# RabbitFarm

### 2022-11-27

The Weekly Challenge 192 (Prolog Solutions)

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

## Part 1

*You are given a positive integer, $n. Write a script to find the binary flip.*

### Solution

```
bits(N, Bits):-
bits(N, [], Bits).
bits(0, Bits, Bits):-!.
bits(N, BitsAccum, Bits):-
B is N /\ 1,
N0 is N >> 1,
bits(N0, [B|BitsAccum], Bits).
bits_reverse(B, RB):-
Flipped is xor(B, 1),
number_chars(Flipped, [RB]).
binary_flip(N, NBitsReversed):-
bits(N, Bits),
maplist(bits_reverse, Bits, BitsReversed),
number_chars(NBitsReversed, ['0','b'|BitsReversed]).
```

### Sample Run

```
$ gprolog --consult-file prolog/ch-2.p
| ?- binary_flip(5, BinaryFlip).
BinaryFlip = 2
yes
| ?- binary_flip(4, BinaryFlip).
BinaryFlip = 3
yes
| ?- binary_flip(6, BinaryFlip).
BinaryFlip = 1
yes
```

### Notes

I learned a slightly obscure bit (no pun intended!) of information about Prolog's handling
of binary numbers this week. If you prepend '0','b' to a list of characters, or the ascii
code equivalents to a list of codes, representing binary digits then `number_chars/2`

(or
`number_codes/2`

) will automatically convert to decimal.

The solution to the whole problem is:

Convert the number to a list of bits (

`bits/2`

).Flip the bits with an xor

Convert the list of flipped bits to decimal using the

`number_chars/2`

method.

## Part 2

*You are given a list of integers greater than or equal to zero, @list. Write a script to
distribute the number so that each members are same. If you succeed then print the total
moves otherwise print -1.*

### Solution

```
:-dynamic(moves/1).
moves(0).
equal_distribution(ListIntegers, _):-
length(ListIntegers, L),
sum_list(ListIntegers, S),
Average is S / L,
F is floor(Average),
C is ceiling(Average),
F \== C,
fail.
equal_distribution(ListIntegers, ListEqualDistribution):-
length(ListIntegers, L),
sum_list(ListIntegers, S),
Average is S / L,
F is floor(Average),
C is ceiling(Average),
F == C,
length(ListEqualDistribution, L),
equal_distribution(ListIntegers, F, ListEqual),
delete(ListEqual, F, ListEqualAverageDeleted),
length(ListEqualAverageDeleted, ListEqualAverageDeletedLength),
((ListEqualAverageDeletedLength == 0,
ListEqualDistribution = ListEqual);
equal_distribution(ListEqual, ListEqualDistribution)), !.
distribute(Average, [X, Y], [S, T]):-
X < Average,
X < Y,
S is X + 1,
T is Y - 1,
moves(Moves),
succ(Moves, M),
retract(moves(Moves)),
asserta(moves(M)).
distribute(Average, [X, Y], [S, T]):-
X > Average,
X > Y,
S is X - 1,
T is Y + 1,
moves(Moves),
succ(Moves, M),
retract(moves(Moves)),
asserta(moves(M)).
distribute(Average, [X, Y], [S, T]):-
((X == Average; X == Y);
(X < Average, X > Y)
),
S = X,
T = Y.
equal_distribution([A, B|[]], Average, [X, Y|[]]):-
maplist(distribute(Average),[[A, B]], [[X, Y]]).
equal_distribution(ListIntegers, Average, [X|T]):-
append([A, B], RestIntegers, ListIntegers),
maplist(distribute(Average),[[A, B]], [[X, Y]]),
equal_distribution([Y|RestIntegers], Average, T).
main(ListIntegers, Moves):-
retract(moves(_)),
asserta(moves(0)),
(equal_distribution(ListIntegers, _), moves(Moves), !);
Moves = -1.
```

### Sample Run

```
$ gprolog --consult-file prolog/ch-2.p
| ?- main([1, 0, 5], Moves).
Moves = 4
(1 ms) yes
| ?- main([0, 2, 0], Moves).
Moves = -1
yes
| ?- main([0, 3, 0], Moves).
Moves = 2
yes
```

### Notes

The rules that must be followed are:

1) You can only move a value of '1' per move

2) You are only allowed to move a value of '1' to a direct neighbor/adjacent cell.

