how to put the results in a table or array in mathematica?

Hi I have a list of numbers for example k_1,k_2,...k_n, and f is a function. Now I apply f on the list of numbers and I need those numbers such that f is increasing,i.e.

f(k_i)>f(k_j) for any i>j .

I can get the results number k_i's each in different line, but I need the results in one table separated with comma or something else and counting the number of results.

For example:

k = Table[k1, k2, k3, k4, k5, k6, k开发者_开发技巧7, k8, k9, k10];
count = 0;
i=1;
For[j = i, j <= 10, j++, 
  If[f[k[[j]]] - f[k[[i]]] > 0, i = j; Print["k", i];
   count = count + 1]];
Print["count= ", count]

I got the result like:

k2
k3
k5
k9
count=4

but I need the results to be together:

{k2,k3,k5,k9} 
count=4

any idea?

thanks

---

Instead of Print, you could do AppendTo, ie

list={};AppendTo[list,5]

It might be good to start learning functional programming approach as Mathematica has tools to make it efficient, your above code might look something like this

pairs = Partition[list, 2, 1];
increasingPairs = Select[pairs, f[First[#]] < f[Last[#]] &];
Last /@ increasingPairs

---

You seem to want the longest increasing subsequence. The simplest and most efficient way I am aware of to get it in Mathematica is the following:

lis[f_, vals_List] := LongestCommonSequence[#, Sort[#]] &[Map[f, vals]];

Example:

In[8]:= lis[# &, {5, 3, 6, 1, 5, 7}]

Out[8]= {5, 6, 7}

In principle, the answer is not unique - there may be several different longest increasing subsequences with the same length.