Perl Weekly Challenge: Stringy DI and Paired Equals

I dunno. I saw “DI string” and thought of Lady Di. It’s Christmas. I’m full of yummy Christmas food and not firing on all cylinders.

Onward to Perl Weekly Challenge 249!

Task 1: Equal Pairs

You are given an array of integers with even number of elements.

Write a script to divide the given array into equal pairs such that:

a) Each element belongs to exactly one pair.
b) The elements present in a pair are equal.

Example 1

Input: @ints = (3, 2, 3, 2, 2, 2)
Output: (2, 2), (3, 3), (2, 2)

There are 6 elements in @ints.
They should be divided into 6 / 2 = 3 pairs.
@ints is divided into the pairs (2, 2), (3, 3), and (2, 2) satisfying all the conditions.

Example 2

Input: @ints = (1, 2, 3, 4)
Output: ()

There is no way to divide @ints 2 pairs such that the pairs satisfy every condition.

Approach

Ok, this reminds me of PWC 237’s Task 2, where we wound up counting the integers in our input list and subtracting them from that count instead of pulling them off a list. In this case, I think a similar approach would work: loop over the input list and count up how many of each integer we have. If we don’t have an even number of each integer, we can fail immediately because we can’t satisfy condition b. Then we pull integers off the count by twos.

Raku

sub equalPairs(@ints) {
  my @pairs;
  my %num_count;
  # count how many of each int we have
  for @ints -> $num {
    %num_count{$num}++;
  }
  # first, make sure we have even numbers of each integer
  for %num_count.kv -> $k, $v {
    next if $v % 2 == 0; # it's even, we can make pairs
    return @pairs; # we have an odd number, can't make pairs
  }
  # now make pairs from those integers
  for %num_count.kv -> $k, $v {
    my $count = $v; # the values $k, $v are read-only
    while ($count > 0) {
      @pairs.push( [$k, $k] );
      $count -= 2;
    }
  }
  return @pairs;
}

View the entire Raku script for this task on GitHub.

Perl

sub equalPairs(@ints) {
  my @pairs;
  my %num_count;
  # count how many of each int we have
  foreach my $num ( @ints ) {
    $num_count{$num}++;
  }
  # first, make sure we have even numbers of each integer
  foreach my $k ( keys %num_count ) {
    my $v = $num_count{$k};
    next if $v % 2 == 0; # it's even, we can make pairs
    return @pairs; # we have an odd number, can't make pairs
  }
  # now make pairs from those integers
  foreach my $k ( keys %num_count ) {
    my $count = $num_count{$k};
    while ($count > 0) {
      push @pairs, [$k, $k];
      $count -= 2;
    }
  }
  return @pairs;
}

View the entire Perl script for this task on GitHub.

Python

from collections import Counter

def equalPairs(nums):
    pairs = []
    num_count = Counter()
    # count how many of each int we have
    for num in nums:
        num_count[num] += 1

    # first, make sure we have even numbers of each integer
    for k, v in dict(num_count).items():
        if v % 2 == 0: # it's even, we can make pairs
            continue
        else:
            return pairs # we have an odd number, no pairs

    # now make pairs from those integers
    for k, v in dict(num_count).items():
        count = v # the values k, v are read-only
        while count > 0:
            pairs.append( [k, k] )
            count -= 2

    return pairs

View the entire Python script for this task on GitHub.


Task 2: DI String Match

You are given a string s, consisting of only the characters "D" and "I".

Find a permutation of the integers [0 .. length(s)] such that for each character s[i] in the string:

s[i] == 'I' ⇒ perm[i] < perm[i + 1]
s[i] == 'D' ⇒ perm[i] > perm[i + 1]

Example 1

Input: $str = "IDID"
Output: (0, 4, 1, 3, 2)

Example 2

Input: $str = "III"
Output: (0, 1, 2, 3)

Example 3

Input: $str = "DDI"
Output: (3, 2, 0, 1)

Approach

Again, this reminds me of PWC 237’s Task 2, this time because we sorted the integers so we could pull maximum and minimum integers off a list. In this case, the range 0 .. length(s) is sorted already, but we would take a similar approach to building the output permutation list: if the letter is D, we pull the maximum number off the end of the list, guaranteeing that it will be greater than anything that could come after it. If the letter is I, we pull the minimum number off the beginning of the list, guaranteeing that it will be less than anything that could come after it.

