MIT public class: Introduction to Computer science and programming Python Note 4 function decomposition abstraction and recursion

Lecture4:decomposition and abstraction through functions;introduction to recursion function decomposition abstraction and recursion

Functions function

• Block up into modules decomposition into modules
• Suppress detail ignoring details
• Create "New primitives" how to think about creating primitives
  W3school python functions

 #example code for finding Square roots before  x = 16  ans = 0  if  x >= 0 : while  ans* Ans < X:ans = ans + 1  print   "ans = ' , ans if  Ans*ans! = x: print  x, " is not a perfect square '  else : print  anselse :  Print  x,   

• def keyword
• Function_name (formal parameters) function name (formal parameter)
• return keyword
• None-special value

#example code for finding square roots def sqrt(x):  "" " Returns the square root of x, if X is a perfect square. Prints an error message and returns None otherwise "" "Ans =0  ifX >=0: whileAns*ans < X:ans = ans +1      ifAns*ans! = x:PrintX' is not a perfect square '          return None      Else:returnAnsElse:PrintX' is a negative number '        return None

Local binding does not affect global binding:
Local bindings (local variables) do not affect global bindings (variables):

def f(x): x=x+1return x>>>x=3>>>z = f(x) >>>print x3 >>>print z4

Farmyard Problem Farm issues:

• Heads, legs
• Numpig + Numchicken = 20 number of pigs + number of chickens = 20
• 4 *numpig + 2*numchicken = 56

 def solve(Numlegs, numheads):     forNumchicksinchRange0, Numheads +1): Numpigs = numheads-numchicks Totlegs =4*numpigs +2*numchicksifTotlegs = = Numlegs:return(Numpigs, Numchicks)return(None,None) def Barnyard():Heads = Int (Raw_input (' Enter number of heads: ')) legs = Int (Raw_input (' Enter number of legs: ')) pigs, chickens = solve (legs, heads)ifPigs = =None:Print ' There is no solution '    Else:Print ' Number of pigs: ', pigsPrint ' Number of chickens: ', chickens

The farmer also kept the spider:

 def solve1(Numlegs, numheads):     forNumspidersinchRange0, Numheads +1): forNumchicksinchRange0, Numheads-numspiders +1): Numpigs = numheads-numchicks-numspiders Totlegs =4*numpigs +2*numchicks +8*numspidersifTotlegs = = Numlegs:return(Numpigs, Numchicks, Numspiders)return(None,None,None) def barnYard1():Heads = Int (Raw_input (' Enter number of heads: ')) legs = Int (Raw_input (' Enter number of legs: ')) pigs, chickens, spiders = solve1 (legs, heads)ifPigs = =None:Print ' There is no solution '    Else:Print ' Number of pigs: ', pigsPrint ' Number of chickens: ', chickensPrint ' Number of spiders: ', spiders

Improved: Output all the solutions:

 def solve2(Numlegs, numheads):Solutionfound =False     forNumspidersinchRange0, Numheads +1): forNumchicksinchRange0, Numheads-numspiders +1): Numpigs = numheads-numchicks-numspiders Totlegs =4*numpigs +2*numchicks +8*numspidersifTotlegs = = Numlegs:Print ' Number of pigs: '+ STR (numpigs) +', ',Print ' Number of chickens: '+str (numchicks) +', ',Print ' Number of spiders: ', Numspiders solutionfound =True    if  notSolutionfound:Print ' There is no solution. '

Recursion recursion

• Base Case–break problem into simplest possible solution to break the problem down into the simplest solution
• Inductive step, or the recursive step induction, recursive steps: Break problem to a simpler version of the same problem and some other STE Ps

# string is palindrome eg. "ABCBA"  def   Ispalindrome   (s) :   "" "Returns True if S is a Palindrome and False otherwise "" " if  Len (s) <=     1 : return  true  else : return  s[0 ] = = S[-1 ] and  ispalindrome (S[1 :-< span class= "Hljs-number" >1 ])  

# 付波纳切fibonacci数列def fib(x):    """Return fibonacci of x, where x is a non-negative int"""    if0or1return1    elsereturn fib(x-1) + fib(x-2)

MIT public class: Introduction to Computer science and programming Python Note 4 function decomposition abstraction and recursion