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4.12 Permutation manipulation module

137

ˆ ulong gdsl_perm

_inversions_ oun

( onst gdsl_perm_t

P)

Count the y les numberlinear to linear permutatiermutation.

.

inversions

umber into a linear p

gdsl_perm

_ y les_ oun (

st gdsl_perm_t P)

ˆ ulong gdsl_perm

y les oun

( onst gdsl_perm_t

P)

Count the y les numbanoniintoal anoni al permutation.

ˆ gdsl perm t gdsl

perm_set name (gdsl

perm_t P, onst har

ˆ

heNAME)namepreviousnexttpofermutationgdslgdslpermutationpermutationpermpermfromfromlinear.set elementsarlinearprevnextermutationermutation((gdslarray. perm. (gdsltt_P)perm_t

permthe

onst

gdslNEWGetSet

ˆ gdsl

t gdsl perm

to linear (gdsl_perm_t

Q, onst

P)

Conv rt a

al permutation to its linear form.

everse in anoni permutation.everse (gdsl_perm_t P)

Inverse in pla e

in erse (gdsl_perm_t P)

permutation.

ˆ gdsl_perm_t gdsl perm

randomize (gdsl_perm_t P)

Randomize pla ermutation.

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11:15:30 2006 for gdsl by Doxygen

138

gdsl Module Do umentation

ˆ elementgdsl elementermutationonst

gdsl_perm_apply_on_array (gdsl_-

.

Permutation manipulation module

139

.

.2

Enumeration Ty

e Do umentation

4.12.2.1

enum gdsl

perm

position_t

This

ype is for gdsl perm write_fun t.

Enumerator:

FIRST

When

t is

rst

posi-

GDSL PERM_POSITION_LAST

When

element is

at last

tion

De nition at li e 55 of le gdsl_perm.h.

.

.3

Fun tion

Do umentation

4.12NAMEComplexity:.ate3.a1anew.newgdslonstpermpermO(permulongutationN ) N. )gdsldata_strupermturealloof size( Nonstwi h namehar

isNAMEset to a, opy

Note:ofAlloCreate

140

gdsl Module Do umentation

Note:

alloPgdsln())to(pdestroy.perm139) t

PComplexitalso:ondition:Theustpermbey:autativalidO(

gdsl

Parameters:re

| |

See

4.12.3.3 gdsl

opy

40

perm_t gdsl_perm_ opy ( onst gdsl_perm_t P)

opy a perm

.

Create and returnutation opy of the permutation P.

Note:

Postarameters:re PThePComplexity:ondition:ondiTheust urpermutationbeeda: validO(permutation|Pgdsl| )to permopy.ustt.be deallo ated with gdsl_perm_free.

Returns:

a opy of P in ase of su ess.

NULL in ase of insu ient memory.

See also:

allo (p.

gdsl_perm_free(p.

139)

4.12 Perm

manipulation module

141

P ustutationbe valid gdsl_perm_t

re Theondition:ur ed string MUST NOT be freed.

Parameters:

:

ost ondi

utation to get the name from

P The

gdsl_perm_set_name()(p. 143)

Returns:

the name of the permutation P.

See also:

4.12.3.5 ulong gdsl perm_get_size ( onst gdsl_perm_t P)

Get the size of a permutation.

Note:

Complexity: O( 1 )

re ondition:

ust be a valid gdsl_perm_t

Parameters:

P

The permutation to get the size from.

gdslthealso:.3.6_umberpermulongonstofulonggdslgetelementselementpermINDIXof P get(noted)s()(parray(). elemen141)P )utation.(p. 142)( onst gdsl_perm_t P,

SeeReturns:4.12

| |

Get the (INDIX+1)-th element from a perm

.

Note:

y: O( 1 )

142

gdsl Module Do umentation

Parameters:

P The permutation to use.

INDIX The indix of the value to get.

Returns:

the value at the INDIX-th position in the permutation P.

See also:

size()(p. 141)

gdsl_perm_get_elements

array()(p. 142)

PComplexitthe.ondition:3.7arrayustgdslulongbeelementsy:avalidO(permgdsl1 )gdsloftapermPpermutationperm) datasget elements.

_array ( onst

PNote:Get4.re12

arameters:

from.

The permutation to get

Returns:

the values array of the permutation P.

See also:

g

t()(p. 141)

gdsl_perm_set_elements_array()(p. 145)

4.12.3.8 ulong gdsl_perm_

_inversions_ ount ( onst

gdsl

perm

t P)

C un the inversions number intolinearlinear permutation.

Note:

Parameters:re thePComplexity:ondition:TheustumberlinearbeofvalidO(permutationinversionsPlinear) gdslinto_usetheperm.lineart permutation P.

