plotting the number of actions for ex i=i+1 ( action), pgd=n/i ( action), pgd=n(action)

function pgd = entier(n)
   i = 2;
   while i≤n/2 & mod(n,i)~-0
    i = i+1;
   end
   if mod(n,i)==0
    pgd = n/i;
   else
    pgd = n;
   end
  end

[Roger Stafford]

In this example you are seeking the smallest divisor of n which is greater than one. However, it isn't necessary to go all the way to n/2. You can stop at sqrt(n) because if there isn't a divisor by that point, you won't find any others less than n. (Of course none of this has anything to do with counting "actions".)

Answer 1

[AJ von Alt]

You can create a variable to count the number of actions taken and increment it every time an action is take. Have your function return that variable and store it for later plotting.

function [pgd , nActions] = entier(n)
    nActions = 0;
    i = 2;
    while i<=n/2 && mod(n,i)~=0
        i = i+1;
        nActions = nActions + 1;
    end
    if mod(n,i)==0
        pgd = n/i;
        nActions = nActions + 1;
    else
        pgd = n;
        nActions = nActions + 1;
    end
end

[Walter Roberson]

The line

while i<=n/2 && mod(n,i)~=0

requires at least two actions, one for the division and one for the mod() calculation. I would also suggest that if assignment is to be treated as an action, that comparison would have to be an action as well, remembering the && comparison should also be an action. Then one needs to take into account that && "short circuits" and so the mod() and comparison to 0 would not require actions if i<=n/2 is false.

[AJ von Alt]

Good catch! If the user wants to count the modulo and logical operations in addition to the ones listed in the title, some rework would be in order. Ime used & instead of && in his original implementation, so if he sticks with elementwise AND rather than my short circuit AND, he at least won't have to worry about short circuiting.