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Saturday, January 29, 2011

Trace lambda in Scheme to display recursion tree

When doing recursions in Scheme programming sometime its useful to see the growth of the recursion tree for debugging or even to get an intuition about approaches to improve the algorithm like dynamic programming. Following is a pure recursive insertion sort, obviously not the efficient implementation, yet it illustrate the use of trace procedure.

(define insert (lambda (val sorted)
(if (null? sorted)
(list val)
(if (< val (car sorted))
(cons val sorted)
(cons (car sorted) (insert val (cdr sorted)))))))

(define sort (lambda (vals)
(if (null? vals)
vals
(insert (car vals) (sort (cdr vals))))))

(trace insert)
(trace sort)





(sort '(7 6 5 9 3 4 2 8))

|(sort (7 6 5 9 3 4 2 8))
| (sort (6 5 9 3 4 2 8))
| |(sort (5 9 3 4 2 8))
| | (sort (9 3 4 2 8))
| | |(sort (3 4 2 8))
| | | (sort (4 2 8))
| | | |(sort (2 8))
| | | | (sort (8))
| | | | |(sort ())
| | | | |()
| | | | (insert 8 ())
| | | | (8)
| | | |(insert 2 (8))
| | | |(2 8)
| | | (insert 4 (2 8))
| | | |(insert 4 (8))
| | | |(4 8)
| | | (2 4 8)
| | |(insert 3 (2 4 8))
| | | (insert 3 (4 8))
| | | (3 4 8)
| | |(2 3 4 8)
| | (insert 9 (2 3 4 8))
| | |(insert 9 (3 4 8))
| | | (insert 9 (4 8))
| | | |(insert 9 (8))
| | | | (insert 9 ())
| | | | (9)
| | | |(8 9)
| | | (4 8 9)
| | |(3 4 8 9)
| | (2 3 4 8 9)
| |(insert 5 (2 3 4 8 9))
| | (insert 5 (3 4 8 9))
| | |(insert 5 (4 8 9))
| | | (insert 5 (8 9))
| | | (5 8 9)
| | |(4 5 8 9)
| | (3 4 5 8 9)
| |(2 3 4 5 8 9)
| (insert 6 (2 3 4 5 8 9))
| |(insert 6 (3 4 5 8 9))
| | (insert 6 (4 5 8 9))
| | |(insert 6 (5 8 9))
| | | (insert 6 (8 9))
| | | (6 8 9)
| | |(5 6 8 9)
| | (4 5 6 8 9)
| |(3 4 5 6 8 9)
| (2 3 4 5 6 8 9)
|(insert 7 (2 3 4 5 6 8 9))
| (insert 7 (3 4 5 6 8 9))
| |(insert 7 (4 5 6 8 9))
| | (insert 7 (5 6 8 9))
| | |(insert 7 (6 8 9))
| | | (insert 7 (8 9))
| | | (7 8 9)
| | |(6 7 8 9)
| | (5 6 7 8 9)
| |(4 5 6 7 8 9)
| (3 4 5 6 7 8 9)
|(2 3 4 5 6 7 8 9)
(2 3 4 5 6 7 8 9)

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business brokerThe Merina Kingdom (ca. 1540–1897) was a pre-colonial south-eastern African state that dominated most of what is now Madagascar. It spread outward from Imerina, the central highlands region primarily inhabited by the Merina ethnic group with a modern and historic political capital at Antananarivo and a spiritual and former political capital at Ambohimanga.

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Since the 30 June 1997 release of the first novel Harry Potter and the Philosopher's Stone , the books have gained immense popularity, critical acclaim and commercial success worldwide.The series has also had some share of criticism, including concern for the increasingly dark tone. As of June 2011, the book series has sold about 450 million copies and has been translated into 67 languages, and the last four books have consecutively set records as the fastest-selling books in history.

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