Question

Written in expanded form, the usual factorial function is n! = n middot (n - 1) middot (n - 2) ... 3 middot 2 middot 2 middot 1. The difference between elements in the product is always 1. It can be writ in recursive form as n! = n middot (n - 1)! (e.g., 10! = 10 middot 9!, 23! * 23 middot 22!, 4! = 4 3!, etc.). The purpose of this problem is to generalize the factorial function that the difference between dements in the product is always a given positive integer k. One passible generalization is the skip factorial function, denoted by nuke. The skip factorial is defined recursively for positive integers n and k by the equation nuke = n middot (n - k)!_k, where nuke = n when n lessthanorequalto k. Thus, for example. 15!_4 = 15 middot 11!_4 = 15 middot 11 middot 7!_4 = 15 middot 11 middot 7 middot 3!_4 = 15 middot 11 middot 7 middot 3 = 3465. Some further examples of the skip factorial, written in expanded form, are 12!_2 = 12 middot 10 middot 8 middot 6 middot 4 2 = 46080, 23!_3 = 23 middot 20 middot 17 middot 14 middot 11 middot 8 middot 5 middot 2 = 96342400. 193!_37 = 193 middot 156 middot 119 middot 82 middot 45 middot 8 = 105765791040. Write a recursive Matlab, function called skipfact.m which will calculate the value of the skip factorial wheu given two positive integers n and k. if either of n or k is not an integer the function should return the Hag value -1 If either of n or k fa no positive the function should return the Hag value -2. Program Specifications and sample function calls are given below. input parameter n a positive integer input parameter k a positive integer output parameter val the value of n!_k

Answer 1

In the following, the required code is attached along with sample output for the given data. Coding and Output screensho octave:40> function [val]skipfact (n, k) val 1; % for n θ, val I. Init cond if floor(n) n &&-isinf(n) %Checking if +ve integer but not infinity for i -n:-1*k: 1 %check until 1 val val * i; end end if n < θ %negative val = -2; end if floor(n) ~= n 11 isinf(n) %Not positive integers val 1; end end skipfact(7,1) %calling skipfact (23,3) skipfact (193,37) skipfact (9.2,3) skipfact(-9.2,3) skipfact(-8,3) for given sample data ans= 5040 ans# 9634240Θ ans1.0577e+11 ans1 ans -1

function [val] = skipfact(n,k)
   val = 1; % for n = 0, val = 1. Init cond
   if floor(n) == n && ~isinf(n) %Checking if +ve integer but not infinity
       for i = n:-1*k:1 %check until 1
           val = val * i;
       end
   end
   if n < 0 %negative
       val = -2;
   end
   if floor(n) ~= n || isinf(n) %Not positive integers
       val = -1;
   end
end

skipfact(7,1) %calling for given sample data
skipfact(23,3)
skipfact(193,37)
skipfact(9.2,3)
skipfact(-9.2,3)
skipfact(-8,3)