Raku

sub diStringMatch($str) {
  my @permutation;
  # first, generate the list of integers
  # we're making permutations of
  my @nums = 0 .. $str.chars;
  # now let's generate our permutation
  for $str.split('', :skip-empty) -> $c {
    if ($c eq 'D') {
      # take the largest number available
      @permutation.push( @nums.pop() );
    }
    else {
      # take the smallest number available
      @permutation.push( @nums.shift() );
    }
  }
  # add last remaining number
  @permutation.push( @nums[0] );

  return @permutation;
}

View the entire Raku script for this task on GitHub.

Perl

sub diStringMatch($str) {
  my @permutation;
  # first, generate the list of integers
  # we're making permutations of
  my @nums = 0 .. length($str);
  # now let's generate our permutation
  foreach my $c ( split(//, $str) ) {
    if ($c eq 'D') {
      # take the largest number available
      push @permutation, pop(@nums);
    }
    else {
      # take the smallest number available
      push @permutation, shift(@nums);
    }
  }
  # add last remaining number
  push @permutation, $nums[0];

  return @permutation;
}

View the entire Perl script for this task on GitHub.

Python

def diStringMatch(str):
    permutation = []
    # first, generate the list of integers
    # we're making permutations of
    nums = list(range(len(str)+1))
    # now let's generate our permutation
    for c in str:
        if c == 'D':
            # take the largest number available
            permutation.append( nums.pop(-1) )
        else:
            # take the smallest number available
            permutation.append( nums.pop(0) )
    # add last remaining number
    permutation.append( nums[0] )

    return permutation

View the entire Python script for this task on GitHub.


Here’s all my solutions in GItHub: https://github.com/packy/perlweeklychallenge-club/tree/master/challenge-249/packy-anderson

Perl Weekly Challenge: The Shortest Distance between Submatrix Sums

I’m not even going to try to come up with something clever to tie this to music; just thinking about the first task makes my brain swim. So I’m tackling the second task first.

Perl Weekly Challenge 248

Task 2: Submatrix Sum

You are given a NxM matrix A of integers.

Write a script to construct a (N-1)x(M-1) matrix B having elements that are the sum over the 2x2 submatrices of A,

b[i,k] = a[i,k] + a[i,k+1] + a[i+1,k] + a[i+1,k+1]

Example 1

Input: $a = [
              [1,  2,  3,  4],
              [5,  6,  7,  8],
              [9, 10, 11, 12]
            ]

Output: $b = [
               [14, 18, 22],
               [30, 34, 38]
             ]

Example 2

Input: $a = [
              [1, 0, 0, 0],
              [0, 1, 0, 0],
              [0, 0, 1, 0],
              [0, 0, 0, 1]
            ]

Output: $b = [
               [2, 1, 0],
               [1, 2, 1],
               [0, 1, 2]
             ]

Approach

The approach here is fairly straightforward: accept the input matrix, determine the size M and N, then run through the calculations to determine the elements for the sums of the 2×2 submatricies. Jorg Sommrey was even kind enough to give us the formula.

Raku

sub submatrixSum(@a) {
  # subtract 1 because we're 0-indexed
  my $M = @a.elems - 1;    # rows
  my $N = @a[0].elems - 1; # columns
  # we are ASSUMING the matrix is consistent with
  # each row having the same number of columns
  my @b;
  for 0 .. $M - 1 -> $i {
    for 0 .. $N - 1 -> $k {
      @b[$i;$k] = @a[$i;  $k] + @a[$i;  $k+1]
                + @a[$i+1;$k] + @a[$i+1;$k+1];
    }
  }
  return @b;
}

View the entire Raku script for this task on GitHub.

Perl

sub submatrixSum(@a) {
  my $M = $#a;       # rows
  my $N = $#{$a[0]}; # columns
  # we are ASSUMING the matrix is consistent with
  # each row having the same number of columns
  my @b;
  foreach my $i ( 0 .. $M - 1 ) {
    push @b, [];
    foreach my $k ( 0 .. $N - 1 ) {
      $b[$i]->[$k] = $a[$i]->[$k]   + $a[$i]->[$k+1]
                   + $a[$i+1]->[$k] + $a[$i+1]->[$k+1];
    }
  }
  return @b;
}

View the entire Perl script for this task on GitHub.

Python

def submatrixSum(a):
    # subtract 1 because we're 0-indexed
    M = len(a) - 1    # rows
    N = len(a[0]) - 1 # columns
    # we are ASSUMING the matrix is consistent with
    # each row having the same number of columns
    b = []
    for i in range(M): # range is 0 .. M-1
        row = []
        for k in range(N):
            row.append( a[i  ][k] + a[i  ][k+1] +
                        a[i+1][k] + a[i+1][k+1] )
        b.append(row)
    return b

View the entire Python script for this task on GitHub.


