Science Forums 2

[phillip1882]

were you able to get the practice problem? it should look something like this...

x = float(raw_input("what value would you like to square root? "))
a = 0
b = x
temp = x/2
while temp*temp < x-.001 or temp*temp > x+.001:
   print temp
   if temp*temp <x:
      a = temp
      temp = (a +b)/2
   else:
      b = temp
      temp = (a+b)/2
print temp

in lesson 2 we explored conditional statements. in lesson 3 we'll explore functions.
a function is basically a piece of code that you write when you want to reuse it.
for example, i could rewrite the sqrt code above to be...

def sqroot(x):
   a = 0
   b = x
   temp = x/2
   while temp*temp < x-.001 or temp*temp > x+.001:
   etc.

and replace the print x with return x. then if i saved it as mymath.py, i could later access it. for example...

import mymath
n = 10
val = mymath.sqroot(n)

val will now approximately be the square root of 10. this can be quite handy, and you can write functions to do pretty much anything. lets take a recursive example. a recursive function is a function which calls itself, until it reaches a terminating condition.

def fibonacci(a,b,n):
   if n ==0:
      return a
   elif n ==1:
      return b
   else:
      a =a+b
      b = a+b
      n= n-2
      val =fibonacci(a,b,n)
      return val

x = fibonacci(1,1,7)
print x

in case you can't guess, the above code produces a modified fibonacci sequence. in this particular case, you can pick any two start values, and go as high as you like, within reason. let's trace the recursive calls, just so you can see what this code is doing.
first, fib is called with parameters 1,1,and 7.
then a gets the value 1, b also 1, and n gets 7.
so it runs though the two checks for n, find them both false, then sets a to be 1+1 =2, b to be 2+1 = 3, and n to be 5. then it calls fib again with these parameters.
a = 2+3 = 5, b = 5+3 = 8, n = 3.
a = 5 +8 = 13, b = 13 +8 = 21, n = 1.
finally one of the terminating conditions is met. 21 gets returned up the path 3 times before finally becomes val, then val gets returned.
now would be a good time to go over global and local variables i think.
the names are pretty self descriptive, but basically a global variable is known to everything, whereas a local variable in only known to that particular function. lets do a quick example to display the difference.

def increment1():
   global x
   x = x+1
   return x

def increment2(y):
   y = y+1
   return y

x = 5
z = increment1()
print z, x

y = 5
z = increment2(y)
print z, y

at first it may seem like you want global variables all the time, but for recursive functions they can be very hard to deal with. (try declaring a and b global in the fib function and see what you get.) for most purposes you need the local version, but there are cases that crop up when global is needed. well that's it for this lesson.
two homework problems, write a recursive function that does factorials. (x *(x-1) *(x-2) etc down to 1.) found that one too easy? try a recursive function that does all permutations of 1, 2, 3, 4, 5, 6.