RabbitFarm

The examples used here are from the weekly challenge problem statement and demonstrate the working solution.

Part 1

You are given an array of integers. Write a script to return the number of reverse pairs in the given array.

Solution

reverse_pair(X, Y, Z):-
    (X =\= Y, X > Y + Y, Z = 1, !); Z = 0.
reverse_pairs([], 0).    
reverse_pairs([H|T], ReversePairs):-
    reverse_pairs(T, R),
    maplist(reverse_pair(H), T, RP),
    sum_list(RP, Sum),
    ReversePairs is R + Sum.  

Sample Run

% gprolog --consult-file prolog/ch-1.p
| ?- reverse_pairs([1, 3, 2, 3, 1], ReversePairs).  

ReversePairs = 2

yes
| ?- reverse_pairs([2, 4, 3, 5, 1], ReversePairs).  

ReversePairs = 3

yes
| ?- 

Notes

reverse_pair/3 implements the reverse pair criteria and is called via a maplist/3 in reverse_pairs/3 which recurses over the list and counts up all Reverse Pairs found.

Part 2

You are given an array of positive integers (>=1). Write a script to return the floor sum.

Solution

floor_sum_pair(X, Y, Z):-
    Z is floor(X / Y).

floor_sum(Integers, FloorSum):-
    floor_sum(Integers, Integers, FloorSum).
floor_sum([], _, 0).    
floor_sum([H|T], L, FloorSum):-
    floor_sum(T, L, F),
    maplist(floor_sum_pair(H), L, FS),
    sum_list(FS, Sum),
    FloorSum is F + Sum.  

Sample Run

% gprolog --consult-file prolog/ch-2.p 
| ?- floor_sum([2, 5, 9], FloorSum).

FloorSum = 10

yes
| ?- floor_sum([7, 7, 7, 7, 7, 7, 7], FloorSum).

FloorSum = 49

(1 ms) yes
| ?- 

Notes

The process here is, co-incidentally, much the same as the first part above. We recurse over the list and use a maplist/3 to build an incremental sum at each step.

References

Challenge 243

The examples used here are from the weekly challenge problem statement and demonstrate the working solution.

Part 1

You are given an array of integers. Write a script to return the number of reverse pairs in the given array.

Solution

use v5.38;
sub reverse_pairs{
    my @integers = @_;
    my @reverse_pairs;
    do{
        my $i = $_;
        do{
            my $j = $_;
            push @reverse_pairs, [$i, $j] if $integers[$i] > $integers[$j] + $integers[$j];
        } for $i + 1 .. @integers - 1;
    } for 0 .. @integers - 1;
    return 0 + @reverse_pairs;
}

MAIN:{
    say reverse_pairs 1, 3, 2, 3, 1;
    say reverse_pairs 2, 4, 3, 5, 1;
}

Sample Run

$ perl perl/ch-1.pl 
2
3

Notes

A reverse pair is a pair (i, j) where:

a) 0 <= i < j < nums.length 

and

b) nums[i] > 2 * nums[j].

I've been on a bit of a recursion kick recently, but I didn't have the appetite for it this week. A nested loop and we're done!

Part 2

You are given an array of positive integers (>=1). Write a script to return the floor sum.

Solution

use v5.38;
use POSIX;
sub floor_sum{
    my @integers = @_;
    my $floor_sum;
    do{
        my $i = $_;
        do{
            my $j = $_;
            $floor_sum += floor($integers[$i] / $integers[$j]);
        } for 0 .. @integers - 1;
    } for 0 .. @integers - 1;
    return $floor_sum;
}

MAIN:{
    say floor_sum 2, 5, 9;
    say floor_sum 7, 7, 7, 7, 7, 7, 7;
}

Sample Run

$ perl perl/ch-2.pl 
10
49

Notes

See above comment about not being as recursive this week!

References

Challenge 243