Problem of the Day  Rich old man tells his 2 children he will hold a race to decide who gets his fortune. SLOWEST  Winner is one who owns SLOWEST horse.  1 st two weeks, race is aimless mess, never to end  Missing their families, kids consult a wise man  Upon leaving the wise man, kids jump on horses  Race at top speed  Race at top speed to the city.  What did the wise man say?

Problem of the Day  Rich old man tells his 2 children he will hold a race to decide who gets his fortune. SLOWEST  Winner is one who owns SLOWEST horse.  1 st two weeks, race is aimless mess, never to end  Missing their families, kids consult a wise man  Upon leaving the wise man, kids jump on horses  Race at top speed  Race at top speed to the city.  What did the wise man say? ride the other's horse!  He told them to ride the other's horse!

CSC 212 – Data Structures

 All elements available when stored in a List  Without removing a thing can access all elements  Add element anywhere in the List  For existing location, set changes element in-place  List s implement Iterable interface  iterator() returns Iterator over elements  Instance of 2 nd class returned by this method  Iterable makes it easy to access elements  Use for-each to handle any Iterable instance List ADT

 But List s still differ in how they are organized  To use ArrayList need absolute index (an int )  Positions (references) used by NodeList  Ideally have ADT with both sets of methods  Could use both absolute & relative ordering  Conversion methods enable jumping back-and-forth Identical Access w/ Iterable?

 But List s still differ in how they are organized  To use ArrayList need absolute index (an int )  Positions (references) used by NodeList  Ideally have ADT with both sets of methods Identical Access w/ Iterable?

 But List s still differ in how they are organized  To use ArrayList need absolute index (an int )  Positions (references) used by NodeList  Ideally have ADT with both sets of methods Identical Access w/ Iterable?

 But List s still differ in how they are organized  To use ArrayList need absolute index (an int )  Positions (references) used by NodeList  Ideally have ADT with both sets of methods Identical Access w/ Iterable?

Sequence ADT  Combines D EQUE, I NDEX L IST, & P OSITION L IST  Includes all methods defined by these interfaces  Adds 2 methods to convert between systems  Get Position at index using atIndex(i)  indexOf(pos) returns index of a Position

Sequence ADT  Combines D EQUE, I NDEX L IST, & P OSITION L IST  Includes all methods defined by these interfaces  Adds 2 methods to convert between systems  Get Position at index using atIndex(i)  indexOf(pos) returns index of a Position

Sequence ADT  Combines D EQUE, I NDEX L IST, & P OSITION L IST  Includes all methods defined by these interfaces  Adds 2 methods to convert between systems  Get Position at index using atIndex(i)  indexOf(pos) returns index of a Position

Sequence ADT  Combines D EQUE, I NDEX L IST, & P OSITION L IST  Includes all methods defined by these interfaces  Adds 2 methods to convert between systems  Get Position at index using atIndex(i)  indexOf(pos) returns index of a Position

interface Sequence extends IndexList, PositionList, Deque { public Position atIndex(int r) throws BoundaryViolationException; public int indexOf(Position p) throws InvalidPositionException; }  As ADT, must be implementation independent  Specify Position okay, but not it's implementation array linked list  S EQUENCE class free to use array or linked list S EQUENCE Interface

 Actually used by all of Java’s List classes  Combines everything so far into one simple idea  Can serve as basis of S TACK, Q UEUE, or D EQUE  Small, simple databases built from Sequence s  Basic building block for many other structures  Many use S EQUENCE somewhere in implementation  Need to know how Position & index works  Use big-Oh costs to select which implementation Why Use a Sequence?

 Actually used by all of Java’s List classes  Combines everything so far into one simple idea  Can serve as basis of S TACK, Q UEUE, or D EQUE  Small, simple databases built from Sequence s  Basic building block for many other structures  Many use S EQUENCE somewhere in implementation  Need to know how Position & index works  Use big-Oh costs select which implementation  Use big-Oh costs to select which implementation Why Use a Sequence?

 Easier & faster if nodes doubly-linked  Position -based methods come from N ODE L IST  To find indices, need to traverse Node s  Could use Node s via getNext() & getPrev()  next() & prev() if want Position traversal Linked list-based Sequence Node s List

Implementing atIndex(i) Node s List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

 Suppose call was: atIndex(3) i  3 trav Implementing atIndex(i) Node s List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

 Suppose call was: atIndex(3) i  3 trav Implementing atIndex(i) Node s List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

Node s  Suppose call was: atIndex(3) i  3 2 trav Implementing atIndex(i) List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

Node s  Suppose call was: atIndex(3) i  trav Implementing atIndex(i) List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

Node s  Suppose call was: atIndex(3) i  trav Implementing atIndex(i) List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

Position  Suppose call was: atIndex(3) i  trav Implementing atIndex(i) List Algorithm atIndex(i) if (i < 0) OR (i ≥ size()) then throw BoundaryViolationException fi

Node s  Suppose call was: atIndex(3) i  trav Implementing atIndex(i) List Algorithm atIndex(i) if (i 0) do trav  next(trav) i-- endwhile return trav

Array-based Sequence  Based on IndexList  Use and resize array  Easy to implement  Store elements in array S 0123 N-1 List

Array-based Sequence S 0123 N-1 List

Array-based Sequence  Array of Position s  Can be used in methods  Position contains:  Element  Index in array  No next or prev links  Instead use the index  Update index when Position shifted 0123 S 0123 N-1 List Position

Array-based Sequence Algorithm next(pos) if (pos == S[size()-1]) then throw BoundaryViolation… else idx  pos.getIndex() return S[idx+1] fi end 0123 S 0123 N-1 List Position

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ 012 S 0123 N-1 List Position

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ 013 S 0123 N-1 List Position

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ 023 S 0123 N-1 List Position

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ 123 S 0123 N-1 List Position

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ 123 S 0123 N-1 List Position 0

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ for i  size() downto 1 do S[i]  S[i-1] S[i].setIndex(i) endfor S[0]  new Node(0, e) size++ end 123 S 0123 N-1 List Position 0

Array-based Sequence Algorithm addFirst(e) /* Resize array if needed */ for i  size() downto 1 do S[i]  S[i-1] S[i].setIndex(i) endfor S[0]  new Node(0, e) size++ end 123 S 0123 N-1 List Position 0

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