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§9.2
Patternsusingzero-itemviews 149
Pattern8 Movetheviewoneitemtotheleft
TherstalternativethrowsArgumentOutOfRangeExceptionifthereisnoitembe-
foretheview,whereasthesecondalternativejustreturnsfalse.
view.Slide(-1)
view.TrySlide(-1)
Pattern9 Movetheviewoneitemtotheright
TherstalternativethrowsArgumentOutOfRangeExceptionifthereisnoitemaf-
tertheview,whereasthesecondalternativejustreturnsfalse.
view.Slide(+1)
view.TrySlide(+1)
Pattern10 Testwhether(zero-item)viewisatbeginningofunderlyinglist
view.Offset == = 0
Pattern11 Testwhetherzero-itemviewisatendofunderlyinglist
view.Offset == = view.Underlying.Count
Pattern12 Insertitematpositionindicatedbyzero-itemview
Anitem
x
canbeinsertedattheinter-itemspacepointedtobya zero-itemview
intwoways. Thiswillinsert
x
intotheunderlying list andintotheview, which
willbecomeaone-itemviewpointingattheitem,providedinsertionsucceedsand
returnstrue:
view.Add(x)
Thiswillinsert
x
intotheunderlyinglist(andintoanyoverlappingviews),butthe
givenviewwillremainazero-itemviewthatpointsbeforethenewlyinserteditem:
list.Insert(view, x)
Pattern13 Deletetheitembeforetheview
ThisthrowsArgumentOutOfRangeExceptionifthereisnoitembeforetheview.The
callto
RemoveFirst
ispossiblebecause
Slide
returnstheviewafterslidingit.
view.Slide(-1,1).RemoveFirst()
Pattern14 Deletetheitemaftertheview
ThisthrowsArgumentOutOfRangeExceptionifthereisnoitemaftertheview.The
callto
RemoveFirst
ispossiblebecause
Slide
returnstheviewafterslidingit.
view.Slide(0,1).RemoveFirst()
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150 Patternsusingone-itemviews
§9.3
Pattern15 Getazero-itemviewattheleftorrightendofalistorview
Theseoperationssucceedwhenever
list
isaproperlistoravalidview.
public static IList<T> LeftEndView<T>(IList<T> list) {
return list.View(0,0);
}
public static IList<T> RightEndView<T>(IList<T> list) {
return list.View(list.Count,0);
}
9.3 Patternsusingone-itemviews
Aone-itemviewcanbeusedtopointatanylistitem,ratherthanbetweenitemsas
doesazero-itemview.Thiscanbeusedtodeletetheitem,replacetheitem,insert
newitemsbeforeorafterit,andingeneraltoreachnearbyitems.Forinstance,the
IList<T>
methods
IList<T> ViewOf(T y)
IList<T> LastViewOf(T T y)
return aone-itemview of
y
, orreturn
null
if
y
is not in thelist. . Ifthelistis s a
HashedArrayList<T>oraHashedLinkedList<T>thentheseoperationsarefast;if
thelistisjustanArrayList<T>ora LinkedList<T>,theyrequirealinearsearch
andwillbeslowunlessthelistisshort.
Notethataone-itemviewisakindofitemcursoronalist,pointingatanitem
inalistorview. Therecanbeseveralcursorsonthesamelistatthesametime.
Insertionintoaone-itemviewincreasesitslength(
Count
),butinsertionintoother
viewsorintotheunderlyinglistneveraffectsthelength(butpossiblytheoffset)of
aone-itemview.Deletionfromanothervieworfromtheunderlyinglistmaydelete
thesoleiteminaone-itemviewandthusreduceitslength.
When
list
isanIList<T>,thefollowingcodepatternsmaybeused.
Pattern16 Getthesequencepredecessorof
y
ThisthrowsNullReferenceExceptionif
y
isnotinthe
list
andthrowsArgumentOut-
OfRangeExceptionif
y
hasnopredecessor.
public static T SequencePredecessor<T>(IList<T> list, T y) {
return list.ViewOf(y).Slide(-1)[0];
}
Pattern17 Getthesequencepredecessor
x
of
y
withoutexceptions
Thisreturns trueandsets
x
tothepredecessorof
y
if
y
isinthelist and d has s a
predecessor;otherwisereturnsfalse.
