| 16 January 2024 | Challenge 252 |
Special Zeroes
Task 1: Special Numbers
Submitted by: Mohammad S Anwar
You are given an array of integers, @ints.
Write a script to find the sum of the squares of all special elements of the given array.
An element $int[i] of @ints is called special if i divides n, i.e. n % i == 0.
Where n is the length of the given array. Also the array is 1-indexed for the task.
Example 1
Input: @ints = (1, 2, 3, 4)
Output: 21
There are exactly 3 special elements in the given array:
$ints[1] since 1 divides 4,
$ints[2] since 2 divides 4, and
$ints[4] since 4 divides 4.
Hence, the sum of the squares of all special elements of given array:
1 * 1 + 2 * 2 + 4 * 4 = 21.
Example 2
Input: @ints = (2, 7, 1, 19, 18, 3)
Output: 63
There are exactly 4 special elements in the given array:
$ints[1] since 1 divides 6,
$ints[2] since 2 divides 6,
$ints[3] since 3 divides 6, and
$ints[6] since 6 divides 6.
Hence, the sum of the squares of all special elements of given array:
2 * 2 + 7 * 7 + 1 * 1 + 3 * 3 = 63
Solution
We need to sum over the squared values of all elements having an 1-based index that divides the size of @ints.
There is divisors in Math::Prime::Util that provides all divisors of a given number and there is PDL that can pick slices off, calculate the element-wise power of and the sum over an ndarray.
Putting these together in a single statement:
use PDL;
use PDL::NiceSlice;
use Math::Prime::Util 'divisors';
sub snss {
sum pdl(@_)->(indx(divisors @_) - 1) ** 2
}
See the full solution.
Task 2: Unique Sum Zero
Submitted by: Mohammad S Anwar
You are given an integer, $n.
Write a script to find an array containing $n unique integers such that they add up to zero.
Example 1
Input: $n = 5
Output: (-7, -1, 1, 3, 4)
Two other possible solutions could be as below:
(-5, -1, 1, 2, 3) and (-3, -1, 2, -2, 4).
Example 2
Input: $n = 3
Output: (-1, 0, 1)
Example 3
Input: $n = 1
Output: (0)
Solution
There are trivial solutions for even and odd values of $n:
- pairs of positive and negative integers with the same absolute value are distinct and sum to zero
- adding a zero to such a list keeps the sum at zero, but provides an odd number of elements
This results in:
use experimental 'signatures';
sub uniq_sum_zero ($n) {
(-$n / 2 .. -1, (0) x ($n % 2), 1 .. $n / 2);
}
See the full solution.