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Recursion-Data Structures-Lecture Slides, Slides of Data Structures and Algorithms

Amrita Vishwa VidyapeethamData Structures and Algorithms

This lecture was delivered by Prof. Sunil Bhedi at Amrita Vishwa Vidyapeetham for Data Structures. It includes: Recursion , Person , Drink , Define , Clear , Elegant , Code , Best , Processed

Typology: Slides

2011/2012

Uploaded on 07/20/2012

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30/09/04 1
Recursion
• When a predicate calls itself within its body we say
the clause is recursing
1) drinks(alan,juice).
2) likes(alan,coffee).
3) likes(heather,coffee).
4) likes(Person,Drink):-
drinks(Person,Drink).
5) likes(Person,Somebody):-
likes(Person,Drink),
likes(Somebody,Drink).
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30/09/04 1

Recursion

  • When a predicate calls itself within its body we say

the clause is recursing

1) drinks(alan,juice).

2) likes(alan,coffee).

3) likes(heather,coffee).

4) likes(Person,Drink):-

drinks(Person,Drink).

5) likes(Person,Somebody):-

likes(Person,Drink),

likes(Somebody,Drink).

30/09/04 2

Why use recursion?

  • It allows us to define very clear and elegant code.
    • Why repeat code when you can reuse existing code.
  • Relationships may be recursive

e.g. “X is my brother if X is my brother‟s brother.”

  • Data is represented recursively and best processed

iteratively.

  • Grammatical structures can contain themselves
  • Ordered data: each element requires the same processing
  • Allows Prolog to perform complex search of a

problem space without any dedicated algorithms.

30/09/04 4

Structure unification

  • 2 structures will unify if
    • the functors are the same,
    • they have the same number of components,
    • and all the components unify.

| ?- person(Nm,london,Age) = person(bob,london,48). Nm = bob, Age = 48? yes | ?- person(Someone,_,45) = person(harry,dundee,45). Someone = harry? yes

  • (A plain underscore „_‟ is not bound to any value. By using it you

are telling Prolog to ignore this argument and not report it.)

30/09/04 5

Structure unification (2)

  • A structure may also have another structure as a

component.

|?-addr(flat(4),street(‘Home Str.’),postcode(eh8_9lw))

= addr(flat(Z),Yy,postcode(Xxx)). Z = 4, Yy = street(‘Home Str.’), Xxx = eh8_9lw? yes

  • Unification of nested structures

works recursively:

  • first it unifies the entire structure,
  • then it tries to unify the nested structures.

Remember to close brackets!

Reported variables are ordered according to number of characters in the variable name.

30/09/04 7

Lists

  • A collection of ordered data.
  • Has zero or more elements enclosed by square

brackets („[ ]‟) and separated by commas („,‟).

[a]  a list with one element

[]  an empty list

1 2 3 1 2

[34,tom,[2,3]]  a list with 3 elements where the

3 rd^ element is a list of 2 elements.

  • Like any object, a list can be unified with a variable

|?- [Any, list, ‘of elements’] = X. X = [Any, list, ‘of elements’]? yes

30/09/04 8

List Unification

  • Two lists unify if they are the same length and all their

elements unify.

|?-[a,B,c,D]=[A,b,C,d]. |?-[(a+X),(Y+b)]=[(W+c),(d+b)].

A = a, W = a,

B = b, X = c,

C = c, Y = d?

D = d? yes

yes

|?- [[X,a]]=[b,Y]. |?-[[a],[B,c],[]]=[X,[b,c],Y].

no B = b,

X = [a], Y = []? yes

Length 1 Length 2

30/09/04 10

Head and Tail

|?-[a,b,c,d]=[Head|Tail]. |?-[a,b,c,d]=[X|[Y|Z]]. Head = a, X = a, Tail = [b,c,d]? Y = b, yes Z = [c,d]; yes

|?-[a] = [H|T]. |?-[a,b,c]=[W|[X|[Y|Z]]]. H = a, W = a, T = []; X = b, yes Y = c, Z = []? yes

|?-[] = [H|T]. |?-[a|[b|[c|[]]]]= List. no List = [a,b,c]? yes