Task 1: Shortest Distance

You are given a string and a character in the given string.

Write a script to return an array of integers of size same as length of the given string such that:

distance[i] is the distance from index i to the closest occurrence
of the given character in the given string.

The distance between two indices i and j is abs(i - j).

Example 1

Input: $str = "loveleetcode", $char = "e"
Output: (3,2,1,0,1,0,0,1,2,2,1,0)

The character 'e' appears at indices 3, 5, 6, and 11 (0-indexed).
The closest occurrence of 'e' for index 0 is at index 3, so the distance is abs(0 - 3) = 3.
The closest occurrence of 'e' for index 1 is at index 3, so the distance is abs(1 - 3) = 2.
For index 4, there is a tie between the 'e' at index 3 and the 'e' at index 5,
but the distance is still the same: abs(4 - 3) == abs(4 - 5) = 1.
The closest occurrence of 'e' for index 8 is at index 6, so the distance is abs(8 - 6) = 2.

Example 2

Input: $str = "aaab", $char = "b"
Output: (3,2,1,0)

Approach

The approach we should take is pretty much outlined in the description of the example: first generate a list of what indices the target character occurs at, then calculate the closest occurrence based on abs(x - y) where x and y are the positions of the current character and an occurrence of the target character.

Raku

sub shortestDistance($str, $char) {
  # split the string into an array of characters
  my @strchar = $str.split('', :skip-empty);
  # find the positions of the target $char
  my @pos = (0 .. @strchar.end).grep: { @strchar[$_] eq $char };

  my @output;
  for 0 .. @strchar.end -> $i {
    # find the distances
    my @distance = @pos.map: { abs($i - $_) };
    # find the minimum distance
    @output.push( @distance.min );
  }
  return @output;
}

View the entire Raku script for this task on GitHub.

Perl

sub shortestDistance($str, $char) {
  # split the string into an array of characters
  my @strchar = split(//, $str);
  # find the positions of the target $char
  my @pos = grep { $strchar[$_] eq $char } 0 .. $#strchar;
  
  my @output;
  foreach my $i ( 0 .. $#strchar ) {
    # find the distances
    my @distance = map { abs($i - $_) } @pos;
    # find the minimum distance
    push @output, min(@distance);
  }
  return @output;
}

View the entire Perl script for this task on GitHub.

Python

def shortestDistance(s, c):
    # split the string into an array of characters
    strchar = list(s)
    # find the positions of the target char
    pos = [ x for x in range(len(s)) if strchar[x] == c ]

    output = []
    for i in range(len(s)):
        # find the distances
        distance = [ abs(i - p) for p in pos ]
        # find the minimum distance
        output.append(  min(distance) )
    return output

View the entire Python script for this task on GitHub.


Here’s all my solutions in GItHub: https://github.com/packy/perlweeklychallenge-club/tree/master/challenge-248/packy-anderson

Perl Weekly Challenge: Writing Letter Pairs to Santa

When the tasks have “letter” and “Santa”, there’s only one thing that came to my mind: Wakko Warner.

Onward to Perl Weekly Challenge 247!

Task 1: Secret Santa

Secret Santa is a Christmas tradition in which members of a group are randomly assigned a person to whom they give a gift.

You are given a list of names. Write a script that tries to team persons from different families.

Example 1

The givers are randomly chosen but don't share family names with the receivers.

Input: @names = ('Mr. Wall',
                 'Mrs. Wall',
                 'Mr. Anwar',
                 'Mrs. Anwar',
                 'Mr. Conway',
                 'Mr. Cross',
                );

Output:

    Mr. Conway -> Mr. Wall
    Mr. Anwar -> Mrs. Wall
    Mrs. Wall -> Mr. Anwar
    Mr. Cross -> Mrs. Anwar
    Mr. Wall -> Mr. Conway
    Mrs. Anwar -> Mr. Cross

Example 2

One gift is given to a family member.

Input: @names = ('Mr. Wall',
                 'Mrs. Wall',
                 'Mr. Anwar',
                );

Output:

    Mr. Anwar -> Mr. Wall
    Mr. Wall -> Mrs. Wall
    Mrs. Wall -> Mr. Anwar

Approach

Ok, so this is like last week where we’re randomly picking elements from a list, but there are two added twists: when picking the gift recipient for person X, we always want to exclude person X from the result (so nobody is giving a gift to themselves), and we prefer to select a gift recipient who has a different family name. But we also want to make sure nobody is getting gifts from more that one person.

