TimeConstrained for Table?

Question

Let's say that I have a function f[i] that takes quite a while to evaluate (evaluation time is different for different i) and I'd like to have as many values of f[i] as possible, for i = 1, 2, 3, ..., but in a specified amount of time (say, one minute) I want to stop evaluation and return values for i = 1, ... iFeasible (there is no way to calculate iFeasible before full computation). Basically, what I want to achieve is:

TimedConstainedTable[expr, {i, imin, imax}, maxTime]

To simplify: "If evaluating Table[expr, {i, imin, imax}] takes more time than maxTime, detect it, and return Table[expr, {i, imin, iFeasible}] (but do not evaluate values of expr for i = imin, ..., iFeasible again; extract them somehow from interrupted evaluation)."

It is super easy to implement:

list = {}; TimeConstrained[Do[AppendTo[list, f[i]], {i, 10^6}], 60, list]

but also very inefficient. Any improvement would be great.

Answer 1

Construction like this may help you.

    res = Reap@TimeConstrained[
      Do[Sow[f[i]]; Pause[0.1], {i, 1, 30}],
      1(*here number of seconds*)
    ]
    (*{$Aborted, {{f[1], f[2], f[3], f[4], f[5], f[6], f[7], f[8], f[9], f[10]}}}*)

for extractoin result use res[[2,1]]

Answer 2

Thank you molekyla777 for your answer. :) I tried very similar construction with Reap/Sow, but it did not work for some odd reason. Thank you very much again.

It would be very convenient for me to have TimeConstrainedTable[...] function. Therefore i molded molekyla777's answer to this:

SetAttributes[TimeConstrainedTable, HoldAll];

TimeConstrainedTable[expr_, iter__, time_] := Reap[TimeConstrained[Do[Sow[expr], iter], time]][[2, 1]]

and it seems to work just like Table (as I intend). For some reason though, if we evaluate:

i=0;

TimeConstrainedTable[f[i,j], {i, 10^6}, {j,5, 10}, 0.001]

it works perfectly, but "i" in notebook, in TimeConstrainedTable line, stays black, which seems weird to me (Table makes "i" blueish). Is it something to worry about? Can I "make it blueish" (indicate it is a variable with special use)? ^.- Here's clarifying screenshot: