⊃⍵}¨¨⍵))¨⍵}∘a¨o
	⍝ Scale a vector by its GCD.
	s←⊢÷∨/
	⍝ Generate an identity matrix of the given size.
	i←∘.=⍨⍳
	⍝ Compute a right inverse of the given non-square matrix.
	r←⍉+.×(⌹⊢+.×⍉)
	⍝ Compute the smallest nontrivial integer solution to the given
	⍝ singular homogeneous integer coefficient system.
	h←s(+/i∘(1↓⍴)-r+.×⊢)
	weights←h f
	∇

	WriteUPC←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 7, Task 2 - WriteUPC
	⍝ Put your code and comments below here

	⍝ Ensure input length is exactly 11.
	11≠≢⍵:¯1
	⍝ Ensure input contains only single digits.
	~∧/⍵∊¯1+⍳10:¯1
	⍝ Convert decimal to binary.
	DB←2∘⊥⍣¯1
	⍝ Beginning and ending digits.
	BE←DB 5
	⍝ Middle digits.
	MD←0,BE,0
	⍝ Even parity barcode digits 0-9 converted to decimal then ASCII.
	DG←'rflB\NPDHt'
	⍝ Convert input to bit array (tacking the check digit on the end).
	TD←,⍉DB ⎕UCS DG[1+⍵,CheckDigit ⍵]
	⍝ Negate left bits for parity, and insert start, middle, end bits.
	42{↑,/BE(~⍺↑⍵)MD(⍺↓⍵)BE}TD
	}

	pv←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 5, Task 2 - pv
	⍝ Put your code and comments below here

	⍝ Given an ⍺ of cash flows and an ⍵ of corresponding interest
	⍝ rates, compute the present value.
	⍝
	⍝ The present value is the dot product between the current values
	⍝ and the reciprocal of 1 + the cumulative interest rates.
	⍺+.÷×\1+⍵
	}

	revp←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 4, Task 1 - revp
	⍝ Put your code and comments below here

	⍝ Complement pairs AT and CG are equidistant from the space.
	d←'AC GT'
	⍝ Replace complements by equal and opposite integers.
	e←¯3+d⍳⍵
	⍝ Table of indexes up to ⍺ with a sliding ⍵-width window.
	i←{↑⍵,/⍳⍺}
	⍝ Moving width index tables for widths in range [4,12].
	m←(≢⍵)i¨2+2×⍳5
	⍝ Tables of complement numbers for each window width.
	n←e∘(⊣⌷⍨∘⊂)¨m
	⍝ Location and length pairs for each reverse palindrome.
	↑↑,/(((⍸(∧/0∘=)),¨¯1∘↑∘⍴)(⊢+⌽))¨n
	}

	rr←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 5, Task 1 - rr
	⍝ Put your code and comments below here

	⍝ Given an ⍺ of cash flows and an ⍵ of corresponding interest
	⍝ rates, compute the future values for each (⍺[i],⍵[i]) pair.
	⍝
	⍝ The previous results are appended to the current result
	⍝ at each step of the reduction.
	1↓⌽⊃{⍵,⍨⊃⍺+⊃⍵×1+1↓⍺}/⌽⍺,¨⍵
	}

	sset←{
	⍝ 2020 APL Problem Solving Competition Phase II
	⍝ Stub function for Problem 4, Task 2 - sset
	⍝ Put your code and comments below here

	⍺←2
	m←1000000∘\|
	⍝ Compute 2*⍵ (mod 1e6) using the right-to-left binary method.
	⍝ NOTE: Conversion of ⍵ to binary is implicit. Normally, one
	⍝ would expect that ⍵ must be converted with (2∘⊥⍣¯1), but
	⍝ in this specific case, it works without it. Bug or feature?
	(≢⍵)=≢⍺:m⍤×/⍵/⍺ ⋄ (⍺,⍨m2*⍨1↑⍺)∇ ⍵
	}

	u←(⊂¯1 0)∘+

	:EndNamespace
	:EndNamespace