# Let's determine the sum of the first n positive integers
# For example, Sum(5) = 1+2+3+4+5 = 15
def Sum(n):
if n==1: return 1
else: return n + Sum(n-1)
Sum(5)
15
# Let's compute the product of the first n positive integers
# For example, Factorial(5) = 1*2*3*4*5 = 120
def Factorial(n):
if n==1: return 1
else: return n * Factorial(n-1)
Factorial(5)
120
# Let's computer the number of paths from (0,0) to (x,y)
# For example, Paths(4,3) = 35 by our analysis from tonight.
def Paths(x,y):
if x==0: return 1
elif y==0: return 1
else: return Paths(x-1,y)+Paths(x,y-1)
Paths(4,3)
35
# Let's solve the Towers of Hanoi problem
# Label the three towers A, B, C, with StartTower = A and TargetTower = C
def Hanoi(n, StartTower, TargetTower, OtherTower):
if n==1:
print("Move disk 1 from", StartTower, "to", TargetTower)
else:
Hanoi(n-1, StartTower, OtherTower, TargetTower)
print("Move disk", n, "from", StartTower, "to", TargetTower)
Hanoi(n-1, OtherTower, TargetTower, StartTower)
Hanoi(4,'Tower A','Tower C','Tower B')
Move disk 1 from Tower A to Tower B Move disk 2 from Tower A to Tower C Move disk 1 from Tower B to Tower C Move disk 3 from Tower A to Tower B Move disk 1 from Tower C to Tower A Move disk 2 from Tower C to Tower B Move disk 1 from Tower A to Tower B Move disk 4 from Tower A to Tower C Move disk 1 from Tower B to Tower C Move disk 2 from Tower B to Tower A Move disk 1 from Tower C to Tower A Move disk 3 from Tower B to Tower C Move disk 1 from Tower A to Tower B Move disk 2 from Tower A to Tower C Move disk 1 from Tower B to Tower C