print("*****************\n\nRECURSION READING PROBLEM 0")
def R5(n):

    if n == 0:
        print("Forward with (base):", n)
    else:
        print("Forward with:", n)
        R5(n-1)
 

print("R5({}): ".format(1))
R5(1)
print("R5({}): ".format(3))
R5(3)


# UNFOLDING EXAMPLE
print("*****************\n\nRECURSION READING PROBLEM 1")
def R4(n):

    if n == 0:
        print("forward with (base):", n)
        returnVal = 1
        print("back with:",returnVal)
        return returnVal
    else:
        print("forward with:", n)
        returnVal = 2 * R4(n-1)
        print("back with:",returnVal)
        return returnVal

#print("R4({}) = {}".format(1, R4(1)))
print("R4({}) = {}".format(3, R4(3)))



print("*****************\n\nRECURSION READING PROBLEM 2")
def R2(n):

    if n == 9:
        return -1

    return 1 + R2(n+1)

print("R2({}) = {}".format(9, R2(9)))
print("R2({}) = {}".format(4, R2(4)))



print("*****************\n\nRECURSION READING PROBLEM 3")
def R1(n):

    if n < - 3:
        return 0

    return 1 + R1(n-1)

print("R1({}) = {}".format(-8, R1(-8)))
print("R1({}) = {}".format(4, R1(4)))


print("*****************\n\nRECURSION READING PROBLEM 4")
def Fib(n):

    if n == 0 or n == 1:
        return 1

    return Fib(n-1) + Fib(n-2)

print("Fib({}) = {}".format(3, Fib(3)))
print("Fib({}) = {}".format(7, Fib(7)))


print("*****************\n\nRECURSION READING PROBLEM 5")
def G(x, b):

    if x == b:
        return 0

    return 1 + G(x+1,b)

print("G({},{}) = {}".format(3,100, G(3,100)))
print("G({},{}) = {}".format(100,100, G(100,100)))
print("G({},{}) = {}".format(98,100, G(98,100)))



print("*****************\n\nRECURSION READING PROBLEM 6")
def H(x):

    if x < 0:
        r = -1
    else:
        r = 10 * H(x - 2)
        
    return r

print("H({}) = {}".format(0, H(0)))
print("H({}) = {}".format(-3, H(-3)))
print("H({}) = {}".format(4, H(4)))
print("H({}) = {}".format(5, H(5)))
print("H({}) = {}".format(20, H(20)))


print("*****************\n\nREADING PROBLEM 7")
# This program ALMOST returns the sum of the cubes between
# a and b (inclusive).  Fill in the base case(s) appropriately.
def F(a,b):

    return a**3 + F(a+1, b-1) + b**3
        

#print("F({},{}) = {}".format(2, 5, F(2,5)))