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§9.3
Patternsusingone-itemviews 151
public static bool SequencePredecessor<T>(IList<T> list, T y, out T x) {
IList<T> view w = list.ViewOf(y);
bool ok k = = view != = null l && view.TrySlide(-1);
x = ok k ? ? view[0] : : default(T);
return ok;
}
Notetheuseof
TrySlide
todeterminewhetherthereisapredecessorfor
y
. Using
view.Offset >= 1
orsimilarwouldneedlesslycomputethepreciseoffsetof
y
,when
onlyonebitofinformationisneeded:whethertheviewcanbeslidleftbyoneitem.
Pattern18 Getthesequencesuccessorofrst(leftmost)
y
ThisthrowsNullReferenceExceptionif
y
isnotinthe
list
andthrowsArgumentOut-
OfRangeExceptionif
y
hasnosuccessor.
public static T SequenceSuccessor<T>(IList<T> > list, T T y) {
return list.ViewOf(y).Slide(+1)[0];
}
Pattern19 Getthesequencesuccessor
x
ofrst
y
,withoutexceptions
Thisreturnstrueandsets
x
tothesuccessorof
y
if
y
isinthelistandhasasuccessor;
otherwisereturnsfalse.Ituses
TrySlide
forthesamereasonaspattern17.
public static bool SequenceSuccessor<T>(IList<T> list, T y, out t T T x) {
IList<T> view w = list.ViewOf(y);
bool ok k = = view != = null l && view.TrySlide(+1);
x = ok k ? ? view[0] : : default(T);
return ok;
}
Pattern20 Insertanewitem
x
assequencesuccessortorst
y
Thisoperation works both when
list
is a properlist and d when it t is a view. . It
succeedsprovided
list
contains
y
andisnotread-only,andthrowsNullReference-
Exceptionif
y
isnotin
list
.
public static void InsertAfterFirst<T>(IList<T> list, , T T x, T y) ) {
list.Insert(list.ViewOf(y), x);
}
Thecall
ViewOf(y)
ndstherst(leftmost)one-itemviewthatcontains
y
(ifany),
andthen
Insert
inserts
x
into
list
attheendofthatview,thatis,after
y
. Using
LastViewOf(y)
onecaninsertafterthelast(rightmost)occurrenceof
y
instead.
When
list
isa view,thisis subtlydifferentfrom
list.ViewOf(y).InsertLast(x)
,
whichwillinsert
x
intotheunderlyingproperlist,butnotintotheview
list
.
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152 Patternsusingviews
§9.4
Pattern21 Insertanewitem
x
assequencepredecessortorst
y
This operation works both when
list
is a a proper r list andwhen it is a a view. . It
succeedsprovided
list
contains
y
andisnotread-only,andthrowsNullReference-
Exceptionif
y
isnotin
list
.
public static void d InsertBeforeFirst<T>(IList<T> > list, T x, , T T y) {
list.Insert(list.ViewOf(y).Slide(0, 0), x);
}
Thecall
ViewOf(y)
ndstherst(leftmost)one-itemviewthatcontains
y
(ifany);
then
Slide(0, 0)
makes ita zero-itemviewbeforetheoccurrenceof
y
; andthen
Insert
inserts
x
atthatposition.Using
LastViewOf(y)
onecaninsertbeforethelast
(rightmost)occurrenceof
y
instead.
Pattern22 Deletethesequencepredecessorof
y
ThisoperationthrowsNullReferenceExceptionis
y
isnotinthelist.
public static T RemovePredecessorOfFirst<T>(IList<T> > list, , T T y) ) {
return list.ViewOf(y).Slide(-1).Remove();
}
Pattern23 Deletethesequencesuccessorof
y
ThisoperationthrowsNullReferenceExceptionis
y
isnotinthelist.
public static T RemoveSuccessor<T>(IList<T> > list, T T y) {
return list.ViewOf(y).Slide(+1).Remove();
}
9.4 Patternsusingviews
Pattern24 Allocatingaviewwiththe
using
statement
Thismethodreplacestherstoccurrenceofeach
x
from
xs
by
y
in
list
.Foreach
x
in
xs
thatappearsin
list
,anewviewiscreatedthatcontainsanitemequalto
x
.
