## to Saddle Points in the Delphi Pascal Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

#### Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

Detect saddle points in a matrix.

So say you have a matrix like so:

``````    0  1  2
|---------
0 | 9  8  7
1 | 5  3  2     <--- saddle point at (1,0)
2 | 6  6  7
``````

It has a saddle point at (1, 0).

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.

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 can see how others have completed the exercise.

``````//******************************************************************
// 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.
//
// For more guidance as you work on this exercise, see
// GETTING_STARTED.md.
//******************************************************************

interface
uses
DUnitX.TestFramework;

const
CanonicalVersion = '1.1.0';

type

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

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]

[Test]
[Ignore]
end;

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

implementation

constructor TTuple<T1, T2>.Create(Value1: T1; Value2: T2);
begin
fValue1 := Value1;
fValue2 := Value2;
end;

values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, 3, 3);
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(1,0);
end;

values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, 0, 0);

SetLength(expected, 0);
end;

values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, 3, 3);
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;

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

values: TArray<TArray<integer>>;
expected: TArray<TTuple<integer,integer>>;
begin
SetLength(values, 3, 3);
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(2,2);
end;

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

interface

uses

type
['{CCD2CAC9-8B71-4EB7-AE1E-8180F7C92260}']
function Calculate:TArray<TTuple<integer,integer>>;
end;

implementation

uses
System.Generics.Collections;

type
private
FValues: TArray<TArray<integer>>;
FNominees: TList<TTuple<integer,integer>>;
procedure FillNominees;
public
function Calculate: TArray<TTuple<integer,integer>>;
constructor Create(aValues:TArray<TArray<integer>>);
destructor Destroy; override;
end;

begin
end;

begin
inherited Create;
FValues := aValues;
FNominees := TList<TTuple<integer,integer>>.Create();
FillNominees;
end;

var
zArrayMaxRow: TArray<integer>;
i, MaxValue: integer;

function RowMaxValue: integer;
var aCol:integer;
begin
result := 0;
for aCol := Low(zArrayMaxRow) to High(zArrayMaxRow) do
begin
if (zArrayMaxRow[aCol] >= result) then
result := zArrayMaxRow[aCol];
end;
end;

var aCol:integer;
begin
for aCol := Low(zArrayMaxRow) to High(zArrayMaxRow) do
begin
if (zArrayMaxRow[aCol] = aMaxValue) then
end;
end;

begin
for i := Low(FValues) to High(FValues) do
begin
zArrayMaxRow := FValues[i];
MaxValue := RowMaxValue;
end;
end;

begin
FNominees.Free;
end;

var
zPoint: TTuple<integer,integer>;
zArrayMinCol: TArray<integer>;
i,j, MaxValue: integer;
isMaxRowisMinCol:boolean;
begin
// It's called a "saddle point" because it is greater than or equal to
// every element in its row and the less than or equal to every element in
// its column.
for i := 0 to pred(FNominees.count) do
begin
zPoint := FNominees.Items[i];
MaxValue := FValues[zPoint.Value1][zPoint.Value2];
isMaxRowIsMinCol := true;
for j := Low(FValues) to High(FValues) do
begin
if (j <> zPoint.Value1) then
begin
zArrayMinCol := FValues[j];
if (MaxValue > zArrayMinCol[zPoint.Value2]) then
begin
IsMaxRowIsMinCol := false;
break;
end;
end;
end;
if ( IsMaxRowIsMinCol ) then
begin
end;
end;
end;

end.``````