# RabbitFarm

### 2022-05-22

#### The Weekly Challenge 165 (Prolog Solutions)

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

## Part 1

Plot lines and points in SVG format.

### Solution

``````
svg-->svg_begin, svg_body, svg_end.
svg_body-->[].
svg_body-->svg_line(_, _, _, _), svg_body.
svg_body-->svg_point(_, _), svg_body.
svg_begin-->['<?xml version="1.0" encoding="UTF-8" standalone="yes"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd"><svg height="100%" width="100%" xmlns="http://www.w3.org/2000/svg" xmlns:svg="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">'].
svg_point(X, Y)-->['<circle cx="', X,'" cy="', Y, '" r="1" />'].
svg_line(X1, Y1, X2, Y2)-->['<line x1="', X1, '" x2="', X2, '" y1="', Y1, '" y2="', Y2, '" style="stroke:#006600;" />'].
svg_end-->[''].

plot([], SVGAccum, SVG):-
phrase(svg_begin, Begin),
flatten([Begin|SVGAccum], SVG).
plot([H|T], SVGAccum, SVG):-
length(H, 2),
[X, Y] = H,
phrase(svg_point(X, Y), Point),
plot(T, [Point|SVGAccum], SVG).
plot([H|T], SVGAccum, SVG):-
length(H, 4),
[X1, Y1, X2, Y2] = H,
phrase(svg_line(X1, Y1, X2, Y2), Line),
plot(T, [Line|SVGAccum], SVG).
plot(Lines, SVG):-
phrase(svg_end, End),
plot(Lines, [End], SVG).

main:-
plot([[53,10], [53, 10, 23, 30], [23, 30]], SVG),
maplist(write, SVG), nl,
halt.
``````

### Sample Run

``````
\$ gprolog --consult-file prolog/ch-1.p
<?xml version="1.0" encoding="UTF-8" standalone="yes"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd"><svg height="100%" width="100%" xmlns="http://www.w3.org/2000/svg" xmlns:svg="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><circle cx="23" cy="30" r="1" /><line x1="53" x2="23" y1="10" y2="30" /><circle cx="53" cy="10" r="1" /></svg>
``````

### Notes

SVG is an XML based format, and so the use of a DCG like this may be unexpected. After all, the "grammar" is really dictated by a known XML schema. Still, the DCG is helpful in that we can describe the sequence and formatting of the statements we expect. From this we can generate the required SVG and even do some basic validation.

## Part 2

Given a list of numbers, generate the skip summations.

### Solution

``````
avg_difference(Avg, V, Difference):-
Difference is V - Avg.

square(X, XSquared):-
XSquared is X * X.

xy(X, Y, XY):-
XY is X * Y.

linear_regression(Points, RegressionLineEndpoints):-
length(Points, NumberPoints),
% 1. Calculate average of your X variable.
maplist(nth(1), Points, Xs),
msort(Xs, XSorted),
nth(NumberPoints, XSorted, XMax),
sum_list(Xs, XSum),
XAvg is XSum / NumberPoints,
% 2. Calculate the difference between each X and the average X.
maplist(avg_difference(XAvg), Xs, XDifferences),
% 3. Square the differences and add it all up. This is Sx.
maplist(square, XDifferences, XDifferencesSquared),
sum_list(XDifferencesSquared, Sx),
% 4. Calculate average of your Y variable.
maplist(nth(2), Points, Ys),
sum_list(Ys, YSum),
YAvg is YSum / NumberPoints,
% 5. Multiply the differences (of X and Y from their respective averages) and add them all together.  This is Sxy.
maplist(avg_difference(YAvg), Ys, YDifferences),
maplist(xy, XDifferences, YDifferences, XY),
sum_list(XY, Sxy),
% 6. Using Sx and Sxy, you calculate the intercept by subtracting Sx / Sxy * AVG(X) from AVG(Y).
M is Sxy / Sx,
B is YAvg - (Sxy / Sx * XAvg),
EndX is XMax + 10,
EndY is M * EndX + B,
RegressionLineEndpoints = [0, B, EndX, EndY].

main:-
Points = [[333,129], [39, 189], [140, 156], [292, 134], [393, 52], [160, 166], [362, 122], [13, 193], [341, 104], [320, 113], [109, 177], [203, 152], [343, 100], [225, 110], [23, 186], [282, 102], [284, 98], [205, 133], [297, 114], [292, 126], [339, 112], [327, 79], [253, 136], [61, 169], [128, 176], [346, 72], [316, 103], [124, 162], [65, 181], [159, 137], [212, 116], [337, 86], [215, 136], [153, 137], [390, 104], [100, 180], [76, 188], [77, 181], [69, 195], [92, 186], [275, 96], [250, 147], [34, 174], [213, 134], [186, 129], [189, 154], [361, 82], [363, 89]],
linear_regression(Points, RegressionLine),
write(RegressionLine), nl.
``````

