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Arrays.pas
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Arrays.pas
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{
Copyright (c) Peter Karpov 2010 - 2018.
Usage of the works is permitted provided that this instrument is retained with
the works, so that any entity that uses the works is notified of this instrument.
DISCLAIMER: THE WORKS ARE WITHOUT WARRANTY.
}
{$IFDEF FPC} {$MODE DELPHI} {$ENDIF}
unit Arrays; ////////////////////////////////////////////////////////////////////////
{
>> Version: 1.5
>> Description
Basic array routines. Part of InvLibs unit collection.
>> Author
Peter Karpov
Email : [email protected]
Homepage : inversed.ru
GitHub : inversed-ru
Twitter : @inversed_ru
>> ToDo
- Repeated append-delete operations worst case complexity analysis
- Do something with all the copypasta
? Split "Permutations" section into Combinatorics unit and implement other
permutation-related routines
- See if any operations are bottlenecks in any programs and optimize them
>> Changelog
1.5 : 2019.11.10 * AppendUnique name typo
1.4 : 2018.12.14 ~ Argument order in SaveToText and SaveToFile
+ SaveToText for TIntArrays
1.3 : 2018.11.08 + Overloaded version of AppendArray for TIntArrays
+ Concat procedure
1.2 : 2017.12.15 + DistanceL2 function
1.1 : 2017.12.08 + RandMinIndex and RandMaxIndex functions
1.0 : 2017.12.02 ~ Renamed the unit to Arrays
~ Renamed AddToArray to Append and AddUnique to AppendUnique
to avoid confusion
~ Renamed Concat to AppendArray
~ Renamed array arithmetics functions
~ Split Basic section into Initialization and Resizing
- Moved DeleteDuplicates procedures to Sorting unit to
untangle dependencies
~ Statistics and Sorting removed from dependencies
- Moved RandPerm and ShuffleArray procedures to RandVars unit
~ Comments cleanup
~ FreePascal compatibility
0.20 : 2015.04.17 ~ Save / Load section reworked
0.19 : 2015.03.09 + ExtendArray procedures
0.18 : 2014.10.06 + LoadIntArray procedure
0.17 : 2014.09.26 + ValueCount function
~ Renamed MarkEqual procedure to MarkValue
0.16 : 2014.08.22 + Concat procedure
0.15 : 2013.12.26 + Permute procedure
+ InvertPerm for in-place permutation inversion
~ Renamed some permutation routines
0.14 : 2013.06.16 + MarkEqual procedure
0.13 : 2013.06.09 + InitArray2D procedure
0.12 : 2013.05.25 + 2D arrays section
0.11 : 2013.03.26 + ConvertToReal procedure
0.10 : 2013.02.06 + SubArray procedure
0.9 : 2013.01.30 ~ Cleaned up types
+ Array multiply-add procedure
0.8.3 : 2011.10.14 ~ Moved to generic types
0.6 : 2011.06.14 - NAlloc field
+ TBoolArray type
+ InitArray procedures
~ Add / Delete section rewritten
+ Linear search procedures
+ DeleteDuplicates procedure
0.5 : 2011.04.15 + "Load, Save" section
+ More overloaded versions
0.4 : 2011.03.17 ~ Sectionized
+ "Permutations" section ("Shuffle" unit assimilated)
+ Tie breaking in binary search
0.1 : 2010.05.13 + Binary search
0.0 : 2010.05.05 + Initial version
Notation: + added, - removed, * fixed, ~ changed
}
interface ///////////////////////////////////////////////////////////////////////////
type
TIntArray = array of Integer;
PIntArray = ^TIntArray;
TIntArrayN =
record
N : Integer;
_ : TIntArray;
end;
PIntArrayN = ^TIntArrayN;
TRealArray = array of Real;
PRealArray = ^TRealArray;
TRealArrayN =
record
N : Integer;
_ : TRealArray;
end;
PRealArrayN = ^TRealArrayN;
TBoolArray = array of Boolean;
PBoolArray = ^TBoolArray;
TRealArray2D = array of array of Real;
TIntArray2D = array of array of Integer;
{-----------------------<< Initialization >>----------------------------------------}
// Initialize A with Len elements
procedure InitArrayN(
var A : TIntArrayN;
Len : Integer = 0);
overload;
procedure InitArrayN(
var A : TRealArrayN;
Len : Integer = 0);
overload;
// Initialize A with Len elements with a given Value
procedure InitArray(
var A : TBoolArray;
Len : Integer;
Value : Boolean);
overload;
procedure InitArray(
var A : TIntArray;
Len : Integer;
Value : Integer);
overload;
procedure InitArray(
var A : TRealArray;
Len : Integer;
Value : Real);
overload;
// Fill A with sequential integers starting from Base
procedure SequentialFill(
var A : array of Integer;
Base : Integer);
overload;
// Return array of length N filled with sequential integers starting from Base