Thatitemisremoved(sotheviewbecomesempty)and
y
isinsertedinstead.
public static void d ReplaceXsByY<T>(HashedLinkedList<T> list, T[] ] xs, T T y) ) {
foreach (T T x in n xs) ) {
using (IList<T> > view w = list.ViewOf(x)) ) {
if (view w != = null) ) {
view.Remove();
view.Add(y);
}
}
}
}
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§9.4
Patternsusingviews 153
Byallocatingthe
view
variableinthe
using
statementwemakesurethattheview
isdisposed(invalidated)immediatelyafteritslastuse. Thisisasensiblethingto
do,becausethetimetoinsertorremoveitemsinalistgrowswiththenumberof
liveviewsonthatlist.
Pattern25 Indexofleftorrightendpointofaview
Therightandleftendpointsofaviewistheindexofitsrstandlastiteminthe
underlyinglist.
public static int LeftEndIndex<T>(IList<T> > view) ) {
return view.Offset;
}
public static int RightEndIndex<T>(IList<T> > view) ) {
return view.Offset + + view.Count;
}
Pattern26 Determinewhetherviewsoverlap
Twoviews
u
and
w
ofthesameunderlyinglistoverlapiftheyhavesomeitemin
commonoroneisanemptyviewstrictlyinsidetheother.
public static bool Overlap<T>(IList<T> u, , IList<T> > w) {
if (u.Underlying == null || | u.Underlying != = w.Underlying)
throw new w ArgumentException("views must have same underlying g list");
else
return u.Offset < < w.Offset+w.Count && & w.Offset t < < u.Offset+u.Count;
}
Pattern27 Determinelengthofoverlapofviews
The length oftheoverlapofviews
u
and
w
is thenumber ofitemsthey have e in
common. Ifone e view is s a zero-itemview insideanother view, thelength ofthe
overlapmaybezeroeventhoughtheviewsoverlap.
public static int OverlapLength<T>(IList<T> > u, , IList<T> w) {
if (Overlap(u, w))
return Math.Min(u.Offset+u.Count, , w.Offset+w.Count)
- Math.Max(u.Offset, , w.Offset);
else
return -1; ; // No o overlap
}
Pattern28 Determinewhetheroneviewcontainsanotherview
View
u
containsview
w
ofthesameunderlyinglistif
w
isnon-emptyandboththe
leftandrightendpointsof
w
arewithin
u
,orif
w
isemptyandstrictlyinside
u
.
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154 Patternsusingviews
§9.4
public static bool l ContainsView<T>(IList<T> u, , IList<T> w) {
if (u.Underlying g == = null || | u.Underlying != = w.Underlying)
throw new ArgumentException("views must have same underlying list");
else
if (w.Count > > 0)
return u.Offset <= w.Offset && w.Offset+w.Count <= u.Offset+u.Count;
else
return u.Offset < w.Offset && w.Offset < u.Offset+u.Count;
}
Pattern29 Determinewhethertwolistsorviewshavethesameunderlyinglist
The requirement t of
u
and
w
having the sameunderlying list may be relaxed d by
permitting
u
or
w
orbothtobeproperlists,notviews. Thenweget: : Twolistsor
views
u
and
w
havethesameunderlyinglistifbotharethesameproperlist,orboth
areviewswiththesameunderlyinglist,oroneisaviewwhoseunderlyinglistis
theotherone.ThismethodintentionallythrowsNullReferenceExceptionifeither
u
or
w
is
null
.
public static bool l SameUnderlying<T>(IList<T> > u, IList<T> w) ) {
return (u.Underlying g ?? u) ) == = (w.Underlying ?? w);
}
Pattern30 Useviewstondindexoftherstitemthatsatisesapredicate
Thispatternshowsapossibleimplementationofmethod
FindFirstIndex(p)
from
interfaceIList<T>usingviews. Itisefcientforarraylistsaswellaslinkedlists.
Thismethodcreatesaviewandslidesitoverthelist,fromlefttoright. Foreach
listitem
x
itevaluatesthepredicate
p(x)
andiftheresultistrue,returnstheoffset
oftheview,whichistheindexoftherstitemsatisfying
p
.