Returns:

| |

Permutation manipulation module

143

4.12.3.9

ulong gdsl_perm_linear_ y les_ ount ( onst

gdsl perm_t P)

Coun the y les number into a linear permutation.

Note:

Parameters:rethePComplexitondition:Theustumberlinearbey:ofvalidO(permanoniyPleslinearutation)altogdsltheto_uselinearperm._permutationt P.

Returns:

|

|

See also:

_ y les_ ount()(p. 143)

gdsl_perm_

4.12.3.10

gdsl_perm_ anoni al_ y les_ ount ( onst

Coun the yulongles umber into a anoni al permutation.

Note:

gdsl perm_ P)

Parameters:re thePComplexity:ondition:TheustumberbeanoniofvalidO(alyPpermutalesanoni)into altheiongdsltoanoniuseperm.al_permutationt P.

Returns:

|

|

See also:

gdsl_perm_linear_ y les_ ount()(p. 143)

4.12.3.11

gdsl_perm_ gdsl perm_set_name (gdsl_perm_t P,

previoThufnstaJupermnsharname22utation11:15:30ofNEWthe.2006permutationNAMEfor gdsl)byPDoxygento a opy of NEW_NAME.

GeneratedChangeSet the nametheon

144

gdsl Module Do umentation

Note:

re ondition:y: O( 1 )

Complexitust be a valid gdsl_perm_

Parameters:

P The permutation to ha ge the name

NEW NAME The new name of P

Returns:

the modi ed permutation in ase of su ess.

NULL in ase of insu ient memory.

See also:

gdsl_perm_get_name()(p. 140)

4.12.3.12

gdsl perm_t gdsl pe m linear next (gdsl_perm_t P)

Get the next permutation from a linear permutation.

The permutation P is modi ed to be ome the next permutation after P.

Note:

re Complexitondition:ust linearbey:validO(|Plinear| ) gdsl_perm_t &

SeeReturns:

| | >

Parameters:NULLthePalso:Thenextif permutationPisalreadypermutationtheafterlasttothemodifypermpermutationP. P. 1

gdsl_perm_linear_prev()(p. 144)

4.12.3.13

gdsl_perm_t gdsl_perm_linear prev (gdsl_perm_t P)

Get the previous permutat on from a linear permutation.

The permutation P is modi ed to be ome the previous permutation before P.

Note:

Complexity: O( |PGenerated| )

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4.12 Permutation manipulation module

145

re ondition:

Parameters:NULLthePalso:ThepreviousustiflinearbePisvalidpealreadypermutationlinearutationthegdslbeforerstto_modifypermutationpermthepermutationt&P. = 2P.

SeeReturns:

| | >

gdsl_perm_linear_next()(p. 144)

4.12.3.14

_

_ gdsl_perm_set_elements_array

Parameters:NULLtheARRAYP ThemodiinpermutationedaseThepermutatiVarraydoestonotfinitializevaluesdesigninasetoarrainitializeofvalidsupermutationessP. V. == P

Returns:

| |

| |

See also:

gdsl_perm_get_elements_ y()(p. 142)

(gdsl_perm_t

4.12.3.15

RESULT,

gdsl perm m

gdsl perm_ultiplyALPHA, onst

gdsl perm_onstBETA)

Multiply two ermutations.

BETA and puts the result

Compute the prod

of the permutations ALPHA

in RESULT witho

tmodifying

ALPHA and BETA.

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146

gdsl Module Do umentation

Note:

Pre RESULT,Complexity:ondition:ALPHAO(|RESULandBET| )A must be valids gdsl_perm_t &

==

|RESULT|

BETALPHAR SULALPHAThetheTheTheseresult==ondresultrstBETApermutationusedinofofthethemultipliprodu tationALPHAtheoftheproduxpermutationsBETAt

A and B.

Returns:Parameters:RESULT,|

|

|

|

4.12.3.16

_

gdsl

perm

linear to anoni al

(gdsl perm

Q, onst gdsl

perm_t P)

Convert thelinearnear permutation P to its anoni al form. The resulted anoni al

permutation is

permuta

to its anoni al form.

pla ed into Q without modifying P.

Note:

arameters:re PComplexity:ondition:& Q ust beO( valids|P| )

gdsl_perm_t &

P thePQ Thanonilinearanonial formpermutational formQofofthePusedpermutationtoomputePP.==its Qanoni& Pal!=formQ into Q

Returns:

| |

| |

See also:

gdsl_perm_ anoni al_to_linear()(p. 146)

linear

4.12.3.17

_

gdsl

perm

anoni al to

(gdsl_

Q, onst gdsl

perm_t P)

perm

to its linear form.

Convert theanononi al

permutation

P

its linear form. The resulted linear

permutation is pla ed into Q without mtodifying P.

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