Programs Developing for Family Trees
c. Kathi Fisler, 2001
Consider the following family tree:
Susan Pat Mike Tom Ann Mary Joe
Assuming we want to write programs to query who is in the tree or to count how many generations are in the tree, what data model could we use?
Consider the following family tree:
Susan Pat Mike Tom Ann Mary Joe
Need to represent: Names Info about people (name, father, mother) (Will ignore other info, like birthday, for now)
Consider the following family tree:
Susan Pat Mike Tom Ann Mary Joe
Need to represent: Names (use symbols) Info about people (name, father, mother) (use structures)
Data Model for Family Trees
How about: A family tree (ftree) is
(make-person symbol ftree ftree)
(define-struct person (name father mother)) [Try making a family tree with this definition]
Making Family Trees
A family tree (ftree) is (make-person symbol ftree ftree) (define-struct person (name father mother)) (make-person `Mary What goes (make-person `Joe ) here? (make-person `Ann (make-person `Tom ...) (make-person `Susan ...)))
Making Family Trees
Follow the data definition! A family tree (ftree) is Must use a (make-person symbol ftree ftree) make-person (define-struct person (name father mother)) (make-person `Mary What goes (make-person `Joe ) here? (make-person `Ann (make-person `Tom ...) (make-person `Susan ...)))
A Broken Family Tree Data Model
Definition requires each parent to be a whole person, with a father and mother (who are also make-persons ...) The definition doesn't allow finite trees! General rule: every recursive data definition needs at least one non-recursive case (ie, a case with no arrows or with a finite chain of arrows)
A New Data Model for Family Trees
A family tree (ftree) is either `unknown [notice this case has no arrows]
(make-person symbol ftree ftree)
(define-struct person (name father mother)) [Try making a family tree with this definition]
Sample Family Trees
`Hallie (make-person `Mary `unknown (make-person `Ann `unknown `unknown)) (make-person `Bernie (make-person `Fred (make-person `Bubba `unknown `unknown) `unknown)) (make-person `Lisa `unknown `unknown))
Programs on Family Trees
Suppose we want to write a program on family trees, but I don't tell you which one ... ;; ftree-func : ftree D ??? (define (ftree-func aftree) ...) How much of this program can you write based on the data definition? [Try it]
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) ...)
What kind of data definition does ftree have?
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [... ...] [... ...]))
What kind of data definition does ftree have? one based on (two) cases ...
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [... ...] [... ...]))
What questions differentiate the cases?
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) [(person? aftree) ...] ...]))
What questions differentiate the cases?
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) [(person? aftree) ...] ...]))
What other information is available in each case?
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) [(person? aftree) ...] ...]))
What other information is available in each case? none in the symbol? case
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) ...] [(person? aftree) (person-name aftree) ... (person-father aftree) ... (person-mother aftree) ...])) What other information is available in each case? selectors in the person? case
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) ...] [(person? aftree) (person-name aftree) ... (person-father aftree) ... (person-mother aftree) ...])) What about the arrows in the data definition?
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) ...] [(person? aftree) (person-name aftree) ... (ftree-func (person-father aftree))... (ftree-func (person-mother aftree)) ...])) What about the arrows in the data definition? add recursive calls
Template on Family Trees
;; ftree-func : ftree D ??? (define (ftree-func aftree) (cond [(symbol? aftree) ...] [(person? aftree) (person-name aftree) ... (ftree-func (person-father aftree))... (ftree-func (person-mother aftree)) ...])) This is the full template for programs over family trees
Practice Problems on Family Trees
;; count-generations : ftree D number ;; return the number of generations in a tree ;; in-family? : ftree name D boolean ;; determines whether name appears in tree
[try each in turn]
count-generations : Solution
;; count-gen : ftree D number ;; counts generations in a family tree (define (count-gen aftree) (cond [(symbol? aftree) 0] [(person? aftree) (+ 1 (max (count-gen (person-father aftree)) (count-gen (person-mother aftree))))])) [the blue text is what we added to the template]
in-family? : Solution
;; in-family? : ftree name Dboolean ;; determines whether name appears in tree (define (in-family? aftree aname) (cond [(symbol? aftree) false] [(person? aftree) (or (symbol=? (person-name aftree) aname) (in-family? (person-father aftree) aname) (in-family? (person-mother aftree) aname))]))
Augmenting the Model
Programmers often augment their initial data models as the problem evolves. We want to augment our family tree model with information on birth-year and eye-color How would you change the model?
