ENGG1811 Computing for Engineers Week 10 Recursion, External Application Interfacing

Transcription

1 ENGG1811 Computing for Engineers Week 10 Recursion, External Application Interfacing ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 1

2 This Week Wednesday am: Will include discussion about assignment 2 Wednesday pm: Will include VBA exam revision examples References Recursion is covered quite nicely at not quite so well in Chapra Section 12.4 Recursion ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 2

3 Recursive Factorial Recursion is implemented through functions or subprograms calling themselves rather than another procedure Works provided the base case is handled and there are sufficient resources to sustain the calculation Function fact(n As Integer) As Long If n = 0 Then Else End If fact = 1 End Function fact = n * fact(n-1) ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 3

4 Tracing Factorial Trace the calculation as with other procedure calls fact(5) = 5 * fact(4) fact(4) = 4 * fact(3) fact(3) = 3 * fact(2) Each function waits for the recursive call to return fact(2) = 2 * fact(1) fact(1) = 1 * fact(0) fact(0) = 1 fact(1) = 1 * 1 = 1 fact(2) = 2 * 1 = 2 fact(4) = 4 * 6 = 24 fact(5) = 5 * 24 = 120 fact(3) = 3 * 2 = 6 Each function uses the value from the recursive call to calculate and return its factorial ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 4

5 Tail Recursion The Factorial function is an example of what s called tail recursion, where each call results in either no recursion (the base case), or one recursive call in an expression Tail recursion produces a sequence, called a stack of pending procedure calls Tail recursion can always be replaced by iteration, which generally consumes less resources ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 5

6 The Dark Side of Recursion Recursion often gets a bad name because implementing some algorithms directly produces horribly inefficient code that reevaluates things over and over. Classic case is the Fibonacci sequence*: Function BadFib(n As Integer) As Long If n <= 1 Then Else End If BadFib = 1 End Function BadFib = BadFib(n-1) + BadFib(n-2) * Regrettably, this is the solution to Chapra s misguided exercise 6, page 417 ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 6

7 tree has n levels Why BadFib is Bad Tracing calls on BadFib produces a tree rather than a simple stack of calls: F(3) is evaluated three times independently F(5) F(6) F(4) F(4) F(3) F(3) F(2) F(3) F(2) F(2) F(1) F(2) F(1) F(1) F(0) F(2) F(1) F(1) F(0) F(1) F(0) F(1) F(0) F(1) F(0) ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 7

8 Recursion in Nature Some things in nature contain elements that are smaller copies of themselves (this is called self-similarity). The branching patterns of creeks and rivers, ferns, cloud patterns and blood vessels are all examples. Anne Burns (Long Island University) has a nice paper on the web (ref below) describing general techniques for creating images such as this one. Nothing in the picture is real. ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 8

9 Fractals Although fractals are not necessarily recursive, they also show self-similarity. This is my favourite, a Newton-Raphson fractal: The picture shows part of the complex plane (Re ±1.6, Im ±1.2). Colours represent how many iterations the N-R algorithm* takes to find a cube root of 1 given that starting point. The dark blue dots are the three roots. Colour coding: blue=1 to 3 iterations, yellow=8, red=12, white=16+. * The Newton-Raphson algorithm for finding the roots of f (x) was described in the lecture on iteration (week 7, slide 8). It applies to complex as well as real functions. ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 9

10 Fractal Self-Similarity More detail is revealed (with the same repeated alien patterns) as the limits are adjusted. The final version s area is 0.06 x 0.04, and white now represents 21+ iterations. ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 10

11 Recursive Drawings We can do a tiny bit of this with the simple drawing tools available in VBA Draw a simple figure, then one or more smaller copies positioned relative to the larger one Copies are drawn recursively Recursion stops when the elements get small enough that the detail can t be seen Can t (easily) convert to iteration unless only one copy (e.g., picture of A- series paper sizes) Source: Wikipedia ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 11

12 pic: Sierpinski Gasket One of the simplest fractals is the Sierpinski gasket, which consists of a triangle with smaller inverted triangular cutouts. Each level removes (or overlays) a white triangle, then applies the same algorithm recursively to each of the surrounding black regions Number of black triangles at depth n is 3 n, but how many white inverted triangles are there? try the Java applet at ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 12

13 Recursive Drawing Procedure General approach: Sub DrawThing(x As Single, y As Single, size As Single) If size < MIN_SIZE Then End If Exit Sub draw figure at position (x, y) ' calculate position of first copy x1 = : y1 = DrawThing(x1, y1, size*scale_factor) ' same for other copies DrawThing(x1, y1, size*scale_factor) End Sub Constant describing the smallest effective size Constant describing the reduction in size for each copy ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 13

