On Fri, 03 Jul 2009 14:34:58 GMT, Alan G Isaac <alan.is...@gmail.com> wrote:
>On 7/3/2009 10:05 AM kj apparently wrote: === 8< === >2. >from scipy.optimize import bisect >def _binary_search(lo, hi, func, target, epsilon): > def f(x): return func(x) - target > return bisect(f, lo, high, xtol=epsilon) > >3. If you don't want to use SciPy (why?), have them >implement http://en.wikipedia.org/wiki/Bisection_method#Pseudo-code >to produce their own `bisect` function. Of course this isn't really pseudo-code, it's VB code with quite poor comments: 'Bisection Method 'Start loop Do While (abs(right - left) > 2*epsilon) 'Calculate midpoint of domain midpoint = (right + left) / 2 'Find f(midpoint) If ((f(left) * f(midpoint)) > 0) Then 'Throw away left half left = midpoint Else 'Throw away right half right = midpoint End If Loop Return (right + left) / 2 and even just throwing away the VB code and leaving the comments does not give a good algorithm: 'Bisection Method 'Start loop 'Calculate midpoint of domain 'Find f(midpoint) 'Throw away left half 'Throw away right half A much better approach to teaching introductory programming in any language at almost any level is to incorporate some "top down problem solving", including writing a method of solution (algorithm) in some reasonably well-defined pseudo-code that can be easily elaborated and translated into one's target language (and, peferably, some reasonable-sized subset of related languages). This pseudo-code should then become comments (or equivalent) for the students to convert to real code, as in: Algorithm bisect (f, left, right, epsilon): # Bisection Method to find a root of a real continuous function f(x): # Assume f(x) changes sign between f(left) and f(right) and # we want a value not further than epsilon from a real root. # Begin with the domain left...right. # While the absolute value of (left - right) exceeds 2*epsilon: # Calculate the midpoint, mid, of the domain. # If the product of f(left) and f(mid) is positive: # Set left to mid; # Otherwise: # Set right to mid. # Return the midpoint of left...right. === And adapting this approach to kj's case is straightforward. Of course, what consitutes a suitable vocabulary and syntax for an algorithm pseudo-code language depends upon the target language(s), the tastes of the instructor, and the point in the lesson or course. My choice is for python+COBOL (as above) initially, soon incorporating the usual arithmetic and relational operators (and how soon and how many at once depends upon the level of the students: for an introductory university/college course in Computer Science or equivalent, where everyone should have a reasonable background in mathemtics notation as a prerequisite, this should be very soon and quite fast), arrays and subscripting, etc. But if we were to write this algorithm or kj's in python-like pseudo-code it would already *be* python codeor very close to it--which is why we should teach intorductory programming in python. Very soon students would be writing algorithms that required very little elaboration to be programs. But without including suitable problem solving and psudo-code algorithm writing there will soon come a time or an example where students are trying to think in code instead of in their natural language and don't have the experience and repertoire to be able to do that well. I hope that's not too pedantic or AR? wayne >hth, >Alan Isaac -- http://mail.python.org/mailman/listinfo/python-list
