How to find the largest product?

Hi, I am trying to solve this homework. could anyone please help me to solve this?

* Write a function max_product that takes v a vector and n, a positive integer, as inputs and computes the largest product of n consecutive elements of v. It returns the product and the index of the element of v that is the first term of the product. If there are multiple such products in v, the function must return the one with the smallest starting index. As an example, the following call >> [product, ind] = max_product([1 2 2 1 3 1],3); will assign 6 to product and 3 to ind since the max 3-term product in the input vector is 2*1*3. If v has fewer than n elements, the function returns 0 and -1, respectively.

[Andrei Bobrov]

Use movsum (>=R2017a) or conv (any version).

[Torsten]

movprod ?

[Andrei Bobrov]

Yes! My typo.

[Stephen23]

@Andrei Bobrov: please show examples of using movsum and conv.

[Andrei Bobrov]

Hi Stephen! See my answer.

Answer 1

[Stephen23]

function [product,ind] = max_product(a,n)
product = 0;
ind = -1;
num = numel(a);
for k = 1:1+num-n
  tmp = prod(a(k:k+n-1));
  if tmp>product
    product = tmp;
    ind = k;
  end
end
end

And tested:

>> [product, ind] = max_product([1 2 2 1 3 1],3)
product =  6
ind =  3
>> [product, ind] = max_product([1 2 2 1 3 9],3)
product =  27
ind =  4
>> [product, ind] = max_product([1 2 2 1 3 9],9)
product = 0
ind = -1

This could be vectorized, or you could use movprod, but using a loop makes the algorithm clear.

Answer 2

[Jan]

And a vectorized version:

function [P, Ind] = max_product(v, n)
X        = v((1:numel(v) - n + 1) + (0:n-1).');
[P, Ind] = max(prod(X, 1));
end

[silvia a]

I have a question if you can explain please: I do not understand how your code handles the situation where the number of elements in the vector is smaller than the index. thank you, silvia

[Jan]

Smaller than which index?

[Walter Roberson]

The "If v has fewer than n elements, the function returns 0 and -1, respectively" part is being asked about.

[Jan]

Thanks, Walter. Another revelation again.

@silvia a: You need a simple if command to catch this the case that numel(v) is smaller than n. Because this is a homework, if left this work to the OP.

[silvia a]

thank you very much for your answer; I have solved it;

I do not know if you guys read these reviews. But I wanted to tell you that your answers and code examples help very much. I am very new to this but trying out your examples really helped me to get started and have a better grasp of things. Thank you!

[Jan]

Dear silvia a, the "guys and girls" here read the comments usually. I'm happy, that I could help you, because this my reason to post answers. You are welcome. I appreciate your feedback, thanks.

Answer 3

[Andrei Bobrov]

Op! Everyone solves someone else's homework ... I also want! :)

[product1, ind] = max(prod(hankel(a(1:end-b+1),a(end-b+1:end)),2))

as function:

function [product1,ind]=max_product(a,b)
    try
        [product1, ind] = max(prod(hankel(a(1:end-b+1),a(end-b+1:end)),2));
    catch
        product1 = 0;
        ind = -1;
    end
end

with conv2:

function [product1,ind]=max_product(a,b)
    try
        [product1, ind] = max(exp(conv2(log(a(:)),ones(b,1),'valid')));
    catch
        product1 = 0;
        ind = -1;
    end
end

with movsum

[product1, ind] = max(exp(movsum(log(a),[0, b-1])));