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# Greycoat21's solution

## to Saddle Points in the Delphi Pascal Track

Published at Jan 29 2020 · 0 comments
Instructions
Test suite
Solution

Detect saddle points in a matrix.

So say you have a matrix like so:

``````    1  2  3
|---------
1 | 9  8  7
2 | 5  3  2     <--- saddle point at column 1, row 2, with value 5
3 | 6  6  7
``````

It has a saddle point at column 1, row 2.

It's called a "saddle point" because it is greater than or equal to every element in its row and less than or equal to every element in its column.

A matrix may have zero or more saddle points.

Your code should be able to provide the (possibly empty) list of all the saddle points for any given matrix.

The matrix can have a different number of rows and columns (Non square).

Note that you may find other definitions of matrix saddle points online, but the tests for this exercise follow the above unambiguous definition.

## Testing

In order to run the tests for this track, you will need to install DUnitX. Please see the installation instructions for more information.

If Delphi is properly installed, and `*.dpr` file types have been associated with Delphi, then double clicking the supplied `*.dpr` file will start Delphi and load the exercise/project. `control + F9` is the keyboard shortcut to compile the project or pressing `F9` will compile and run the project.

Alternatively you may opt to start Delphi and load your project via. the `File` drop down menu.

### When Questions Come Up

We monitor the Pascal-Delphi support room on gitter.im to help you with any questions that might arise.

### Submitting Exercises

Note that, when trying to submit an exercise, make sure the exercise file you're submitting is in the `exercism/delphi/<exerciseName>` directory.

For example, if you're submitting `ubob.pas` for the Bob exercise, the submit command would be something like `exercism submit <path_to_exercism_dir>/delphi/bob/ubob.pas`.

## Source

J Dalbey's Programming Practice problems http://users.csc.calpoly.edu/~jdalbey/103/Projects/ProgrammingPractice.html

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you may request help from a mentor.

``````//******************************************************************
// Hint: You will be using TTuple in your solution.  TTuple is
// declared in this unit.  It will be necessary for you to add
// a uses statement in the interface section of uSaddlePoints.pas.
//******************************************************************

interface
uses
DUnitX.TestFramework;

const
CanonicalVersion = '1.5.0';

type

[TestFixture]
public
[Test]
//    [Ignore('Comment the "[Ignore]" statement to run the test')]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]
end;

TTuple<T1, T2> = record
private
fValue1: T1;
fValue2: T2;
public
constructor Create(aValue1: T1; aValue2: T2);
property Value1 : T1 read fValue1;
property Value2 : T2 read fValue2;
end;

implementation

constructor TTuple<T1, T2>.Create(aValue1: T1; aValue2: T2);
begin
fValue1 := aValue1;
fValue2 := aValue2;
end;

const
rows = 3;
columns = 3;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 9; values[0,1] := 8; values[0,2] := 7;
values[1,0] := 5; values[1,1] := 3; values[1,2] := 2;
values[2,0] := 6; values[2,1] := 6; values[2,2] := 7;

SetLength(expected, 1);
expected[0] := TTuple<integer,integer>.Create(2,1);
end;

const
rows = 0;
columns = 0;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);

SetLength(expected, 0);
end;

const
rows = 4;
columns = 1;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 2;
values[1,0] := 1;
values[2,0] := 4;
values[3,0] := 1;

SetLength(expected, 2);
expected[0] := TTuple<integer,integer>.Create(2,1);
expected[1] := TTuple<integer,integer>.Create(4,1);
end;

const
rows = 1;
columns = 4;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 2; values[0,1] := 5; values[0,2] := 3; values[0,3] := 5;

SetLength(expected, 2);
expected[0] := TTuple<integer,integer>.Create(1,2);
expected[1] := TTuple<integer,integer>.Create(1,4);
end;

const
rows = 3;
columns = 3;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 1; values[0,1] := 2; values[0,2] := 3;
values[1,0] := 3; values[1,1] := 1; values[1,2] := 2;
values[2,0] := 2; values[2,1] := 3; values[2,2] := 1;

SetLength(expected, 0);
end;

const
rows = 3;
columns = 3;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 4; values[0,1] := 5; values[0,2] := 4;
values[1,0] := 3; values[1,1] := 5; values[1,2] := 5;
values[2,0] := 1; values[2,1] := 5; values[2,2] := 4;

SetLength(expected, 3);
expected[0] := TTuple<integer,integer>.Create(1,2);
expected[1] := TTuple<integer,integer>.Create(2,2);
expected[2] := TTuple<integer,integer>.Create(3,2);
end;

const
rows = 3;
columns = 3;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 6; values[0,1] := 7; values[0,2] := 8;
values[1,0] := 5; values[1,1] := 5; values[1,2] := 5;
values[2,0] := 7; values[2,1] := 5; values[2,2] := 6;

SetLength(expected, 3);
expected[0] := TTuple<integer,integer>.Create(2,1);
expected[1] := TTuple<integer,integer>.Create(2,2);
expected[2] := TTuple<integer,integer>.Create(2,3);
end;

const
rows = 2;
columns = 3;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 3; values[0,1] := 1; values[0,2] := 3;
values[1,0] := 3; values[1,1] := 2; values[1,2] := 4;

SetLength(expected, 2);
expected[0] := TTuple<integer,integer>.Create(1,1);
expected[1] := TTuple<integer,integer>.Create(1,3);
end;

const
rows = 3;
columns = 3;
var
values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, rows, columns);
values[0,0] := 8; values[0,1] := 7; values[0,2] := 9;
values[1,0] := 6; values[1,1] := 7; values[1,2] := 6;
values[2,0] := 3; values[2,1] := 2; values[2,2] := 5;

SetLength(expected, 1);
expected[0] := TTuple<integer,integer>.Create(3,3);
end;

initialization
end.``````
``````unit uSaddlePoints;

