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# dgeiger's solution

## to Saddle Points in the Delphi Pascal Track

Published at Sep 02 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

type
Matrix = TArray<TArray<integer>>;

PointsArray = TArray<TTuple<integer,integer>>;

function Calculate: TArray<TTuple<integer,integer>>;

end;

private
FMatrix: Matrix;
FRow: Integer;
FRows: Integer;
FColumn: Integer;
FColumns: Integer;

function RowMax: Integer;
function ColumnMin: Integer;

public
constructor Create(values: TArray<TArray<integer>>);

function Calculate: PointsArray;

end;

implementation

begin
// Here, we just create a new TSaddlePoints object and return it's interface.
end;

var
Col: Integer;
begin
// Since we know that this is a valid array, and that this guarantees at
// least one element, we set the Result to the value of that element.
Result := FMatrix[FRow, 0];

// Now, we scan the rest of the array (if any)
for Col := 1 to FColumns - 1 do
// Is this element the new maximum?
if FMatrix[FRow, Col] > Result then
// Update the result
Result := FMatrix[FRow, Col];
end;

var
Row: Integer;
begin
// Since we know that this is a valid array, and that this guarantees at

// least one element, we set the Result to the value of that element.
Result := FMatrix[0, FColumn];

// Now, we scan the rest of the array (if any)
for Row := 1 to FRows - 1 do
// Is this element the new minimum?
if FMatrix[Row, FColumn] < Result then
// Update the result
Result := FMatrix[Row, FColumn];
end;

var
Min: Integer;
Max: Integer;
Row: Integer;
Column: Integer;
TestValue: Integer;
begin
// First, we'll create a new PointsArray, and set the count of
// saddles points found to zero

// We need to scan each row
for Row := 0 to FRows - 1 do
begin
// Update the FRow field, so we don't have to keep passing the row.
FRow := Row;

// Get the maximum value for this row
Max := RowMax;

// Now, we need to scan each column in this row
for Column := 0 to FColumns - 1 do
begin
// Update the FColumn field, so we don't have to keep passing the row.
FColumn := Column;

// Get the minimum value for this column
Min := ColumnMin;

// Next, we get the value to test
TestValue := FMatrix[Row, Column];

// It's a saddle point only if it's the maximum value in the row
// and the minimum value in the column
if (TestValue = Min) and (TestValue = Max) then
begin

// set the points for this saddle,

// and update the count of saddle points.
end;
end;
end;

// Finally, we return the PointsArray containing the saddles
end;

begin
// First, we need to create the Matrix we store the points in
FMatrix := Values;

// Next we get the number of rows in the Matrix
FRows := Length(FMatrix);

// Are there any rows in the Matrix?
if FRows = 0 then
// No, so this means there can be no columns either.
FColumns := 0
else
// Otherwise, get the number of columns in the Matrix
FColumns := Length(FMatrix[0]);
end;

end.``````