Mutually Referential Structures

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Mutually Referential Structures
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Outline

• Prerequisites
• Structures
• Complex Lists
• Recursion
• Objectives
• Collections that refer to each other
• Example family tree

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Background

• When we built the ancestral tree from the
  children upwards, it was easy because any child
  has only two parents
• However, when we build it downwards, parents may
  have any number of children
• What kind of structure does this suggest for the
  family tree node?

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Family Tree Nodes
person structure (refers to a people-list)
people-list a list of person structures
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Mutual References

• The person structure contains a people-list
• The items in the people-list are other person
  structures
• This circular definition process is called Mutual
  Reference
• Good abstraction suggests that there ought to be
  two functions
• One function (parent-offspring ) determines the
  number of offspring a parent has
• One function (list-offspring ) determines the
  number of offspring on a list

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Example Counting Offspring
Carl, 1926, 1978
Bettina, 1928, 1986
CarlBettina
Fred, 1949, alive
Eva, 1951, alive
Dave, 1948, 1997
Adam, 1946, alive
FredEva
Gustav, 1985, alive
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Program Design

• (parent-offspring person) conditions
• There is no children list -
• There is a children list -
• (list-offspring a-list) conditions
• List is empty -
• List not empty -

return 0 return (list-offspring )
return 0 return (parent-offspring (first) )
(list-offspring (rest))
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Code Used - 1

• (define-struct person (name dob dod children))
• children is a list of 0 or more person nodes
• dod (date of death) will be -1 if they are
  still alive
• parent-offspring person - number
• (define (parent-offspring here)
• (cond (empty? (person-children here)) 1
• else ( 1 (list-offspring
  (person-children here)))))
• list-offspring people-list - number
• (define (list-offspring here)
• (cond (empty? here) 0
• else ( (parent-offspring (first here))
• (list-offspring (rest here)))))

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Code Used - 2

• (define Gustav (make-person 'Gustav 1985 -1
  empty))
• (define FredEva (list Gustav))
• (define Fred (make-person 'Fred 1949 -1
  FredEva))
• (define Eva (make-person 'Eva 1951 -1 FredEva))
• (define Adam (make-person 'Adam 1946 -1 empty))
• (define Dave (make-person 'Dave 1948 1997 empty))
• (define CarlBettina (list Adam Dave Eva))
• (define Carl (make-person 'Carl 1926 1978
  CarlBettina))
• (define Bettina (make-person 'Bettina 1928 1986
  CarlBettina))

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Questions?
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Summary

• You should now know
• Collections that refer to each other
• Example family tree

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