# rpottsoh's solution

## to Saddle Points in the Delphi Pascal Track

Published at Aug 27 2018 · 0 comments
Instructions
Test suite
Solution

#### Note:

This exercise has changed since this solution 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.``````
``````//========================================================================
// For this example solution I utilized Stefen Glienke's
// open-source code library titled Spring4D.  Latest
// version is available here: https://bitbucket.org/sglienke/spring4d
// Spring4D is not absolutely necessary, but it does greatly help
// facilitate a much simpler solution.
//
// Spring4D does include a Tuple record type that I have purposely
// not used in favor of my own, simple, TTuple that I declared in the
// test runner, in order to remove Spring4D dependency for test execution
//========================================================================

interface

type
['{8C41B1A2-335D-4C6D-AF55-9F307F358227}']
function Calculate: TArray<TTuple<integer, integer>>;
end;

implementation
uses SysUtils, Spring.Collections;

type
private
fValues: TArray<TArray<integer>>;
fmaxRows: TArray<integer>;
fminCols: TArray<integer>;
function getMaxRows: TArray<integer>;
function getMinColumns: TArray<integer>;
function Coordinates: IList<TTuple<integer, integer>>;
function ColumnCount: integer;
function RowCount: integer;
function IsSaddlePoint(const coordinate: TTuple<integer, integer>): boolean;
public
constructor create(aValues: TArray<TArray<integer>>);
function Calculate: TArray<TTuple<integer, integer>>;
end;

begin
end;

begin
fValues := copy(aValues);
fmaxRows := getMaxRows;
fminCols := getMinColumns;
end;

var
Row: integer;
Col: integer;
lRow: IList<integer>;
begin
lRow := TCollections.CreateList<integer>;
SetLength(result, RowCount);
for Row := 0 to RowCount - 1 do
begin
for Col := 0 to ColumnCount - 1 do
result[Row] := lRow.Max;
lRow.Clear;
end;
end;

var
Col: integer;
Row: integer;
lColumn: IList<integer>;
begin
lColumn := TCollections.CreateList<integer>;
SetLength(result, ColumnCount);
for Col := 0 to ColumnCount - 1 do
begin
for Row := 0 to RowCount - 1 do
result[Col] := lColumn.Min;
lColumn.Clear;
end;
end;

var
Row, Col: integer;
begin
result := TCollections.CreateList<TTuple<integer, integer>>;
for Row := 0 to RowCount - 1 do
for Col := 0 to ColumnCount - 1 do
end;

begin
end;

begin
if RowCount > 0 then
result := length(fValues[0])
else
result := 0;
end;

begin
result := length(fValues);
end;

var
row, col: integer;
begin
row := coordinate.Value1;
col := coordinate.Value2;
result := (fmaxRows[row] = fValues[row, col]) and
(fminCols[col] = fValues[row, col]);
end;

end.``````