Write down the pseudocode of the factorial of n numbers and create the best-case and worst-caserecurrence relation

Sure, here is the pseudocode for calculating the factorial of a number:

Algorithm Factorial(n)
  if n == 0 then
    return 1
  else
    return n * Factorial(n-1)
  end if
End Algorithm

This pseudocode describes a recursive function that calculates the factorial of a number. The base case is when n equals 0, in which case the function returns 1. For all other values of n, the function returns n multiplied by the factorial of n-1.

Now, let's discuss the best-case and worst-case recurrence relations for this algorithm.

Best-case Recurrence Relation: The best-case scenario for this algorithm is when n equals 0. In this case, the function simply returns 1 and does not make any recursive calls. Therefore, the best-case time complexity is constant, or O(1).

Worst-case Recurrence Relation: The worst-case scenario for this algorithm is when n is a large number. In this case, the function makes n recursive calls, each of which involves a multiplication operation. Therefore, the worst-case time complexity is linear, or O(n).