Honestly, I keep going back and forth about how to do this. Excluding the person from giving a gift to themselves is easy, but coming up with the most efficient way to exclude family members if possible could be solved many different ways. I’m thinking that what I’ll do is maintain a list of recipients, and, for each giver, call a routine that a) removes the giver from the list, and b) removes family members from the list. If after removing family members from the list, the list is empty, family members will be added back.

Raku

And when I started testing my approach, I discovered there was a problem: sometimes, I would pick all the possible recipients for other people, leaving the list with only the giver as a possible recipient:

Output:
    Mr. Cross ->
    Mr. Wall -> Mr. Conway
    Mr. Anwar -> Mrs. Wall
    Mrs. Anwar -> Mr. Wall
    Mr. Conway -> Mrs. Anwar
    Mrs. Wall -> Mr. Anwar

So maybe I need to ensure that everyone gets assigned to someone else FIRST, and then worry about family names. Or… I could just accept that this happens occasionally and rather than adjust my algorithm to prevent it from happening, just add a check to make sure that everyone was assigned a gift recipient, and if not, just re-do my entire list.

Yeah, I’m doing that.

sub findRecipient($giver, %recipients) {
  # since %recipients is passed by reference, we can't
  # modify it, so let's make a copy with the giver removed
  my @recipients = %recipients.keys.grep({ !/$giver/ });

  # split on whitespace and take the last element
  # to get the "family name"
  my $family_name = split(" ", $giver)[*-1];

  # now, make a potential recipient hash
  # excluding family members
  my @non_family_members =
    @recipients.grep({ !/$family_name/ });

  if (@non_family_members > 0) {
    return @non_family_members.pick;
  }
  else {
    return @recipients.pick;
  }
}

sub secretSanta(@names) {
  # let's use a hash to hold the giver/recipient pairings
  my %results;
 
  # put our work in a labelled loop
  ASSIGN_RECIPIENTS: loop {
    # convert the array of names into a hash with names as keys
    my %available_recipients = @names.map: * => 1;

    # now go through each of the names and find a
    # recipient for them
    for @names -> $giver {
      my $recipient =
        findRecipient($giver, %available_recipients);

      # occasionally, we assign recipients so in the last
      # iteration of the for loop the only available
      # recipient is $giver. When that happens, the easiest
      # way to fix things is to just re-do the entire list
      redo ASSIGN_RECIPIENTS if ! defined $recipient;

      %results{$giver} = $recipient;
      %available_recipients{$recipient}:delete;
    }
    last; # exit the labelled loop
  }
  return %results;
}

View the entire Raku script for this task on GitHub.

Perl

For the Perl implementation, I’m finally giving in and using Perl’s function signatures (as I noted last week, they’ve been the default since Perl 5.36, so why shouldn’t I use them?) and to take the place of Raku’s pick, I’m using List::Util’s sample function.

use List::Util qw( sample );

sub findRecipient($giver, $recipients) {
  # since $recipients is a reference to a hash, we can't
  # modify it, so let's make a copy with the giver removed
  my @recipients = grep { !/$giver/ } keys %$recipients;

  # split on whitespace and take the last element
  # to get the "family name"
  my $family_name = (split /\s+/, $giver)[-1];

  # now, make a potential recipient hash
  # excluding family members
  my @non_family_members =
    grep { !/$family_name/ } @recipients;

  if (@non_family_members > 0) {
    return sample(1, @non_family_members);
  }
  else {
    return sample(1, @recipients);
  }
}

sub secretSanta(@names) {
  # let's use a hash to hold the giver/recipient pairings
  my %results;
 
  # put our work in a labelled loop
  ASSIGN_RECIPIENTS: while () {
    # convert the array of names into a hash with names as keys
    my %available_recipients = map { $_ => 1 } @names;

    # now go through each of the names and find a
    # recipient for them
    foreach my $giver ( @names ) {
      my $recipient =
        findRecipient($giver, \%available_recipients);

      # occasionally, we assign recipients so in the last
      # iteration of the for loop the only available
      # recipient is $giver. When that happens, the easiest
      # way to fix things is to just re-do the entire list
      redo ASSIGN_RECIPIENTS if ! defined $recipient;

      $results{$giver} = $recipient;
      delete $available_recipients{$recipient};
    }
    last; # exit the labelled loop
  }
  return %results;
}

I wound up using while () as a standing for Raku’s loop (even though loop is analogous to Perl’s for, using for in Perl to do an unbounded loop would be for (;;), and I just like the while form better).

