| 08 November 2024 | Challenge 293 |
Similar Boomerangs
Task 1: Similar Dominos
Submitted by: Mohammad Sajid Anwar
You are given a list of dominos, @dominos.
Write a script to return the number of dominoes that are similar to any other domino.
$dominos[i] = [a, b] and $dominos[j] = [c, d] are same if either (a = c and b = d) or (a = d and b = c).
Example 1
Input: @dominos = ([1, 3], [3, 1], [2, 4], [6, 8])
Output: 2
Similar Dominos: $dominos[0], $dominos[1]
Example 2
Input: @dominos = ([1, 2], [2, 1], [1, 1], [1, 2], [2, 2])
Output: 3
Similar Dominos: $dominos[0], $dominos[1], $dominos[3]
Solution
A few steps to solve this task:
- turn all dominoes such that the smaller value comes first
- sort the dominoes
- count the number of repetitions of the same domino in the sorted list
- sum over all counts that are larger than one.
use strict;
use warnings;
use PDL;
sub count_similar {
my ($c) = long(@_)->qsort->qsortvec->rlevec;
$c->where($c > 1)->sum;
}
See the full solution to task 1.
Task 2: Boomerang
Submitted by: Mohammad Sajid Anwar
You are given an array of points, (x, y).
Write a script to find out if the given points are a boomerang.
A boomerang is a set of three points that are all distinct and not in a straight line.
Example 1
Input: @points = ( [1, 1], [2, 3], [3,2] )
Output: true
Example 2
Input: @points = ( [1, 1], [2, 2], [3, 3] )
Output: false
Example 3
Input: @points = ( [1, 1], [1, 2], [2, 3] )
Output: true
Example 4
Input: @points = ( [1, 1], [1, 2], [1, 3] )
Output: false
Example 5
Input: @points = ( [1, 1], [2, 1], [3, 1] )
Output: false
Example 6
Input: @points = ( [0, 0], [2, 3], [4, 5] )
Output: true
Solution
From the given three points we get two vectors by taking the difference between two pairs of points. The resulting vectors must not be collinear, i.e. the determinant of the matrix formed by the two vectors must not be zero.
use strict;
use warnings;
use PDL;
use PDL::NiceSlice;
sub is_boomerang {
my $p = long @_;
!!($p(,1:-1) - $p(,0:-2))->determinant
}
See the full solution to task 2.
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.