### Sample Run

``````
\$ gprolog --consult-file prolog/ch-1.p --consult-file prolog/ch-2.p
| ?- Points = [[333,129], [39, 189], [140, 156], [292, 134], [393, 52], [160, 166], [362, 122], [13, 193], [341, 104], [320, 113], [109, 177], [203, 152], [343, 100], [225, 110], [23, 186], [282, 102], [284, 98], [205, 133], [297, 114], [292, 126], [339, 112], [327, 79], [253, 136], [61, 169], [128, 176], [346, 72], [316, 103], [124, 162], [65, 181], [159, 137], [212, 116], [337, 86], [215, 136], [153, 137], [390, 104], [100, 180], [76, 188], [77, 181], [69, 195], [92, 186], [275, 96], [250, 147], [34, 174], [213, 134], [186, 129], [189, 154], [361, 82], [363, 89]],
linear_regression(Points, RegressionLine), append(Points, [RegressionLine], PointsLine), plot(PointsLine, SVG), maplist(write, SVG), nl.
<?xml version="1.0" encoding="UTF-8" standalone="yes"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd"><svg height="100%" width="100%" xmlns="http://www.w3.org/2000/svg" xmlns:svg="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><line x1="0" x2="403" y1="200.13227253558171" y2="79.249802930305563" style="stroke:#006600;" /><circle cx="363" cy="89" r="1" /><circle cx="361" cy="82" r="1" /><circle cx="189" cy="154" r="1" /><circle cx="186" cy="129" r="1" /><circle cx="213" cy="134" r="1" /><circle cx="34" cy="174" r="1" /><circle cx="250" cy="147" r="1" /><circle cx="275" cy="96" r="1" /><circle cx="92" cy="186" r="1" /><circle cx="69" cy="195" r="1" /><circle cx="77" cy="181" r="1" /><circle cx="76" cy="188" r="1" /><circle cx="100" cy="180" r="1" /><circle cx="390" cy="104" r="1" /><circle cx="153" cy="137" r="1" /><circle cx="215" cy="136" r="1" /><circle cx="337" cy="86" r="1" /><circle cx="212" cy="116" r="1" /><circle cx="159" cy="137" r="1" /><circle cx="65" cy="181" r="1" /><circle cx="124" cy="162" r="1" /><circle cx="316" cy="103" r="1" /><circle cx="346" cy="72" r="1" /><circle cx="128" cy="176" r="1" /><circle cx="61" cy="169" r="1" /><circle cx="253" cy="136" r="1" /><circle cx="327" cy="79" r="1" /><circle cx="339" cy="112" r="1" /><circle cx="292" cy="126" r="1" /><circle cx="297" cy="114" r="1" /><circle cx="205" cy="133" r="1" /><circle cx="284" cy="98" r="1" /><circle cx="282" cy="102" r="1" /><circle cx="23" cy="186" r="1" /><circle cx="225" cy="110" r="1" /><circle cx="343" cy="100" r="1" /><circle cx="203" cy="152" r="1" /><circle cx="109" cy="177" r="1" /><circle cx="320" cy="113" r="1" /><circle cx="341" cy="104" r="1" /><circle cx="13" cy="193" r="1" /><circle cx="362" cy="122" r="1" /><circle cx="160" cy="166" r="1" /><circle cx="393" cy="52" r="1" /><circle cx="292" cy="134" r="1" /><circle cx="140" cy="156" r="1" /><circle cx="39" cy="189" r="1" /><circle cx="333" cy="129" r="1" /></svg>
``````

### Notes

This is mainly an implementation of the same linear regression procedure as used in the Perl solution to the same problem. By consulting the solution to the first problem we can then re-use the same plotting code.

## References

Challenge 165

Linear Regression Calculation

posted at: 23:28 by: Adam Russell | path: /prolog | permanent link to this entry