Revised Model, Version 1
A family tree (ftree) is either
`unknown (make-person name number symbol ftree ftree)
(define-struct person (name year eye father mother))
Revised Model, Version 2
An info is a (make-info name number symbol) A family tree (ftree) is either
`unknown (make-person info ftree ftree)
(define-struct person (data father mother)) info (define-struct (name year eye))
Which Model is Better?
Model 1 is a little simpler, because it has fewer data definitions (and fewer arrows) Model 2 is more flexible, because we can add new info about a person without changing the data definition or template for people Model 2 is probably a better choice in the long run [develop a template for model 2]
Template on Revised Family Trees
;; ftree-func : ftree D??? (define (ftree-func aftree) (cond [(symbol? aftree) ... ] [(person? aftree) (info-func (person-data aftree)) ... (ftree-func (person-father aftree))... (ftree-func (person-mother aftree)) ...])) ;; info-func : info D??? (define (info-func an-info) (info-name an-info) ... (info-year an-info) ... (info-eye an-info) )
Notice we now have two template functions, because we have two complex data definitions
Template on Revised Family Trees
;; ftree-func : ftree D??? (define (ftree-func aftree) (cond [(symbol? aftree) ... ] [(person? aftree) (info-func (person-data aftree)) ... (ftree-func (person-father aftree))... (ftree-func (person-mother aftree)) ...])) ;; info-func : info D??? (define (info-func an-info) (info-name an-info) ... (info-year an-info) ... (info-eye an-info) )
Notice that the recursive calls match the arrows in the data definition! (3 arrows, 3 calls)
Templates become truly useful (even invaluable) when data definitions get long or refer to each other (ie, have many arrows crossing between them) We expect you to use them.
Practice Problems on Family Trees 2
;; count-blue-eyed : ftree D number return number of blue-eyed people in tree ;; has-old-and-blue? : ftree number D boolean ;; determines whether tree contains a blueeyed ;; person born before given year ;; gather-green-eyed : ftree D list[name] ;; construct list of names of green-eyed people [try each in turn] ;;
has-old-and-blue? : Solution
;; has-old-and-blue? : ftree num D boolean (define (has-old-and-blue? aftree yr) (cond [(symbol? aftree) false ] [(person? aftree) (or (old-and-blue? (person-data aftree) yr) (has-old-and-blue? (person-father aftree) yr) (has-old-and-blue? (person-mother aftree) yr)))])) ;; old-and-blue? : info number Dboolean ;; true if person has blue eyes and was born before given year (define (old-and-blue? an-info born-before) (and (< (info-year an-info) born-before) (symbol=? `blue (info-eye an-info))))
Descendant Family Trees
Current model is ancestor-based : each person refers to her parents. Hard to access information about someone's children Let's create a new model in which parents refer to their children instead of the other way around
Descendant Family Trees: Data Defn
A parent is a structure
(make-parent symbol number symbol list-ofchildren) (define-struct parent (name year eye children))
A list-of-children is either
empty, or (cons parent list-of-children)
[where do we need arrows?]
Descendant Family Trees: Data Defn
A parent is a structure
(make-parent symbol number symbol list-ofchildren) (define-struct parent (name year eye children))
A list-of-children is either
empty, or (cons parent list-of-children)
[try writing examples from this data defn]
Descendant Family Trees: Examples
(define Marypar (make-parent `Mary 1975 `blue empty)) (make-parent `Susan 1925 `green (cons (make-parent `Ann 1943 `blue (cons Marypar empty)) (cons (make-parent `Pat 1949 empty)
Descendant Family Trees: Data Defn
A parent is a structure
(make-parent symbol number symbol list-ofchildren) (define-struct parent (name year eye children))
A list-of-children is either
empty, or (cons parent list-of-children)
[try writ...