Tree Data Structures: Family Trees

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Tree Data StructuresFamily Trees

• CMSC 11500
• Introduction to Computer Programming
• October 25, 2002

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Roadmap

• Recap Family trees
• Data definition Structures of structures
• Traversing tree data structures
• Collecting information from subtrees
• Recursive data, recursive traversal
• All-blue-eyed-ancestors
• Count-ancestors
• how-deep
• Summary

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Data Definition

• A family-tree is
• unknown, or
• (make-ft name eye-color mother father)
• where name, eye-color are symbols mother,father
  are family-tree
• (define-struct ft (name eye-color mother father)
• (make-ft Granny Blue unknown unknown)
• (make-ft John Brown
• (make-ft Mom Green () ())..)

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Things to do with Family Trees

• Find ancestor(s) with certain traits
• e.g. eye-color, born before some date
• Find all traits for all relatives
• Compute relations between individuals
• Determine if they are related by blood

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All-blue-eyed-ancestors

• Get all ancestors (not just first)
• Contract a-b-e-a family-tree -gt (listof symbol)
• Purpose Find all blue-eyed-ancestors
• Helper append
• (append (a b c) (a b c)) -gt (a b c a b c)
• (define (append list1 list2)
• (cond ((null? list1) list2)
• (else (cons (car list1) (append (cdr
  list1) list2)))

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All-blue-eyed-ancestors
(define (a-b-e-a aft) (cond
((eq? unknown aft) ())
((ft? aft)
(if (eq? (ft-eye-color aft) blue)
(cons (ft-name aft)
(append (a-b-e-a (ft-mother aft))
(a-b-e-a (ft-father aft))))
(append (a-b-e-a (ft-mother aft))
(a-b-e-a (ft-father aft))))))))
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All-blue-eyed-ancestors
(define (a-b-e-a aft) (cond
((eq? unknown aft) ())
(else (let ((in-parents
(append (a-b-e-a (ft-mother aft))
(a-b-e-a (ft-father aft)))))
(if (eq? (ft-eye-color aft) blue)
(cons (ft-name aft) in-parents) in-parents))))))

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Count-Ancestors

• Contract family-tree -gt number
• Purpose To compute number of ancestors of
  family-tree node

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Count-ancestors
(define (count-ancestors aft) (cond
((eq? unknown aft) 0)
((ft? aft)
( 1
(count-ancestors (ft-mother aft))
(count-ancestors (ft-father aft))))))
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Count-ancestors
(define (count-ancestors aft)
(count-ancestors-iter aft 0))
(define (count-ancestors-iter aft anc-count)
(cond
((eq? unknown aft) anc-count)
((ft? aft)
(
(count-ancestors-iter (ft-mother aft) (
anc-count 1)) (count-ancestors-iter (ft-father
aft) ( anc-count 1))))))
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How-deep

• Contract family-tree -gt number
• Purpose To compute depth to most remote ancestor

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How-deep
(define (how-deep aft) (cond
((eq? unknown aft) 0)
((ft? aft)
( 1 (max (how-deep (ft-mother aft)))
(how-deep (ft-father aft)))))
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Summary

• Family trees
• Tree-structured data
• Recursive data definition, recursive traversal
• recursive calls self-referential parts in
  d.d.
• Different functions -gt different combiners
• Count-ancestors
• How-deep , max
• All-blue-eyed-ancestors append

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Next Time

• Data structures and analysis
• Binary trees
• Sets Binary search trees