procedure SequentialFill(
var A : TIntArray;
N : Integer;
Base : Integer);
overload;
procedure SequentialFill(
var A : TIntArrayN;
N : Integer;
Base : Integer);
overload;
{-----------------------<< Conversion >>--------------------------------------------}
// Convert integer array A into real array B
procedure ConvertToReal(
var B : TRealArray;
const A : TIntArray);
overload;
procedure ConvertToReal(
var B : TRealArrayN;
const A : TIntArrayN);
overload;
{-----------------------<< Resizing >>----------------------------------------------}
// Resize A to NewLen, fill new elements with Value
procedure ExtendArray(
var A : TIntArray;
NewLen : Integer;
Value : Integer);
overload;
procedure ExtendArray(
var A : TRealArray;
NewLen : Integer;
Value : Real);
overload;
procedure ExtendArray(
var A : TBoolArray;
NewLen : Integer;
Value : Boolean);
overload;
// Set the length of A to its true value
procedure SetTrueLength(
var A : TIntArrayN);
overload;
procedure SetTrueLength(
var A : TRealArrayN);
overload;
{-----------------------<< Element swapping and reversal >>-------------------------}
// Swap i-th and j-th elements of A
procedure Swap(
var A : TRealArrayN;
i, j : Integer);
overload;
procedure Swap(
var A : TRealArray;
i, j : Integer);
overload;
// Reverse [i .. j] section of A. If i >= j, A is left unchanged.
procedure Reverse(
var A : array of Integer;
i, j : Integer);
{-----------------------<< Arithmetics >>-------------------------------------------}
// Add Value to the elements of A
procedure ArrayAdd(
var A : TRealArray;
Value : Real);
// Substract Value from the elements of A
procedure ArraySub(
var A : TRealArray;
Value : Real);
// Multiply the elements of A by Value
procedure ArrayMul(
var A : TRealArray;
Value : Real);
// Divide the elements of A by Value
procedure ArrayDiv(
var A : TRealArray;
Value : Real);
// Add B * C to A
procedure ArrayMulAdd(
var A : TRealArray;
const B : TRealArray;
C : Real);
// The dot product between A and B
function DotProduct(
var A, B : TRealArray
) : Real;
// The Euclidean distance between A and B
function DistanceL2(
const A, B : TRealArray
) : Real;
{-----------------------<< Element addition and removal >>---------------------------}
// Append Value to A
procedure Append(
var A : TIntArrayN;
Value : Integer);
overload;
procedure Append(
var A : TRealArrayN;
Value : Real);
overload;
// Append B to A
procedure AppendArray(
var A : TRealArray;
const B : TRealArray);
overload;
procedure AppendArray(
var A : TIntArray;
const B : TIntArray);
overload;
// Concatenate A and B into C
procedure Concat(
var C : TRealArray;
const A, B : TRealArray);
overload;
procedure Concat(
var C : TIntArray;
const A, B : TIntArray);
overload;
// Append Value to A if it is distinct from all the elements,
// return if it was appended. Uses linear search, ~N time.
function AppendUnique(
var A : TIntArrayN;
Value : Integer
) : Boolean;
// Delete the element with a given Index from A
procedure DeleteIndex(
var A : TIntArrayN;
Index : Integer);
overload;
procedure DeleteIndex(
var A : TRealArrayN;
Index : Integer);
overload;
// Delete all the elements with a given Value from A.
procedure DeleteValue(
var A : TIntArray;
Value : Integer);
overload;
procedure DeleteValue(
var A : TIntArrayN;
Value : Integer);
overload;
{-----------------------<< Permutations >>------------------------------------------}
// Create NewData by permuting Data according to Perm
procedure Permute(
var NewData : TIntArray;
const Data,
Perm : TIntArray);
overload;
// Permute Data according to Perm
procedure Permute(
var Data : TIntArray;
const Perm : TIntArray);
overload;
// Return the Inverse permutation of A: A[Inverse[X]] = X.
procedure InvertPerm(
var Inverse : TIntArray;
const A : array of Integer);
overload;
// Invert permutation A
procedure InvertPerm(
var A : TIntArray);
overload;
{-----------------------<< Search >>------------------------------------------------}
// Return the result of binary search in the [Left, Right] section of array A sorted
// in ascending order. If there are multiple occurences of Value in the array, index
// of any of them may be returned. If the Value is not found, closest greater /
// lesser element is returned in case of positive / negative TieBreak respectively.
