1. def f(n): if (n == 0): return else: print(“*”) return f(n-1) f(3)

2. def f(x): if (x == 1): return x else: return(x + f(x-1)) print(f(4)) def f2(x): if (x == 1): return str(x) else: return(str(x) + f2(x-1)) print(f2(4))

3. def f(x): return(x + f(x-1)) print(f(4)) def f2(x): if (x == 1): return x else: return(x + f2(x+1)) print(f2(4)) def f3(x): if (x == 1): return x else: return(x + f3(x-2)) print(f3(4))

4. def f(x): if (x == 1): return x else: return(x + f(x-1)) print(f(4)) def f2(x): if (x == 1): return str(x) else: return(str(x) + f2(x-1)) print(f2(4)) Stack in memory f(4) = 4 + ?f(3)? f(3) = 3 + ?f(2)? f(2) = 2 + ?f(1)? f(1) = 1 __________________________ f2(4) = "4" + f2(3) f2(3) = "3" + f2(2) f2(2) = "2" + f2(1) f2(1) = "1"

5. def f3(x,y): if (y == 1): return (x) else: return(x * f3(x,y-1)) print(f3(3,3)) print(f3(2,4)) Memory Stack f3(3,3) = 3*f3(3,2) f3(3,2) = 3*f3(3,1) f3(3,1) = 3 f3(2,4) 2*f3(2,3) f3(2,3) = 2*f3(2,2) f3(2,2) = 2*f3(2,1) f3(2,1) = 2 27 9 16 8 4

6. def f5 (a): if (a <= 0): return(1) elif ((a%2) ==0): return (f5(a - 1)) else: return (a*f5(a-1)) print(f5(6)) print(f5(5)) print(f5(-1)) def f6(x): if (x <= 1): return str(x) else: return(f6(x-1) + str(x) ) print(f6(5)) def f7(a,b): if (b <= 0): return(a) elif((b%3)== 0): return(f7(a+1,b-1)) else: return(f7(a,b-1)) print(f7(0,13))

7. def listrec(x,ls): if x == len(ls): return(0) else: return(ls[x]+ listrec(x+1,ls)) listarr = [3,2,7,3,1] print(listrec(0,listarr)) def lr2(x,y,ls): if x == len(ls): return(y) elif (ls[x] > y): y=ls[x] return(lr2(x+1,y,ls)) else: return(lr2(x+1,y,ls)) listarr = [3,2,7,3,1] print(lr2(0,0,listarr))

8. def rec(a,x,y): if (x == len(a)): return 0 elif (a[x] in y): return 1 + rec(a,x+1,y) else: return rec(a, x+1, y) a = "catamaran" y = "aeiou" print(str(rec(a,0,y)))

9. def rec(a,x,y): if (x == len(a)): return "" elif (a[x] in y): return rec(a,x+1,y) else: return (a[x] + rec(a, x+1, y)) a = "catamaran" y = "aeiou" print(str(rec(a,0,y)))

10. def f2(lv,x,num,ct): if (x == len(lv)): return ct elif (lv[x] == num): return(f2(lv,x+1,num,ct+1)) else: return(f2(lv,x+1,num,ct)) listvar = [1,3,7,2,1,8,0,1,6,4,1,2,3,7] print (f2(listvar,0,1,0))

11. from random import * def sl(list,new): if len(list) == 1: new.append(list.pop()) return(new) x = randrange(0,len(list)) new.append(list.pop(x)) return(sl(list,new)) list = ["m","o","t","h","e","r"] new = [] print(sl(list,new))

12. (Cool, but challenging) def f4 (a, b): if (b == 0): return (a) if (a < b): return f4 (b, a) else: return f4 (b, a%b) print(f4(27,12)) print(f4(25,50)) print(f4(15,20))

13. def g(start,finish,lv): return("lv[" + str(start) + ":" + str(finish) + "] is" + str(lv[start:finish])) listvar = ["cat","dog","bug","echidna","aardvark"] print(g(2,4,listvar))

14.  Variables defined outside of all functions  These variables can then be used by all functions  example: s = 32 def f(): print (s ) f() def g() return(s/8) #did I change s? print(g()) def h(): ls = [0] * s return(ls) print(h())

15. x = [] y = 6 def f(): for k in range(y): x.append(0); return f() def g(): print(x); return g() def h(): y = "hello"; z = "bye" return(y) print(h()); print(z) #??? def j(): print(y) j()

16. a = "catamaran" y = "aeiou" def rec(x): if (x == len(a)): return "" elif (a[x] in y): return rec(x+1) else: return (a[x] + rec(x+1,)) print(rec(0)) print (a) def addit(x): if x == len(a): return"" elif x %2 == 1: return("ipa"+ a[x] + addit(x+1)) else: return(a[x] + addit(x+1)) print(addit(0)) a = "catamaran" y = "aeiou" def rec(x): if (x == len(a)): return "" elif (a[x] in y): return rec(x+1) else: return (a[x] + rec(x+1,)) a = (rec(0)) print (a) def addit(x): if x == len(a): return"" elif x %2 == 1: return("ipa"+ a[x] + addit(x+1)) else: return(a[x] + addit(x+1)) print(addit(0))

17. from random import * mat = [] x = -1 def createmat(): x = randrange(5,10) y = randrange(5,10) for k in range(x): mat.append([]) for l in range(y): mat[k].append(0) return def modifydi(): for k in range(len(mat)): for l in range(len(mat[0])): if (k == l): mat[k][l]=x if (len(mat) - k) == l: mat[k][l]=x return def main(): createmat() modifydi() main()