Why not throw in itertools.cycle while you're at it? ;-) pi = sum(4. / (1+x) * itertools.cycle((1,-1)).next() for x in range(0, 4 * n, 2))
I'd also be so tempted just to call the file 'approximate' (read it with extension...) Let's also not forget about integer division... 2008/10/23 bob gailer <[EMAIL PROTECTED]>: > Monte Milanuk wrote: > > Hello all, > > New guy here, so go easy on me ;) > > We save the whips and chains for the more hardened questers. Newcomers get > the feathers. > > > I'm starting to work my way through Python Programming by Zelle, and have > hit a bit of a wall on one of the programming exercises in Chapter 3 (#15 if > anyone has the book handy). > > What the question ask is: Write a program that approimates the value of pi > by summing the terms of this series: 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11+... > The program should ask the user for 'n', the number of terms to sum, and > then output the sum of the first 'n' terms of this series. > > Where I am running into problems is how to do the '-' & '+', depending on > the value of 'n'. i.e. if 'n' = 3, it's going to be a - & an +, if 'n' =5 > its going to be -, +, -, +, etc. How to make that work in terms of an > algorithm is making my head hurt (and its so early in the book yet... ;) ) > > There are many ways to handle this. Others have given some hints. > > The simplest IMHO is to set the range stride to 4 instead of 2 and then use > x += 4.0/i - 4.0/(i + 2). > > You could also use a multiplier (let's call it m) that alternates between 1 > and -1. Roughly: > > x = 0 > m = 1 > for in in range... > x += 4.0/i*m > m = -m > > For more generality and anticipating more complex algorithms: > > import operator > ops = (operator.add, operator.sub) > x = 0 > m = 0 > for in in range... > x = ops[m](x, 4.0/i) > m = 1-m > > And just for the heck of it you could write 2 for loops, each with a stride > of 4. The first would just add all the fractions to be added and the second > would add all the fractions to be subtracted, then combine them. Throwing in > the sum function and generator expressions: > pi = sum(4.0/i for i in range(1, n*2, 4)) - sum(4.0/i for i in range(3, n*2, > 4)) > > Applying sum and generator expressions to my original solution you get: > pi = sum(4.0/i - 4.0/(i + 2) for i in range(1, 4*n, 4)) > > Ah I can go on can't I? A lot more than you asked for! > > -- > Bob Gailer > Chapel Hill NC > 919-636-4239 > When we take the time to be aware of our feelings and > needs we have more satisfying interatctions with others. > Nonviolent Communication provides tools for this awareness. > As a coach and trainer I can assist you in learning this process. > What is YOUR biggest relationship challenge? > > _______________________________________________ > Tutor maillist - Tutor@python.org > http://mail.python.org/mailman/listinfo/tutor > > -- Richard "Roadie Rich" Lovely, part of the JNP|UK Famile www.theJNP.com _______________________________________________ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