// It is possible to specify Left = -1, TieBreak = Negative or Right = Length(A),
// TieBreak = Positive so these out of bounds indices are returned if the Value is
// lesser or greater than any array element.
function BinarySearch(
const A : TRealArray;
Left, Right : Integer;
Value : Real;
TieBreak : Integer
) : Integer;
overload;
function BinarySearch(
const A : TRealArrayN;
Left, Right : Integer;
Value : Real;
TieBreak : Integer
) : Integer;
overload;
// If A contains Value, return Success and Index of its fisrt occurence,
// Fail and -1 otherwise
function FindValue(
var Index : Integer;
const A : TIntArray;
Value : Integer
) : Boolean;
overload;
function FindValue(
var Index : Integer;
const A : TIntArrayN;
Value : Integer
) : Boolean;
overload;
// Return whether A contains Value
function InArray(
const A : TIntArray;
Value : Integer
) : Boolean;
overload;
function InArray(
const A : TIntArrayN;
Value : Integer
) : Boolean;
overload;
// Return Marked array in which 1s indicate the occurence of Value in A and the
// rest of the elements are 0
procedure MarkValue(
var Marked : TIntArray;
const A : TIntArray;
Value : Integer);
// Count the number of occurences of Value in A
function ValueCount(
const A : TIntArray;
Value : Integer
) : Integer;
// Return the index of minimal element of A, break ties randomly
function RandMinIndex(
const A : array of Real
) : Integer;
// Return the index of maximal element of A, break ties randomly
function RandMaxIndex(
const A : array of Real
) : Integer;
{-----------------------<< 2D arrays >>---------------------------------------------}
// A := B
procedure AssignArray2D(
var A : TRealArray2D;
const B : TRealArray2D);
// Initialize 2D array
procedure InitArray2D(
var A : TIntArray2D;
Nx, Ny : Integer;
Value : Integer);
// Transpose B
procedure Transpose(
var A : TRealArray2D;
const B : TRealArray2D);
// Convert A to its Scanline representation
procedure ToScanline(
var Scanline : TRealArray;
const A : TRealArray2D);
{-----------------------<< Load, Save >>--------------------------------------------}
// Load A from a text file located at Path
function LoadFromText(
var A : TRealArrayN;
const Path : AnsiString
) : Boolean;
overload;
function LoadFromText(
var A : TRealArray;
const Path : AnsiString
) : Boolean;
overload;
function LoadFromText(
var A : TIntArray;
const Path : AnsiString
) : Boolean;
overload;
// Save A to a text file located at Path
function SaveToText(
const Path : AnsiString;
const A : TRealArray
) : Boolean;
overload;
function SaveToText(
const Path : AnsiString;
const A : TIntArray
) : Boolean;
overload;
// Save A to a file located at Path
function SaveToFile(
const Path : AnsiString;
const A : TRealArray
) : Boolean;
implementation //////////////////////////////////////////////////////////////////////
uses
InvSys,
Math; // MaxIntValue
{-----------------------<< Initialization >>----------------------------------------}
// Initialize A with Len elements
procedure InitArrayN(
var A : TIntArrayN;
Len : Integer = 0);
overload;
begin
A.N := Len;
SetLength(A._, Len);
end;
procedure InitArrayN(
var A : TRealArrayN;
Len : Integer = 0);
overload;
begin
A.N := Len;
SetLength(A._, Len);
end;
// Initialize A with Len elements with a given Value
procedure InitArray(
var A : TBoolArray;
Len : Integer;
Value : Boolean);
overload;
var
i : Integer;
begin
SetLength(A, Len);
for i := 0 to Len - 1 do
A[i] := Value;
end;
procedure InitArray(
var A : TIntArray;
Len : Integer;
Value : Integer);
overload;
var
i : Integer;
begin
SetLength(A, Len);
for i := 0 to Len - 1 do
A[i] := Value;
end;
procedure InitArray(
var A : TRealArray;
Len : Integer;
Value : Real);
overload;
var
i : Integer;
begin
SetLength(A, Len);
for i := 0 to Len - 1 do
A[i] := Value;
end;
// Fill A with sequential integers starting from Base
procedure SequentialFill(
var A : array of Integer;
Base : Integer);
overload;
var
i : Integer;
begin
for i := 0 to Length(A) - 1 do
A[i] := Base + i;
end;
// Return array of length N filled with sequential integers starting from Base
procedure SequentialFill(
var A : TIntArray;
N : Integer;
Base : Integer);
overload;
begin
SetLength(A, N);
SequentialFill(A, Base);
end;
procedure SequentialFill(
var A : TIntArrayN;
N : Integer;
Base : Integer);
overload;
begin
A.N := N;
SequentialFill(A._, N, Base);
end;
{-----------------------<< Resizing >>----------------------------------------------}
// Resize A to NewLen, fill new elements with Value
procedure ExtendArray(
var A : TIntArray;
NewLen : Integer;
Value : Integer);
overload;
var
i, OldLen : Integer;
begin
OldLen := Length(A);
SetLength(A, NewLen);
for i := OldLen to NewLen - 1 do
A[i] := Value;
end;
procedure ExtendArray(
var A : TRealArray;
NewLen : Integer;
Value : Real);
overload;
var
i, OldLen : Integer;
begin
OldLen := Length(A);
SetLength(A, NewLen);
for i := OldLen to NewLen - 1 do
A[i] := Value;
end;
procedure ExtendArray(
var A : TBoolArray;
NewLen : Integer;
Value : Boolean);
overload;
var
i, OldLen : Integer;
begin
OldLen := Length(A);
SetLength(A, NewLen);
for i := OldLen to NewLen - 1 do
A[i] := Value;
end;
// Set the length of A to its true value
procedure SetTrueLength(
var A : TIntArrayN);
overload;
begin
SetLength(A._, A.N);
end;
procedure SetTrueLength(
var A : TRealArrayN);
overload;
begin
SetLength(A._, A.N);
end;
{-----------------------<< Conversion >>--------------------------------------------}
// Convert integer array A into real array B of length Len
procedure ConvertToReal(
var B : TRealArray;
const A : TIntArray;
Len : Integer);
overload;
var
i : Integer;
begin
SetLength(B, Len);
for i := 0 to Len - 1 do
B[i] := A[i];
end;
// Convert integer array A into real array B
procedure ConvertToReal(
var B : TRealArray;
const A : TIntArray);
overload;
begin
ConvertToReal(B, A, Length(A));
end;
procedure ConvertToReal(
var B : TRealArrayN;
const A : TIntArrayN);
overload;
begin
B.N := A.N;
ConvertToReal(B._, A._, A.N);
end;
{-----------------------<< Element swapping and reversal >>-------------------------}
// Swap i-th and j-th elements of A
procedure Swap(
var A : TRealArrayN;
i, j : Integer);
overload;
var
Temp : Real;
begin
Temp := A._[i];
A._[i] := A._[j];
A._[j] := Temp;
end;
procedure Swap(
var A : TRealArray;
i, j : Integer);
overload;
var
Temp : Real;
begin
Temp := A[i];
A[i] := A[j];
A[j] := Temp;
end;
// Reverse [i .. j] section of A. If i >= j, A is left unchanged.