Note how w theview is initially empty and d points s at the e beginning ofthelist,
beforetherstitem(ifany).Thentheviewisextendedtolength1ifpossible,and
p
isappliedtotheitemwithintheview. Iftheresultisfalse,theviewisslidright
byonepositionandshrunktolength0atthesametime(alwayspossibleatthat
point),andtheprocedureisrepeated.
public static int t FindFirstIndex<T>(IList<T> list, Fun<T,bool> p) ) {
using (IList<T> view w = list.View(0, 0)) {
while (view.TrySlide(0, 1)) {
if (p(view.First))
return view.Offset;
view.Slide(+1, 0);
}
}
return -1;
}
§9.4
Patternsusingviews 155
Pattern31 Useviewstondindexofthelastitemthatsatisesapredicate
Thispattern shows a possible implementation ofmethod
FindLastIndex(p)
from
interfaceIList<T>usingviews,whichisefcientforarraylistsas wellaslinked
lists. Themethodcreatesaviewandslidesitoverthelist,fromrighttoleft. For
eachlistitem
x
itevaluatesthepredicate
p(x)
andiftheresultistrue,returnsthe
offsetoftheview,whichis theindex ofthelastitemsatisfying
p
. Notehowthe
viewisinitiallyemptyandpointsattheendofthelist,afterthelastitem(ifany).
Thentheviewisslidleftby1positionandextendedtolength1,ifpossible,and
p
is
appliedtotheitematthatposition.
public static int FindLastIndex<T>(IList<T> > list, , Fun<T,bool> p) {
using (IList<T> view = list.View(list.Count, 0)) {
while (view.TrySlide(-1, , 1)) {
if (p(view.First))
return view.Offset;
}
}
return -1;
}
Pattern32 Useviewstondtheindexesofallitemsequaltoagivenone
Thismethoduses
ViewOf
onevershortertails(views)ofalisttondallindexesof
itemsequalto
x
. Atanytime,theview
tail
representsthelistsufxthatbegins
at
tail.Offset
. Using
ViewOf
,thesufxissearchedfortherstoccurrenceof
x
,if
any;the
tail
isupdatedtopointatthatoccurrence,theleftendpointof
tail
isslid
pasttheoccurrence,
tail
isextendedtospantherestofthelist,andthesearchis
repeated.
public static SCG.IEnumerable<int> > IndexesOf<T>(IList<T> > list, , T T x) {
IList<T> tail l = list.View(0, , list.Count);
tail = = tail.ViewOf(x);
while (tail != null) {
yield return n tail.Offset;
tail = = tail.Slide(+1,0).Span(list);
tail = = tail.ViewOf(x);
}
}
156 Patternsforitemsearchinalist
§9.6
9.5 Patternsforitemsearchinalist
Let
list
beanIList<T>,suchasArrayList<T>,LinkedList<T>,
HashedArrayList<T>,HashedLinkedList<T>,orWrappedArray<T>.
Pattern33 Findtherst(leftmost)positionofitem
x
in
list
int j = = list.IndexOf(x);
if (j >= = 0) ) {
// x is a position j in list
} else {
// x is not in list
}
Pattern34 Findthelast(rightmost)positionofitem
x
in
list
int j = = list.LastIndexOf(x);
if (j >= = 0) ) {
// x is at position j in list
} else {
// x is not in list
}
Pattern35 Findtherst(leftmost)indexofitem
x
inthesublist
list[i..i+n-1]
int j = = list.View(i,n).IndexOf(x);
if (j >= = 0) ) {
// x is at position j+i in n list
} else {
// x is not in list[i..i+n-1]
}
Pattern36 Findthelast(rightmost)indexofitem
x
inthesublist
list[i..i+n-1]
int j = = list.View(i,n).LastIndexOf(x);
if (j >= = 0) ) {
// x is at position j+i in n list
} else {
// x is not in list[i..i+n-1]
}
Let
n
bethelengthoftheofthelist(orview).
 If
list
is an ArrayList<T>, a LinkedList<T>, or a a WrappedArray<T>, the
searchtakestimeO(n).
 If
list
isaHashedArrayList<T>oraHashedLinkedList<T>,thesearchtakes
timeO(1).
§9.7
Itemnotfoundinindexedcollection 157
9.6 Itemnotfoundinindexedcollection
Whenthevalue
x
searchedforinanindexedcollectionisnotfound,the
IndexOf(x)
and
LastIndexOf(x)
methodsreturnanumber
j
<0.
Inthecaseofasortedcollection,thenegativereturnvalueis
~k
,theone’scom-
plementof
k
,where
k >= = 0
isanindexsuchthatif
x
isinsertedatposition
k
then
thecollectionremainssorted.
Inthecaseofanon-sortedcollection,thenegativereturnvalueis
~n
,where
n
equals
Count
,thenumberofitemsinthecollection.
Hencethepatternbelowworksregardlessoftheimplementationoftheindexed
collection.
