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CS 341 Programming Language Design and Implementation

CS 341 Programming Language Design and Implementation. Administrative HW #5 is out ― due Monday, 2/17 @ 9pm Quiz #2? Also next Monday, 2/17 Switching back to F#... Programming day! Let's start with sorting…. Startup an F# environment , either will work: http://ideone.com Visual Studio

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CS 341 Programming Language Design and Implementation

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  1. CS 341 Programming Language Design and Implementation • Administrative • HW #5 is out ― due Monday, 2/17 @ 9pm • Quiz #2? Also next Monday, 2/17 • Switching back to F#... • Programming day! • Let's start with sorting… CS 341 -- 12 Feb 2014

  2. Startup an F# environment, either will work: • http://ideone.com • Visual Studio • Copy-paste timing code: • "Sorting.fs" • http://www.joehummel.net/uploads/cs341-sorting.fs • Take a minute to run & review code… • start with Main • creates 2 lists, sorts using built-in List.sort function CS 341 -- 12 Feb 2014

  3. Exercise 1 • Selection sort: • Algorithm: find min, move to front, sort the rest… • note that min(L) and remove(e, L) are defined for you • use ordinary (not tail) recursion, 4-5 lines of code… // // selection sort: // let rec selectionsort(L)= . . let Main argv = . . printfn "" runit("selection sort", selectionsort, list1) runit("selection sort", selectionsort, list2) CS 341 -- 12 Feb 2014

  4. Exercise 2 Hint: to split lists, use List.filter — like map, but keeps only those elements where function returns true. 7-8 lines of code… • Quicksort… • select first element as pivot • split remainder into two lists L1, L2: elements <= pivot, elements > pivot • sort L1 and L2 recursively • put pieces back together into a single list // // quicksort: // let rec quicksort(L)= . . let Main argv = . . printfn "" runit("quick sort", quicksort, list1) runit("quick sort", quicksort, list2) CS 341 -- 12 Feb 2014

  5. Timing… • Start to increase the size of the generated list… • 1,000 elements • 10,000 elements • 100,000 elements • 1,000,000 elements comment out call to selectionsort at this point :-) CS 341 -- 12 Feb 2014

  6. Why is quicksort so much slower? • It's not the recursive calls • the recursion is not that deep • It's the excessive list building • the @ operator is building new lists every time… • Solution? • merge sort using :: operator as much as possible… . . quicksort(left) @ [pivot] @ quicksort(right) element :: list // doesn't require constructing a new list: CS 341 -- 12 Feb 2014

  7. Tail recursion? • There was an earlier question about tail recursion: • Automatically, no… • "single-call" recursion (e.g. min) can be rewritten — using helper function and extra "accumulator" parameter • "multi-call" recursion (e.g. quicksort) is not easily rewritten • and rewrite requires use of a stack, so there's no benefit to the TR "Can all recursive functions be rewritten as tail-recursive?" CS 341 -- 12 Feb 2014

  8. Exercise 3 // // standard deviation of L = list of numbers: // // Hint 1: think higher-order // Hint 2: System.Math.Sqrt(…) // let stddev(L)= . . • Standard deviation: CS 341 -- 12 Feb 2014

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