View the entire Perl script for this task on GitHub.

Python

Python doesn’t have named loops, so it was just easier to set a variable if we encountered our error condition and, if it’s set to True, recursively call the function again.

from random import sample
import re

def findRecipient(giver, recipients):
    # exclude the giver from the recipient list
    possible_recipients = [
        name for name in recipients if name != giver
    ]

    # if there are no possible recipients, bail early
    if len(recipients) == 0:
        return None

    # split on whitespace and take the last element
    # to get the "family name"
    family_name = re.compile((giver.split())[-1])

    # now, make a potential recipient list
    # excluding family members
    non_family_members = [
        name for name in possible_recipients \
            if not family_name.search(name)
    ]

    # sample() returns a LIST, so just return the first elem
    if len(non_family_members) > 0:
        return sample(non_family_members, 1)[0]
    else:
        return sample(recipients, 1)[0]

def secretSanta(names):
    # let's use a dictionary to hold the giver/recipient
    # pairings
    results = {}
 
    # copy the names into a new list
    available_recipients = names.copy()

    # now go through each of the names and find a
    # recipient for them
    must_redo = False
    for giver in names:
        recipient = findRecipient(giver, available_recipients)
        if recipient is None:
            must_redo = True
        results[giver] = recipient
        available_recipients.remove(recipient)

    if must_redo:
        return secretSanta(names)
    else:
        return results

View the entire Python script for this task on GitHub.


Task 2: Most Frequent Letter Pair

You are given a string S of lower case letters 'a'..'z'.

Write a script that finds the pair of consecutive letters in S that appears most frequently. If there is more than one such pair, chose the one that is the lexicographically first.

Example 1

Input: $s = 'abcdbca'
Output: 'bc'

'bc' appears twice in `$s`

Example 2

Input: $s = 'cdeabeabfcdfabgcd'
Output: 'ab'

'ab' and 'cd' both appear three times in $s and 'ab' is lexicographically smaller than 'cd'.

Approach

This feels fairly straightforward: take the first two characters of the string, count them as a pair. Discard the first character from the string, then repeat the process with the new first two characters of the string, until there’s only one character in the string left. A hash is perfect for keeping track of the pairs we’ve counted.

The wrinkle is that we need to handle when more than one pair has the same count.

Having to sort on frequency and then some natural order reminds me of the second task in PWC 233.

Raku

use Lingua::Conjunction;
use Lingua::EN::Numbers;

sub pairCount($string) {
  my $s = $string; # make a copy so we can modify it
  my %count;
  while ($s.chars > 1) {
    my $pair = substr($s, 0..1); # the first two characters
    %count{$pair}++;          # count the pair
    $s = substr($s, 1, *); # remove the first character
  }
  return %count;
}

sub mostFrequentPair($s) {
  # count the letter pairs
  my %pairs = pairCount($s);

  # sort the pairs by their counts
  my @sorted = %pairs.keys.sort: {
    # sort by count first
    %pairs{$^b} <=> %pairs{$^a}
    ||
    # then by lexicographical order
    $^a cmp $^b
  };

  my @max_pair  = shift(@sorted); # pull off first value
  my $max_count = %pairs{@max_pair[0]}; # get it's count

  while ( %pairs{@sorted[0]} == $max_count ) {
    # there are pairs on the sorted list that have the
    # same count, so let's put them on the list, too
    @max_pair.append( shift(@sorted) );
  }
  my $explain;

  # set aside the pair that sorted to the top
  my $first_pair = @max_pair[0];

  # now quote all the pairs
  @max_pair = @max_pair.map: { qq{'$_'} };

  # make the count an english word
  my $count =  ($max_count == 1) ?? 'once'      # 🎶
            !! ($max_count == 2) ?? 'twice'     # 🎶
            !! cardinal($max_count) ~ ' times'; # a lady 🎶

  # and format the explanation
  if (@max_pair == 1) {
    $explain = "'$first_pair' appears $count in \$s";
  }
  else {
    my $str = qq{|list| appear $count in \$s and }
            ~ qq{'$first_pair' is lexicographically smallest.};
    $explain = conjunction @max_pair, :$str;
  }

  return $first_pair, $explain;
}

View the entire Raku script for this task on GitHub.

