Recursion for Factorial

• What is a subproblem of the factorial problem that is of the same form?

• n! = n × (n-1) × (n-2) × ... 2 × 1

• But (n-1) × (n-2) × ... 2 × 1 = (n-1)!

• So, n! = n × (n-1)!

• Similarly, (n-1)! = (n-1) × (n-2)!

• And so on, till eventually, 1! = 1

• An alternative mathematical definition of factorial is:

  n!	=	1 if n=1
  	=	n × (n-1)! otherwise

• The Base Case Imperative: In a recursive procedure, all roads must lead to a base case.