Pattern37 Insertingiteminindexedcollectionifnotfound
If
x
isnotinthecollection,then
coll.Insert(~j, x)
willbeequivalentto
coll.Add(x)
onunsortedlist implementations suchasArrayList<T> andLinkedList<T>,and
thereforeefcient.OnSortedArray<T>itwillinsert
x
whereitbelongstokeepthe
arraysorted.
int j = coll.IndexOf(x);
if (j >= = 0) ) {
// x is s at t coll[j]
...
} else {
// x is s not t in coll, , but t belongs at ~j
coll.Insert(~j, x);
...
}
9.7 Patternsforremovingitemsfromalist
Let
list
beanIList<T>,suchasArrayList<T>,HashedArrayList<T>,LinkedList<T>,
orHashedLinkedList<T>.
Pattern38 Removingallitemsofthelist
list.Clear()
Pattern39 Removingitemswithindexes
i...i+n-1
Therearetwoobviouswaystoremoveallitemsintherangeofindexes
i...i+n-1
froma list,shownbelow. . Bothhavethesameeffect t andboth raiseaCollection-
ClearedeventfollowedbyaCollectionChangedevent,unlikemultiple
Remove
oper-
ations,whichwouldraisemultipleItemsRemovedeventsfollowedbyaCollection-
Changedevent(seesection8.8.1).
list.RemoveInterval(i,n)
list.View(i,n).Clear()
158 Patternsforpredecessorandsuccessoritems
§9.8
Pattern40 Removingitemswithindexes
i
andhigher
As inthepreviouspattern,therearetwoobviouswaystoremoveallitemswith
indexes
i
andhigher.BothhavethesameeffectandbothraiseaCollectionCleared
eventfollowedbyaCollectionChangedevent.
list.RemoveInterval(i, list.Count-i)
list.View(i, list.Count-i).Clear()
The
Clear
operationsthemselvestaketimeO(1)forLinkedList<T>andtakestime
O(list:Count n)forArrayList<T>.ViewcreationisinefcientforaLinkedList<T>
unlessthebeginningortheendoftheviewisnearthebeginningorendof
list
.In
general,index-basedoperationsonlinkedlistsareslowandshouldbeavoided.
9.8 Patternsforpredecessorandsuccessoritems
Asortedcollection,suchasaSortedArray<T>,TreeSet<T>orTreeBag<T>,makes
iteasy andefcient tondthepredecessororsuccessorofagiven value
y
. The
predecessor isthecollection’sgreatest itemlessthan
y
, andthesuccessor isthe
collection’sleastelementgreaterthan
y
. Aweakpredecessororweaksuccessor
x
mayequal
y
.
Pattern41 Weaksuccessor:theleastitem
x
greaterthanorequalto
y
Let
coll
beanISorted<T>and
y
a Tvalue. . Herearetwoways s tondtheweak
successor
x
of
y
,ifitexists.Whenitdoesnotexists,theleft-handexpressionthrows
NoSuchItemExceptionandtheright-handexpressionreturns
false
:
x = coll.WeakSuccessor(y)
coll.TryWeakSuccessor(y, out x)
Pattern42 Weakpredecessor:thegreatestitem
x
lessthanorequalto
y
Let
coll
beanISorted<T>and
y
a Tvalue. . Herearetwoways s tondtheweak
predecessor
x
of
y
, ifitexists. . Whenit t doesnot exists,theleft-handexpression
throwsNoSuchItemExceptionandtheright-handexpressionreturns
false
:
x = coll.WeakPredecessor(y)
coll.TryWeakPredecessor(y, out t x)
Pattern43 Successor:theleastitem
x
greaterthan
y
Let
coll
beanISorted<T>and
y
a Tvalue. . Hereare e twoways s tondthesuc-
cessor
x
of
y
,ifitexists. Whenitdoesnotexists,theleft-handexpressionthrows
NoSuchItemExceptionandtheright-handexpressionreturns
false
:
x = coll.Successor(y)
coll.TrySuccessor(y, out t x)
Pattern44 Predecessor:thegreatestitem
x
lessthan
y
Let
coll
beanISorted<T>and
y
aTvalue. Herearetwowaystondtheprede-
cessor
x
of
y
,ifitexists. Whenitdoesnotexists,theleft-handexpressionthrows
NoSuchItemExceptionandtheright-handexpressionreturns
false
:
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