Programming in Lisp; Instructor: Alok Mehta Programming in Lisp Recursion, Data Abstraction, Mapping, Iteration

Programming in Lisp; Instructor: Alok Mehta2 Example: Both-ends  Define a procedure that gives both ends of a list > (setf itinerary ’(Albany NYC Chicago Seattle Anchorage)) > (both-ends itinerary) (ALBANY ANCHORAGE)  Three steps  Get first element > (first itinerary) ALBANY  Get last element > (first (last itinerary)) ANCHORAGE  Combine the two > (list (first itinerary) (first (last itinerary)))  Define procedure > (defun both-ends (l) (list (first l) (first (last l))))

Programming in Lisp; Instructor: Alok Mehta3 Error handling  Both-ends with error handling (defun both-ends (l) (if (listp l) (case (length l) (0 NIL) (1 (list (first l) (first l))) (t (list (first l) (first (last l))))) NIL))

Programming in Lisp; Instructor: Alok Mehta4 DoTimes  DOTIMES is Lisp’s way of doing iteration  C/C++ for (i=0; i<n; i++) { }  Lisp (dotimes (i n) )  First parameter is a list with three elements –counter variable (e.g. i) –number of times to iterate (e.g. n)  Counter variable (i) ranges from 0 to n-1  Optional return value can be specified (default is NIL) (dotimes (i n return_value) )

Programming in Lisp; Instructor: Alok Mehta5 Factorial  Definition of Factorial  C++ Implementation int factorial (int x) { int i,f; f = 1; for (i=1; i<=x; i++) f = f * i; return f; }  Lisp Implementation (defun factorial (n) (let ((f 1)) (dotimes (i n) (setf f (* f (+ i 1)))) f )  Tip: Compute factorial(100) using C/C++ and Lisp

Data Structures (Mehta)6 Recursively Calculating Factorial  Mathematical Definition of Factorial  C/C++ Implementation long Factorial (long X) { if (X <= 1) return 1; else return X * Factorial(X-1); }  Lisp Implementation (defun recursive-factorial (x) (if (<= x 1) 1 (* x (recursive-factorial (- x 1)))))

Programming in Lisp; Instructor: Alok Mehta7 Recursive calls  Show recursion when calling (recursive-factorial 4) Begin (recursive-factorial 4) Since 4>1, evaluate 4 * (recursive-factorial 3) Begin (recursive-factorial 3) Since 3>1, evaluate 3 * (recursive-factorial 2) Begin (recursive-factorial 2) Since 2>1, evaluate 2*(recursive-factorial 1) Begin (recursive-factorial 1) Since 1<=1, return 1 End (recursive-factorial 1), returns 1 2 * (recursive-factorial 1) = 2 * 1 = 2 End (recursive-factorial 2), returns 2 3 * (recursive-factorial 2) = 3 * 2 = 6 End (recursive-factorial 3), returns 6 4 * (recursive-factorial 3) = 4 * 6 = 24 End (recursive-factorial 4), returns 24

Data Structures (Mehta)8 Fibonacci Numbers  Mathematical Definition of Fibonacci Numbers  Sequence X Fib(X)  Recursive Solution (defun fib (x) (cond ((= x 0) 0) ((= x 1) 1) (t (+ (fib (- x 1)) (fib (- x 2))))))

Programming in Lisp; Instructor: Alok Mehta9 Fib(6) Function calls

Programming in Lisp; Instructor: Alok Mehta10 Recursive Definition of Length  Length (defun mylength (l) (if (endp l) 0 (+ 1 (mylength (rest l)))))  Alternate definition (defun mylength2 (l) (mylength2-aux l 0)) (defun mylength2-aux (l count) (if (endp l) count (mylength2-aux l (+ count 1))))  Note  All recursive calls simply return the final value evaluated.  No additional computations

Programming in Lisp; Instructor: Alok Mehta11 Tail Recursion  Tail Recursion  The final expression of a function is a recursive call  No additional computations are done to that expression –That is, return value is JUST the result of the recursive call  Lisp handles tail recursion efficiently  Mylength is not tail recursive  Mylength2 is tail recursive  Example:  Write a function to produce N atoms with value ‘A’. > (produce-list-of-a 5) ; Example call (A A A A A)

Programming in Lisp; Instructor: Alok Mehta12 Produce-list-of-a  Using dotimes (defun produce-list-of-a (n) (let ((la NIL)) (dotimes (i n la) (push 'A la))))  Recursion, not tail recursive (defun produce-list-of-a (n) (if (= n 0) nil (cons 'A (produce-list-of-a (- n 1)))))  Recursion, with tail recursion (defun produce-list-of-a (n) (produce-list-of-a-aux n NIL)) (defun produce-list-of-a-aux (n list-so-far) (if (= n 0) list-so-far (produce-list-of-a-aux (- n 1) (cons 'A list-so-far))))

