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Functional Programming Techniques: Tail Recursion and Inductive Construction Examples

Learn basic techniques in functional programming, including tail recursion and inductive list construction, with examples like factorial and sum of numbers. Explore Quicksort implementation in both inductive and tail recursion.

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Functional Programming Techniques: Tail Recursion and Inductive Construction Examples

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  1. Creating Functional Programs Brad Vander Zanden

  2. Basic Techniques • Tail Recursion • Use continuation arguments if necessary • Akin to pre-processing a list • Inductive Construction • Akin to post-processing a list

  3. Factorial • Inductive Construction (define fact (lambda (n) (cond ((= n 0) 1) ((= n 1) 1) (#t (* n (fact (- n 1)))))))

  4. Factorial • Tail Recursion Construction (define fact (lambda (n) (letrec((factHelper (lambda (n productThusFar) (cond ((= n 0) productThusFar) ((= n 1) productThusFar) (#t (factHelper (- n 1) (* n productThusFar))))))) (factHelper n 1))))

  5. Sum of Numbers • Inductive Construction (define sumList (lambda (L) (cond ((null? L) 0) (#t (+ (car L) (sumList (cdr L)))))))

  6. Sum of Numbers • Tail Recursion Construction (define sumList (lambda (L) (letrec((sumListHelper (lambda (L sumThusFar) (cond ((null? L) sumThusFar) (#t (sumListHelper (cdr L) (+ (car L) sumThusFar))))))) (sumListHelper L 0))))

  7. Quicksort • Inductive Construction (define qsortPartition (lambda (pivot L) (if (null? L) (cons '() '()) (let* ((result (qsortPartition pivot (cdr L))) (lesserList (car result)) (greaterList (cdr result))) (if (< (car L) pivot) ; add the head of L to the lesserList (cons (cons (car L) lesserList) greaterList) ; add the head of L to the greaterList (cons lesserList (cons (car L) greaterList)))))))

  8. Quicksort • Tail Recursion Construction (define qsortPartition (lambda (pivot L L1 L2) (if (null? L) (cons L1 L2) ; return L1 and L2 once L is exhausted (let ((firstElement (car L))) (if (< firstElement pivot) ; add head of L to L1 and partition rest of L (qsortPartition pivot (cdr L) (cons firstElement L1) L2) ; add head of L to L2 and partition rest of L (qsortPartition pivot (cdr L) L1 (cons firstElement L2)))))))

  9. Quicksort • Either construction (define qsort (lambda (L) (if (null? L) L (let* ((result (qsortPartition (car L) (cdr L) '() '())) (lesserList (car result)) (greaterList (cdr result))) (append (qsortlesserList) (list (car L)) (qsortgreaterList))))))

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