14 H-Trees The following is from the Princeton reference. Recursive graphics. Simple recursive drawing schemes can lead to pictures that are remarkably intricate. For example, an H-tree of order n is defined as follows: The base case is do nothing for n = 0. The reduction step is to draw, within the unit square three lines in the shape of the letter H [then] four H-trees of order n 1, one connected to each tip of the H with the additional provisos that the H-trees of order n 1 are centered in the four quadrants of the square, halved in size. Question: What size will the entire picture be compared to the first H? (This is related to Zeno s Paradox about Achilles and the Tortoise) ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 14

15 size H-Trees Apart from drawing a canvas, the algorithm for drawing an H-Tree centred on (x,y) is just (x+hsize,y-hsize) HTree(x,y,size) :- If size < MIN_SIZE Then Exit Sub End If hsize = size/2 ' half-size Draw horizontal line through (x,y) of length size Draw vertical lines through (x-hsize,y) and (x+hsize,y) HTree x-hsize, y+hsize, hsize ' bottom left HTree x-hsize, y-hsize, hsize ' top left HTree x+hsize, y-hsize, hsize ' top right HTree x+hsize, y+hsize, hsize ' bottom right (x,y) Use a separate subprogram to draw the lines, so you can apply the attributes consistently and once only hsize ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 15

16 H-Tree Demo See the demo workbook. To make it more useful as a learning tool, the following have been added a ClearDrawing subroutine a DrawCanvas subroutine (shape reference saved) a depth parameter, indicating how many calls are active colours, derived from the depth a visible stack, showing the depth in boxes timings, to demonstrate inefficiencies in VBA s collections Most important parts are the subprograms DrawHTree, HTree itself and DrawLine Depending on your processor, the picture will take a couple of minutes to draw, and the drawing rate will slow down as each line is added to the shape collection. ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 16

17 Office Interfacing All MS Office applications can start and interact with any other Office app For example, Excel can start Word and transfer data from a sheet to a table Word can start Outlook and send s (if an server is available) Excel can obtain data from an Access database (though this requires a lot of fiddling around) Other kinds of interface (if you re interested) Loading data into Excel from a table on a web page (but easier via the UI) Opening a browser window with a specified URL (which may include parameters) ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 17

18 Example: Creating a Word Doc ' Example adapted from Shepherd, Excel VBA Sub Test_Word() Dim objwordapp As Word.Application ' reference to Word (the app) Dim objworddoc As Word.Document ' ref to a newly created doc Set objwordapp = CreateObject("Word.Application") Set objworddoc = objwordapp.documents.add With objworddoc.sections(1).range.text = "My new Word Document".SaveAs "c:\mytest.doc" ' must use full pathname.close End With ' These are required to make sure MS Word shuts down completely Set objworddoc = Nothing Set objwordapp = Nothing End Sub ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 18

19 Object Reference Settings Unfortunately this fails to satisfy the compiler. The error points to Word.Application Select Tools References on the VBE menu, scroll to Microsoft Word 12 * Object Library and check. Press OK. * or largest value: 10=Office2002, 11=Office2003, 12=Office2007, 14 = Office2010 (there is no 13!) ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 19

20 Worked Examples 1 This is the end of the new VBA material (all together now, a big groan of disappointment) Some short worked examples of the kind that could be set for the final exam will follow. A bearing is an angle measured clockwise from North A back bearing is the bearing that is exactly opposite a given bearing. Bearings lie between 0 and 360 degrees. For example, if I'm sighting a landmark at that has a compass bearing of 110 degrees (slightly South of East), the back bearing is 290 degrees (slightly North of West). The back bearing is the bearing from the landmark back to me. Write a VBA function BackBearing that returns the back bearing for any given bearing, expressed in degrees between 0.0 (inclusive) and (exclusive). ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 20

21 Worked Examples 2 Write a VBA subprogram that candy-stripes the active worksheet. Candy-striping fills the background of every second row with a faint grey colour. Stop with the first empty cell in column A. Use the macro recorder to gather information about colouring rows, then work on the loop to apply the fills. ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 21

22 3 Worked Examples A worksheet contains rainfall data for Liverpool, NSW for the month of April 2009, downloaded from A domestic water tank is fed from the guttering of a house. Given the roof area, tank capacity and initial amount of water in the tank, complete the worksheet using a VBA procedure. Assume no water is drawn from the tank over the month. Analysis: how much water does 1mm of rain produce per m 2 of area? Named cells RoofArea and TankCapacity VBA fills in this column ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 22

23 Summary Recursion is a natural way to express some algorithms tail recursion can be replaced by iteration care must be taken to avoid recursion that re-evaluates the same thing over and over drawing recursive pictures may help in understanding how recursion works Sometimes you need to think creatively about solutions Office apps can create and manipulate documents and data through the use each other s object models expressed in VBA. ENGG1811 UNSW, CRICOS Provider No: 00098G W10 slide 23