Programming in Lisp; Instructor: Alok Mehta13 Count-Atoms  Write function to count number of atoms in an expr (sqrt (+ (expt x 2) (expt y 2))) has eight atoms (defun count-atoms (l) (cond ((null l) 0) ((atom l) 1) (t (+ (count-atoms (first l)) (count-atoms (rest l))))))

Data Structures (Mehta)14 Tower of Hanoi  Three pegs, S(start), T(temp), E(end)  N disks  Goal: Move disks from peg S to peg E  Restriction: Larger disk can’t be placed on top of smaller disk STE

Programming in Lisp; Instructor: Alok Mehta15 Tower of Hanoi  Solution to Tower of Hanoi (defun hanoi-aux (n start end temp) (if (> n 1) (hanoi-aux (- n 1) start temp end)) (print (list start end)) (if (> n 1) (hanoi-aux (- n 1) temp end start))) (defun hanoi (n) (hanoi-aux n 'S 'E 'T))  Example Runs > (hanoi 2) (S T) (S E) (T E) NIL > (hanoi 3) (S E) (S T) (E T) (S E) (T S) (T E) (S E) NIL

Programming in Lisp; Instructor: Alok Mehta16 &Optional  Produce-list-of-a function(s) (defun produce-list-of-a (n) (produce-list-of-a-aux n NIL)) (defun produce-list-of-a-aux (n list-so-far) (if (= n 0) list-so-far (produce-list-of-a-aux (- n 1) (cons 'A list-so-far))))  Redefined with optional parameters (defun produce-list-of-a (n &optional list-so-far) (if (= n 0) list-so-far (produce-list-of-a (- n 1) (cons 'A list-so-far))))  Note: optional values are bound to NIL, by default

Programming in Lisp; Instructor: Alok Mehta17 Optional Parameters (cont)  Solution to Hanoi (defun hanoi-aux (n start end temp) (if (> n 1) (hanoi-aux (- n 1) start temp end)) (print (list start end)) (if (> n 1) (hanoi-aux (- n 1) temp end start))) (defun hanoi (n) (hanoi-aux n 'S 'E 'T))  Revised with optional parameters (defun hanoi (n &optional (start 'S) (end 'E) (temp 'T)) (if (> n 1) (hanoi (- n 1) start temp end)) (print (list start end)) (if (> n 1) (hanoi (- n 1) temp end start)))  Note: notice the syntax for initializing optional parameters

Programming in Lisp; Instructor: Alok Mehta18 &Rest  &Rest - Specifies a variable number of arguments  Example: Assume + only accepts 2 arguments. Define “Plus”, a function that adds an arbitrary number of arguments) > (plus 2 3) > (plus )  Solution (defun plus (arg1 &rest other_args) (plus-aux arg1 other_args)) (defun plus-aux (arg1 other_args) (if (null other_args) arg1 (plus-aux (+ arg1 (first other_args)) (rest other_args))))

Programming in Lisp; Instructor: Alok Mehta19 Key Parameters  KEYword parameter  Useful when function has MANY parameters  Most are tied to default values  Examples > (rotate-list '(a b c d e)) ; rotate one element right (E A B C D) > (rotate-list '(a b c d e) :direction 'left) (B C D E A) > (rotate-list '(a b c d e) :distance 2) (D E A B C) > (rotate-list '(a b c d e) :direction 'left :distance 2) (C D E A B)

Programming in Lisp; Instructor: Alok Mehta20 &Key  Use &key to define Key parameters (defun rotate-list (l &key (direction 'right) (distance 1)) (if (eq direction 'left) (rotate-list-left l distance) (rotate-list-right l distance))) (defun rotate-list-right (l n) (if (zerop n) l (rotate-list-right (append (last l) (butlast l)) (- n 1)))) (defun rotate-list-left (l n) (if (zerop n) l (rotate-list-right (append (rest l) (list (first l))) (- n 1))))

Programming in Lisp; Instructor: Alok Mehta21 &Aux  &Aux keyword is used as a shorthand for Let*  Produce-list-of-a using Let* (defun produce-list-of-a (n) (let* ((la NIL)) (dotimes (i n la) (push 'A la))))  Using &Aux (defun produce-list-of-a (n &aux (la NIL)) (dotimes (i n la) (push 'A la)))