This code ended up being a little more complex than I had originally thought it would be.
At the heart of the solution is what I consider a pretty nice application of `maplist/3`

to drive the `distribution/3`

, which is the implementation of the given rules.

We need to track the number of moves taken, not just the final resulting list. Rather than
track the moves using a variable passed to the various predicates handling the
re-distribution it seemed a bit cleaner to me to instead not have so many variables and
`asserta/1`

and `retract/1`

the updated number of moves.

I generally try and avoid the use of the disjunction `(;)/2`

with the exception of small
cases where to use it would unnaturally increase the amount of code. In this problem there
are several such small cases such as whether we set the number of Moves to -1 in the case
of an impossible re-distribution or the condition for detecting that we are done
re-distributing.

## References

posted at: 19:05 by: Adam Russell | path: /prolog | permanent link to this entry

#### Flipping to Redistribute

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

## Part 1

*You are given a positive integer, $n. Write a script to find the binary flip.*

### Solution

```
use v5.36;
sub int2bits{
my($n) = @_;
my @bits;
while($n){
my $b = $n & 1;
unshift @bits, $b;
$n = $n >> 1;
}
return @bits
}
sub binary_flip{
my($n) = @_;
my @bits = int2bits($n);
@bits = map {$_^ 1} @bits;
return oct(q/0b/ . join(q//, @bits));
}
MAIN:{
say binary_flip(5);
say binary_flip(4);
say binary_flip(6);
}
```

### Sample Run

```
$ perl perl/ch-1.pl
2
3
1
```

### Notes

There was once a time when I was positively terrified of bitwise operations. Anything at that level seemed a bit like magic. Especially spooky were the bitwise algorithms detailed in Hacker's Delight! Anyway, has time has gone on I am a bit more confortable with these sorts of things. Especially when, like this problem, the issues are fairly straightforward.

The code here does the following:

converts a given integer into an array of bits via

`int2bits()`

flips the bits using an xor operation (the

`map`

in`binary_flip()`

)converts the array of flipped bits to the decimal equivalent via

`oct()`

which, despite the name, handles any decimal, binary, octal, and hex strings as input.

## Part 2

*You are given a list of integers greater than or equal to zero, @list. Write a script to
distribute the number so that each members are same. If you succeed then print the total
moves otherwise print -1.*

### Solution

```
use v5.36;
use POSIX;
sub equal_distribution{
my(@integers) = @_;
my $moves;
my $average = unpack("%32I*", pack("I*", @integers)) / @integers;
return -1 unless floor($average) == ceil($average);
{
map{
my $i = $_;
if($integers[$i] > $average && $integers[$i] > $integers[$i+1]){$integers[$i]--; $integers[$i+1]++; $moves++}
if($integers[$i] < $average && $integers[$i] < $integers[$i+1]){$integers[$i]++; $integers[$i+1]--; $moves++}
} 0 .. @integers - 2;
redo unless 0 == grep {$average != $_} @integers;
}
return $moves;
}
MAIN:{
say equal_distribution(1, 0, 5);
say equal_distribution(0, 2, 0);
say equal_distribution(0, 3, 0);
}
```

### Sample Run

```
$ perl perl/ch-2.pl
4
-1
2
```

### Notes

The rules that must be followed are:

1) You can only move a value of '1' per move

2) You are only allowed to move a value of '1' to a direct neighbor/adjacent cell.

First we compute the average of the numbers in the list. Provided that the average is a
non-decimal (confirmed by comparing `floor`

to `ceil`

) we know we can compute the
necessary "distribution".

The re-distribution itself is handled just by following the rules and continuously looping until all values in the list are the same.

## References

posted at: 19:04 by: Adam Russell | path: /perl | permanent link to this entry