Perl

use Lingua::EN::Inflexion qw( noun wordlist );

sub pairCount($s) {
  my %count;
  while (length($s) > 1) {
    my $pair = substr($s, 0, 2); # the first two characters
    $count{$pair}++;        # count the pair
    $s = substr($s, 1); # remove the first character
  }
  return %count;
}

sub mostFrequentPair($s) {
  # count the letter pairs
  my %pairs = pairCount($s);

  # sort the pairs by their 
  my @sorted = sort {
    # sort by count first
    $pairs{$b} <=> $pairs{$a}
    ||
    # then by lexicographical order
    $a cmp $b
  } keys %pairs;

  my @max_pair  = shift(@sorted); # pull off first value
  my $max_count = $pairs{$max_pair[0]}; # get it's count

  while ( $pairs{$sorted[0]} == $max_count ) {
    # there are pairs on the sorted list that have the
    # same count, so let's put them on the list, too
    push @max_pair, shift(@sorted);
  }
  my $explain;

  # set aside the pair that sorted to the top
  my $first_pair = $max_pair[0];

  # now quote all the pairs
  my $pair_list = wordlist( map { qq{'$_'} } @max_pair );

  # make the count an english word
  my $count = ($max_count == 1) ? 'once'             # 🎶
            : ($max_count == 2) ? 'twice'            # 🎶
            : noun($max_count)->cardinal . ' times'; # a lady 🎶

  # and format the explanation
  if (@max_pair == 1) {
    $explain = "'$first_pair' appears $count in \$s";
  }
  else {
    $explain = $pair_list . " appear $count in \$s and "
             . "'$first_pair' is lexicographically smallest.";
  }

  return $first_pair, $explain;
}

View the entire Perl script for this task on GitHub.

Python

The last time I needed to do English conjunctions in Python back in PWC 233, I didn’t bother looking for a module to load; I just rolled my own. I’ve borrowed that function here. I’ve also re-uses the Counter type in the collections module I discovered back in PWC 234, and Savoir-faire Linux’s num2words module I used in PWC 237.

I did a bit of searching on how to sort on multiple criteria, and I came across what the Python documentation called the Decorate-Sort-Undecorate idiom: create a list of tuples having the values you want to sort on, then sort the list of tuples, then re-create the list from the sorted tuples. But while I was reading it, I realized that I knew this technique, just under a different name: it’s a Schwartzian Transformation.

from collections import Counter
from num2words import num2words

def conjunction(words):
    if len(words) < 2:
        return(words)
    elif len(words) == 2:
        return(f'{words[0]} and {words[1]}')
    else:
        last = words.pop(-1)
        l = ', '.join(words)
        return(f'{l}, and {last}')

def pairCount(s):
    # instantiate a counter object
    count = Counter()
    while (len(s) > 1):
        pair = s[0:2]    # the first two characters
        count[pair] += 1 # count the pair
        s = s[1:]        # remove the first character
    # convert it back to a dict now that we're done counting
    return dict(count)

def mostFrequentPair(s):
    # count the letter pairs
    pairs = pairCount(s)

    # sort the pairs by their counts
    # use the Decorate-Sort-Undecorate idiom
    # to convert the dict into a list
    decorated = [ (pairs[p], p) for p in pairs.keys() ]
    sorted_tuples = sorted(
        decorated,
        # the - before the first element sorts descending
        key=lambda k: (-k[0], k[1])
    )
    sorted_pairs = [ t[1] for t in sorted_tuples ]

    max_pair = []
    # pull off first value from the sorted pairs
    max_pair.append( sorted_pairs.pop(0) )
    # get it's count
    max_count = pairs[ max_pair[0] ]

    while pairs[ sorted_pairs[0] ] == max_count:
        # there are pairs on the sorted list that have the
        # same count, so let's put them on the list, too
        max_pair.append( sorted_pairs.pop(0) )

    # set aside the pair that sorted to the top
    first_pair = max_pair[0]

    # make the count an english word
    count = (
        'once'  if (max_count == 1) else # 🎶
        'twice' if (max_count == 2) else # 🎶
        num2words(max_count) + ' times'  # a lady 🎶
    )

    # and format the explanation
    if len(max_pair) == 1:
        explain = f"'{first_pair}' appears {count} in \$s"
    else:
        # quote all the pairs
        max_pair = [ f"'{x}'" for x in max_pair]
        explain = f"{conjunction(max_pair)} appear {count} in "
        explain += f"$s and '{first_pair}' is "
        explain += "lexicographically smallest."

    return first_pair, explain

View the entire Python script for this task on GitHub.


