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The Bear's Den

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Which Witch?

This week brings a new occasion for some PDL witchery.

Task 1: Target Index

Submitted by: Mohammad Sajid Anwar


You are given an array of integers, @ints and a target element $k.

Write a script to return the list of indices in the sorted array where the element is same as the given target element.

Example 1

Input: @ints = (1, 5, 3, 2, 4, 2), $k = 2
Output: (1, 2)

Sorted array: (1, 2, 2, 3, 4, 5)
Target indices: (1, 2) as $ints[1] = 2 and $ints[2] = 2

Example 2

Input: @ints = (1, 2, 4, 3, 5), $k = 6
Output: ()

No element in the given array matching the given target.

Example 3

Input: @ints = (5, 3, 2, 4, 2, 1), $k = 4
Output: (4)

Sorted array: (1, 2, 2, 3, 4, 5)
Target index: (4) as $ints[4] = 4

Solution

With which as one of PDL’s “primitive” functions, this task can be solved as a one-liner.

use strict;
use warnings;
use PDL;

sub t_idx {
    my $k = shift;

    which $k == pdl(@_)->qsort;
}

See the full solution.

Task 2: Merge Items

Submitted by: Mohammad Sajid Anwar


You are given two 2-D array of positive integers, $items1 and $items2 where element is pair of (item_id, item_quantity).

Write a script to return the merged items.

Example 1

Input: $items1 = [ [1,1], [2,1], [3,2] ]
       $items2 = [ [2,2], [1,3] ]
Output: [ [1,4], [2,3], [3,2] ]

Item id (1) appears 2 times: [1,1] and [1,3]. Merged item now (1,4)
Item id (2) appears 2 times: [2,1] and [2,2]. Merged item now (2,3)
Item id (3) appears 1 time: [3,2]

Example 2

Input: $items1 = [ [1,2], [2,3], [1,3], [3,2] ]
       $items2 = [ [3,1], [1,3] ]
Output: [ [1,8], [2,3], [3,3] ]

Example 3

Input: $items1 = [ [1,1], [2,2], [3,3] ]
       $items2 = [ [2,3], [2,4] ]
Output: [ [1,1], [2,9], [3,3] ]

Solution

At first glance the given items look like sparse vectors, which is disproved by Example 2, where an index appears twice within the same list. Nevertheless following a sparse vector approach, again utilizing the magic of PDL. The supplementary module PDL::CCS provides a convenient implementation of “compressed column storage” sparse vectors, matrices etc.

use strict;
use warnings;
use PDL;
use PDL::NiceSlice;
use PDL::CCS;

sub merge_items {
    my @pdl = map pdl($_), @_;
    my $which = null->glue(0, map $_((0)), @pdl)->uniq;
    my $sum = PDL::CCS::Nd->newFromWhich($which->dummy(0), zeroes($which),
        missing => 'BAD');
    $sum->indexND($_(0)) += $_(1) for null->glue(1, @pdl)->dog;

    $which->cat($sum->whichVals)->xchg(0, 1);
}

See the full solution.


If you have a question about this post or if you like to comment on it, feel free to open an issue in my github repository.