Lecture 4: Decomposition and abstraction through functions; introduction to recursion

# example code, Lecture 4, Fall 2008def sqrt(x):    ans = 0    if x >= 0:        while ans*ans < x: ans = ans + 1        if ans*ans != x:            print (x, 'if not a prefect square')            return None        else: return ans    else:        print(x, 'is a negative number')        return Nonedef f(x):    x = x + 1    return xdef solve(numLegs, numHeads):    for numChicks in range(0, numHeads + 1):        numPigs = numHeads - numChicks        totLegs = 4*numPigs + 2*numChicks        if totLegs == numLegs:            return [numPigs, numChicks]    return [None, None]def barnYard():    heads = int(input('Enter number of heads:'))    legs = int(input('Enter umber of legs:'))    pigs, chickens = solve(legs, heads)    if pigs == None:        print ('There is no solution')    else:        print ('Number of pigs', pigs)        print ('Number of chickens', chickens)def solve1(numLegs, numHeads):    for numSpiders in range(0, numHeads + 1):        for numChicks in range(0, numHeads - numSpiders + 1):            numPigs = numHeads - numChicks - numSpiders            totLegs = 4*numPigs + 2*numChicks + 8*numSpiders            if totLegs == numLegs:                return [numPigs, numChicks, numSpiders]    return [None, None, None]def barnYard1():    heads = int(input('Enter number of heads:'))    legs = int(input('Enter umber of legs:'))    pigs, chickens, spiders = solve1(legs, heads)    if pigs == None:        print ('There is no solution')    else:        print ('Number of pigs', pigs)        print ('Number of chickens', chickens)        print ('Number of spiders', spiders)def solve2(numLegs, numHeads):    solutionFound = False    for numSpiders in range(0, numHeads + 1):        for numChicks in range(0, numHeads - numSpiders + 1):            numPigs = numHeads - numChicks - numSpiders            totLegs = 4*numPigs + 2*numChicks + 8*numSpiders            if totLegs == numLegs:                print ('Number of pigs' + str(numPigs) + '.')                print ('Number of chickens' + str(numChicks) + '.')                print ('Number of spiders' + str(numSpiders))                solutionFound = True    if not solutionFound: print ('There is no solution')def isPalindrome(s):    if len(s) <= 1: return True    else: return s[0] == s[-1] and isPalindrome(s[1:-1])def isPalindrome1(s,indent):    print (indent, 'ispalindrome called with', s)    if len(s) <= 1:        print (indent, 'About to return True from base case')        return True    else:        ans = s[0] == s[-1] and isPalindrome1(s[1:-1], indent + indent)        print (indent, 'About to return', ans)        return ansdef fib(x):    if x == 0 or x == 1: return 1    else: return fib(x-1) + fib(x-2)