Here’s all my solutions in GItHub: https://github.com/packy/perlweeklychallenge-club/tree/master/challenge-247/packy-anderson

Perl Weekly Challenge: 25 or 6 out of four… ty-nine

Hey, when the first task is “6 out of 49”, I challenge you to not hear Chicago in your head.

Task 1: 6 out of 49

6 out of 49 is a German lottery.

Write a script that outputs six unique random integers from the range 1 to 49.

Output

3
10
11
22
38
49

Approach

We need to generate 6 unique numbers, so we need to quickly check to see if a number we’ve generated is already part of the output set. Sounds like hashes to me.

Raku

Except when I went to refresh my memory about how Raku did random numbers, I remembered that there was a special routine on the List class: pick.

routine pick

multi sub    pick($count, *@list --> Seq:D)
multi method pick(List:D: $count --> Seq:D)
multi method pick(List:D: --> Mu)
multi method pick(List:D: Callable $calculate --> Seq:D)

If $count is supplied: Returns $count elements chosen at random and without repetition from the invocant. If * is passed as $count, or $count is greater than or equal to the size of the list, then all elements from the invocant list are returned in a random sequence; i.e. they are returned shuffled.

In method form, if $count is omitted: Returns a single random item from the list, or Nil if the list is empty

Since it returns a number of elements chosen at random without repetition, there’s all our work done for us. All we need to do is generate a list of integers from 1 to 49:

sub sixOutOfFourtyNine {
  return (1 .. 49).pick(6).sort;
}

I’m sorting the results as well, because that’s how the sample output was presented.

View the entire Raku script for this task on GitHub.

Approach Revision

But now that I’ve got the Raku version under my belt, I’m rethinking my approach. Why generate potentially duplicate random numbers, when I can generate the set of numbers from 1 – 49, and SHUFFLE those numbers, and then just pull the first 6 values off that list.

Perl

use List::Util qw( shuffle );

sub sixOutOfFourtyNine {
  return sort { $a <=> $b } ( shuffle(1 .. 49) )[0 .. 5];
}

View the entire Perl script for this task on GitHub.

Python

Except… when I went to look in the random module in Python to see if it had a shuffle method, I found out that not only did it have one…

random.shuffle(x)

Shuffle the sequence x in place.

To shuffle an immutable sequence and return a new shuffled list, use sample(x, k=len(x)) instead.

So there was a sample method that “Returns a k length list of unique elements chosen from the population sequence. Used for random sampling without replacement.” Bingo! Just what we need!

from random import sample

def sixOutOfFourtyNine():
    return sorted(sample(range(1, 49), 6))

View the entire Python script for this task on GitHub.


Task 2: Linear Recurrence of Second Order

You are given an array @a of five integers.

Write a script to decide whether the given integers form a linear recurrence of second order with integer factors.

linear recurrence of second order has the form

a[n] = p * a[n-2] + q * a[n-1] with n > 1

where p and q must be integers.

Example 1

Input: @a = (1, 1, 2, 3, 5)
Output: true

@a is the initial part of the Fibonacci sequence a[n] = a[n-2] + a[n-1]
with a[0] = 1 and a[1] = 1.

Example 2

Input: @a = (4, 2, 4, 5, 7)
Output: false

a[1] and a[2] are even. Any linear combination of two even numbers with integer factors is even, too.
Because a[3] is odd, the given numbers cannot form a linear recurrence of second order with integer factors.

Example 3

Input: @a = (4, 1, 2, -3, 8)
Output: true

a[n] = a[n-2] - 2 * a[n-1]

Approach

Ok, so to determine if a sequence is a linear recurrence of second order we need to start examining the third element onwards and see if it’s the sum of integer multiples of the previous two values in the sequence (q times the previous value, p times the value before that).

I decided that there has to be an already-established way for solving these, and when I went looking, I found that there is: Cramer’s rule. If we have a linear system

then the values for x and y can be found with this formula:

To render this in our a[n] / p / q notation, then we get

p = (a[2] * a[2] - a[1] * a[3]) / (a[0] * a[2] - a[1] * a[1])
q = (a[0] * a[3] - a[2] * a[1]) / (a[0] * a[2] - a[1] * a[1])

If p and q have integer solutions (and the solutions for elements 0..3 are the same for 1..4), we’ve got a linear recurrence of second order.