interface

uses
Generics.Collections,

type
TCoordinate = Integer;
TPoint = TTuple<TCoordinate, TCoordinate>;
TPoints = TArray<TPoint>;

TValue = Integer;
TVector = TArray<TValue>;
TMatrix = TArray<TVector>;

TManifold = TDictionary<TPoint, TValue>;

function Calculate: TPoints;
end;

implementation

type
private
Manifold: TManifold;
Matrix: TMatrix;
public
function Calculate: TPoints;
end;

function MatrixToManifold(Matrix: TMatrix): TManifold;
var
x, y: TCoordinate;
begin
Result := TManifold.Create;
for y := Low(Matrix) to High(Matrix) do begin
for x := Low(Matrix[y]) to High(Matrix[y]) do begin
TPoint.Create(x, y),
Matrix[y, x]);
end;
end;
end;

var
begin

end;

var
x, y: TCoordinate;
PointToTest: TPoint;
begin
Result := [];
// Test all points
for y := Low(Matrix) to High(Matrix) do begin
for x := Low(Matrix[y]) to High(Matrix[y]) do begin

PointToTest := TPoint.Create(x, y);

Result := Result + [TPoint.Create(y + 1, x + 1)];
end;
end;
end;

// >= every element in the row
// <= every element in the column
var
x, y: TCoordinate;
SearchPoint: TPoint;
SearchValue, Value: TValue;
begin

Result := True;

// Check all row entries,
// any entry greater than Point's -> not Point.IsSaddle
for x := Low(Matrix[Point.Value2]) to High(Matrix[Point.Value2]) do begin

SearchPoint := TPoint.Create(x, Point.Value2);

if  Manifold.TryGetValue(SearchPoint, SearchValue)
and Manifold.TryGetValue(Point, Value)
and (Value < SearchValue) then
Exit(False);

end;

// Check all column entries,
// any entry less than Point's -> not Point.IsSaddle
for y := Low(Matrix) to High(Matrix) do begin

SearchPoint := TPoint.Create(Point.Value1, y);

if  Manifold.TryGetValue(SearchPoint, SearchValue)
and Manifold.TryGetValue(Point, Value)
and (Value > SearchValue) then
Exit(False);

end;
end;

end.``````