list manipulation - Problem with function inside brackets. Bug?

This code adds random digits to lists, and it works fine:

a = {{1}, {2}, {3}};

Do[
  j = RandomInteger[{1, Length[a]}];
  AppendTo[a[[j]], RandomInteger[9]];
  Print[a], {i, 5}];

(* {{1,7},{2},{3}}
   {{1,7},{2,2},{3}}
   {{1,7},{2,2},{3,9}}
   {{1,7},{2,2},{3,9,1}}
   {{1,7,2},{2,2},{3,9,1}}  *)

But if I replace the 'j' inside the [[]] with the definition j in the previous line, everything goes haywire:

a = {{1}, {2}, {3}};
Do[
  AppendTo[a[[RandomInteger[{1, Length[a]}]]], RandomInteger[9]];
  Print[a], {i, 5}];

(* {{1},{1,7},{3}}
   {{1},{1,7},{1,4}}
   {{1,7},{1,7},{1,4}}

   {{1,7},{1,7},{1,7,9}}
   {{1,7,9},{1,7},{1,7,9}} *)

Is this a bug or something I'm doing wrong?

Answer

Here's the issue. In the second (non-working) code,

RandomInteger[{1, Length[a]}]

is evaluated twice, as we can see by Traceing the evaluation:

SeedRandom[2]

a = {{1}, {2}, {3}};
Trace[AppendTo[a[[RandomInteger[{1, Length[a]}]]], RandomInteger[9]], TraceInternal -> True]

1. {RandomInteger[9], 8}


2. AppendTo[a[[RandomInteger[{1, Length[a]}]]], 8]


3. {{a, {{1}, {2}, {3}}}, {{{{a, {{1}, {2}, {3}}}, Length[{{1}, {2}, {3}}], 3}, {1, 3}}, RandomInteger[{1, 3}], 3}, {{1}, {2}, {3}}[[3]], {3}}


4. a[[RandomInteger[{1, Length[a]}]]] = Append[{3}, 8]


5. {Append[{3}, 8], {3, 8}}


6. a[[RandomInteger[{1, Length[a]}]]] = {3, 8}



7. {{{{a, {{1}, {2}, {3}}}, Length[{{1}, {2}, {3}}], 3}, {1, 3}}, RandomInteger[{1, 3}], 2}

We can see in Line 1 that RandomInteger[9] evaluates to 8, so we will be appending 8 to one of the lists. In Line 3, RandomInteger[{1, 3}] evaluates to 3, so we're going to append to a[[3]]. This happens on Line 5, where 8 is appended to {3} to make {3, 8}.

Now, the kicker: In Line 7, RandomInteger[{1, Length[a]}] is evaluated again, so it evaluates to a different number. In this case, it evaluates to 2, so instead of replacing a[[3]], we are replacing a[[2]] with {3, 8}. Hence the output after this evaluation is

a
(* {{1}, {3, 8}, {3}} *)

---

Now, the fix here is to do things the way you're doing it in the first code. I would probably wrap the entire thing in a Module with j as a local variable, but it's the same process.