Raku

sub findPandQ(@a) {
  my $p = (@a[2] * @a[2] - @a[1] * @a[3])
        / (@a[0] * @a[2] - @a[1] * @a[1]);
  my $q = (@a[0] * @a[3] - @a[2] * @a[1])
        / (@a[0] * @a[2] - @a[1] * @a[1]);
  return($p, $q);
}

sub isLinearRecurranceOfSecondOrder(@a) {
  my ($p1, $q1) = findPandQ(@a[0 .. 3]);
  my ($p2, $q2) = findPandQ(@a[1 .. 4]);
  if ($p1 != $p2 || $q1 != $q2) {
    say "Values for P ($p1, $p2) and Q ($q1, $q2) "
      ~ "are not consistent across all five elements";
    return False;
  }
  if ($p1 != $p1.Int || $q1 != $q1.Int) {
    say "Values for P ($p1) and Q ($q1) for first "
      ~ "four elements are not integers";
    return False;
  }
  say "Found integer values for P ($p1) and Q ($q1)";
  return True;
}

Here I’d like to show the output of my script:

$ raku/ch-2.raku
Example 1:
Input: @a = (1, 1, 2, 3, 5)
Found integer values for P (1) and Q (1)
Output: True

Example 2:
Input: @a = (4, 2, 4, 5, 7)
Values for P (0.5) and Q (1) for first four elements are not integers
Output: False

Example 3:
Input: @a = (4, 1, 2, -3, 8)
Found integer values for P (1) and Q (-2)
Output: True

It’s not that there aren’t factors p and q for the sequence in the second example; it’s that the factors aren’t both integers.

View the entire Raku script for this task on GitHub.

Perl

sub findPandQ {
  my @a = @_;
  my $p = ($a[2] * $a[2] - $a[1] * $a[3])
        / ($a[0] * $a[2] - $a[1] * $a[1]);
  my $q = ($a[0] * $a[3] - $a[2] * $a[1])
        / ($a[0] * $a[2] - $a[1] * $a[1]);
  return($p, $q);
}

sub isLinearRecurranceOfSecondOrder {
  my @a = @_;
  my ($p1, $q1) = findPandQ(@a[0 .. 3]);
  my ($p2, $q2) = findPandQ(@a[1 .. 4]);
  if ($p1 != $p2 || $q1 != $q2) {
    say "Values for P ($p1, $p2) and Q ($q1, $q2) "
      . "are not consistent across all five elements";
    return 0;
  }
  if ($p1 != int($p1) || $q1 != int($q1)) {
    say "Values for P ($p1) and Q ($q1) for first "
      . "four elements are not integers";
    return 0;
  }
  say "Found integer values for P ($p1) and Q ($q1)";
  return 1;
}

I don’t know why I’m not using Perl’s function signatures; they’ve been the default since Perl 5.36; but they still don’t feel very perl-ish to me. If I used them, though, the only changes from the Raku version would be

  • $ sigil instead of @ for accessing individual array values
  • . instead of ~ for string concatenation
  • int($var) instead of $var.Int to get the integer portion of a variable
  • Using 1 / 0 for booleans instead of the Raku Bools True / False.

View the entire Perl script for this task on GitHub.

Python

def findPandQ(a):
    p = (
      (a[2] * a[2] - a[1] * a[3])
      /
      (a[0] * a[2] - a[1] * a[1])
    )
    q = (
      (a[0] * a[3] - a[2] * a[1])
      / 
      (a[0] * a[2] - a[1] * a[1])
    )
    return(p, q)


def isLinearRecurranceOfSecondOrder(a):
    (p1, q1) = findPandQ(a[0:4])
    (p2, q2) = findPandQ(a[1:5])
    if p1 != p2 or q1 != q2:
        print(f'Values for P ({p1}, {p2}) ', end='')
        print(f'and Q ({q1}, {q2}) ', end='')
        print(f'are not consistent across all five elements')
        return False
    if p1 != int(p1) or q1 != int(q1):
        print(f'Values for P ({p1}) ', end='')
        print(f'and Q ({q1}) ', end='')
        print(f'for first four elements are not integers')
        return False

    print(f'Found integer values for P ({int(p1)}) ', end='')
    print(f'and Q ({int(q1)})')
    return True

The thing I have to remember about Python slices is that the ending element is not included in the slice. So a[0:3] will give me elements 0, 1, and 2, but not 3.

View the entire Python script for this task on GitHub.


Here’s all my solutions in GItHub: https://github.com/packy/perlweeklychallenge-club/tree/master/challenge-246/packy-anderson