MATLAB: Recursive function for replacing multiple for loops

recursion

Hi I want to implement a recursive function which could replace the following code in Matlab:
p=0.2;
n=10;
a=5;
p1=0;
for i = 0:1:(n-a)
      for j = 0:1:(n-i-a)
            for k = 0:(n-i-j-a)
               for l = 0:(n-i-j-k-a)
                   for m = 0:(n-i-j-k-l-a)
                       p1=p1+(p*(1-p)^i)*(p*(1-p)^j)*(p*(1-p)^k)*(p*(1-p)^l)*(p*(1-p)^m);
                   end
                end
            end
       end
end
I could have used the above code if had a=5 or 10. But in my case, value of n is constant like n=100 and value of a can be up to 100, i.e, n>=a, which makes it difficult to change the number of for loops on each value of a. I will be thankful if someone helps me in implementing such a recursive function which could replace the above for loops.

Best Answer

Hello Ameer, suppose you have d for loops, which means d independent variables i,j,k, ... then your expression reduces to p^d sum (1-p)^(i+j+k+ ...) and by computing the number of times a given sum occurs you can get to the following:
N = n-a;
d = 3     %  this is the number of independent i,i,k, ... variables
          %  which is the number of for loops
p2 = 0;
for q = 0:N
  p2 = p2 + (factorial(q+d-1)/(factorial(q)*factorial(d-1)))*(1-p)^q;
end
p2 = p^d*p2
which appears to agree with your calculation.
Related Question