procedure Reverse(
var A : array of Integer;
i, j : Integer);
begin
while i < j do
begin
Swap(A[i], A[j]);
Inc(i);
Dec(j);
end;
end;
{-----------------------<< Arithmetics >>-------------------------------------------}
// Add Value to the elements of A
procedure ArrayAdd(
var A : TRealArray;
Value : Real);
var
i : Integer;
begin
for i := 0 to Length(A) - 1 do
A[i] := A[i] + Value;
end;
// Substract Value from the elements of A
procedure ArraySub(
var A : TRealArray;
Value : Real);
begin
ArrayAdd(A, -Value);
end;
// Multiply the elements of A by Value
procedure ArrayMul(
var A : TRealArray;
Value : Real);
var
i : Integer;
begin
for i := 0 to Length(A) - 1 do
A[i] := A[i] * Value;
end;
// Divide the elements of A by Value
procedure ArrayDiv(
var A : TRealArray;
Value : Real);
begin
ArrayMul(A, 1 / Value);
end;
// Add B * C to A
procedure ArrayMulAdd(
var A : TRealArray;
const B : TRealArray;
C : Real);
var
i : Integer;
begin
Assert(Length(A) = Length(B));
for i := 0 to Length(A) - 1 do
A[i] := A[i] + B[i] * C;
end;
// The dot product between A and B
function DotProduct(
var A, B : TRealArray
) : Real;
var
i : Integer;
begin
Assert(Length(A) = Length(B));
Result := 0;
for i := 0 to Length(A) - 1 do
Result := Result + A[i] * B[i];
end;
// The Euclidean distance between A and B
function DistanceL2(
const A, B : TRealArray
) : Real;
var
i : Integer;
Sum : Real;
begin
Assert(Length(A) = Length(B));
Sum := 0;
for i := 0 to Length(A) - 1 do
Sum := Sum + Sqr(A[i] - B[i]);
Result := Sqrt(Sum);
end;
{-----------------------<< Element addition and removal >>---------------------------}
// Append Value to A
procedure Append(
var A : TIntArrayN;
Value : Integer);
overload;
begin
with A do
begin
Inc(N);
if N > Length(A._) then
SetLength(A._, 2 * N);
A._[N - 1] := Value;
end;
end;
procedure Append(
var A : TRealArrayN;
Value : Real);
overload;
begin
with A do
begin
Inc(N);
if N > Length(A._) then
SetLength(A._, 2 * N);
A._[N - 1] := Value;
end;
end;
// Append B to A
procedure AppendArray(
var A : TRealArray;
const B : TRealArray);
overload;
var
i, OldLenA,
LenB : Integer;
begin
OldLenA := Length(A);
LenB := Length(B);
SetLength(A, OldLenA + LenB);
for i := 0 to LenB - 1 do
A[OldLenA + i] := B[i];
end;
procedure AppendArray(
var A : TIntArray;
const B : TIntArray);
overload;
var
i, OldLenA,
LenB : Integer;
begin
OldLenA := Length(A);
LenB := Length(B);
SetLength(A, OldLenA + LenB);
for i := 0 to LenB - 1 do
A[OldLenA + i] := B[i];
end;
// Concatenate A and B into C
procedure Concat(
var C : TRealArray;
const A, B : TRealArray);
overload;
begin
C := Copy(A);
AppendArray(C, B);
end;
procedure Concat(
var C : TIntArray;
const A, B : TIntArray);
overload;
begin
C := Copy(A);
AppendArray(C, B);
end;
// Append Value to A if it is distinct from all the elements,
// return if it was appended. Uses linear search, ~N time.
function AppendUnique(
var A : TIntArrayN;
Value : Integer
) : Boolean;
var
Unique : Boolean;
begin
Unique := not InArray(A, Value);
Result := Unique;
if Unique then
Append(A, Value);
end;
// Delete the element with a given Index from A
procedure DeleteIndex(
var A : TIntArrayN;
Index : Integer);
overload;
begin
with A do
begin
Assert(Index < N);
Dec(N);
A._[Index] := A._[N];
if Length(A._) > (2 * N) then
SetLength(A._, N);
end;
end;
procedure DeleteIndex(
var A : TRealArrayN;
Index : Integer);
overload;
begin
with A do
begin
Assert(Index < N);
Dec(N);
A._[Index] := A._[N];
if Length(A._) > (2 * N) then
SetLength(A._, N);
end;
end;
// Delete all the elements with a given Value from A.
procedure DeleteValue(
var A : TIntArray;
Value : Integer);
overload;
var
N, i : Integer;
begin
N := Length(A);
i := 0;
while i < N do
if A[i] = Value then
begin
Dec(N);
A[i] := A[N];
end
else
Inc(i);
SetLength(A, N);
end;
procedure DeleteValue(
var A : TIntArrayN;
Value : Integer);
overload;
begin
SetTrueLength(A);
DeleteValue(A._, Value);
A.N := Length(A._);
end;
{-----------------------<< Permutations >>------------------------------------------}
// Create NewData by permuting Data according to Perm
procedure Permute(
var NewData : TIntArray;
const Data,
Perm : TIntArray);
overload;
var