[treeplayer] Fix Alt$(array) to iterate correctly when used standalone

A standalone Alt$ on a variable-length array, e.g.

```c++
t.Scan("Alt$(x,-1)");
```

only ever evaluated the first element of each entry instead of looping
over the whole array. The combined form `x:Alt$(x,-1)` worked because
the sibling formula `x` drove the iteration, which made the bug easy to
miss.

Root cause: `TTreeFormula::ResetDimensions()` never accounted for the
`kAlternate`/`kAlternateString` actions when computing `fMultiplicity`.
By design, `Alt$` hides its primary operand from the TTreeFormulaManager
so that, in expressions like `arr1+Alt$(arr2,0)`, `arr1` drives the loop
and the alternate pads the entries where `arr2` is too short. But when
`Alt$` is the *only* source of multiplicity there is no sibling to drive
the loop, so the formula collapsed to a single instance.

Fix: in `ResetDimensions()`, after the main operand loop, if the formula
has no other multiplicity (`fMultiplicity == 0`) scan for `kAlternate`/
`kAlternateString` operands and register their primary with the manager
when that primary is itself a genuine array.

Adds two regression tests: **AltDollarVariableArray** (standalone `Alt$`
now loops; `Alt$(x[2],-1)` keeps its fall-back behaviour) and
**AltDollarPadsShorterArray** (the documented `arr1+Alt$(arr2,0)`
padding still iterates over the longer array).

Closes #6378.

🤖 Done with the help of [Claude Code](https://claude.com/claude-code) (Claude Opus 4.8)

Author: guitargeek

tree/treeplayer/src/TTreeFormula.cxx

@@ -5526,6 +5526,40 @@ void TTreeFormula::ResetDimensions() {
       //}
 
    }
+
+   // Handle the case of an Alt$(primary,alternate) expression that provides
+   // the only source of multiplicity, i.e. it's used not alongside another
+   // array that drives the iteration. Example: Scan("Alt$(x,-1)"), instead of
+   // Scan("y-Alt$(x,-1)"). In that case the number of instances must be
+   // dictated by the `primary` array, so we register it with the manager. We
+   // only get here when fMultiplicity == 0, i.e. nothing else in this formula
+   // drives an iteration.
+   if (fMultiplicity == 0) {
+      for (i = 0; i < fNoper; i++) {
+         Int_t action = GetAction(i);
+         if (action == kAlternate || action == kAlternateString) {
+            TTreeFormula *primary = static_cast<TTreeFormula *>(fAliases.UncheckedAt(i));
+            R__ASSERT(primary);
+            switch (primary->GetManager()->GetMultiplicity()) {
+            case 1: // primary is a variable length array: drive a variable length loop
+               fMultiplicity = 1;
+               fManager->Add(primary);
+               break;
+            case 2: // primary is a fixed length array: drive a fixed length loop
+               if (fMultiplicity != 1)
+                  fMultiplicity = 2;
+               fManager->Add(primary);
+               break;
+               // multiplicity 0 (scalar) or -1 (0-or-1 element): nothing to loop
+               // over, leave fMultiplicity at 0
+            }
+            // An Alt$(primary,alternate) expression occupies two consecutive
+            // operands: the `primary` action we just handled, immediately
+            // followed by the `alternate`, which we can skip.
+            ++i;
+         }
+      }
+   }
 }
 
 ////////////////////////////////////////////////////////////////////////////////

tree/treeplayer/test/regressions.cxx

@@ -508,6 +508,89 @@ TEST(TTreeScan, chainNameWithDifferentTreeName)
    }
 }
 
+// Alt$(primary, alternate) used on its own, with 'primary' a variable-length
+// array, must loop over all the elements of the array instead of just the
+// first one. Previously the array dimension of 'primary' was not propagated to
+// the enclosing TTreeFormula manager when Alt$ was the only source of
+// multiplicity, so the formula reported a single instance per entry.
+TEST(TTreeFormulaRegressions, AltDollarVariableArray)
+{
+   TTree t("t", "t");
+   Int_t n = 3;
+   Float_t x[3]{};
+   t.Branch("n", &n);
+   t.Branch("x", &x, "x[n]/F");
+   x[0] = 1;
+   x[1] = 2;
+   x[2] = 3;
+   t.Fill();
+   x[0] = 4;
+   x[1] = 5;
+   x[2] = 6;
+   t.Fill();
+   n = 2;
+   x[0] = -1;
+   x[1] = -2;
+   x[2] = -3;
+   t.Fill();
+   n = 1;
+   x[0] = 0;
+   t.Fill();
+
+   auto evalAll = [](TTree &tree, TTreeFormula &form, Long64_t entry) {
+      tree.LoadTree(entry);
+      const Int_t ndata = form.GetNdata();
+      std::vector<double> values;
+      for (Int_t i = 0; i < ndata; ++i)
+         values.push_back(form.EvalInstance(i));
+      return values;
+   };
+
+   // 1) Standalone Alt$ over the whole array loops over its elements.
+   {
+      TTreeFormula form("form", "Alt$(x,-1)", &t);
+      EXPECT_EQ(form.GetMultiplicity(), 1);
+      const std::vector<std::vector<double>> expected{{1, 2, 3}, {4, 5, 6}, {-1, -2}, {0}};
+      for (Long64_t entry = 0; entry < t.GetEntries(); ++entry)
+         EXPECT_EQ(evalAll(t, form, entry), expected[entry]) << "entry " << entry;
+   }
+
+   // 2) A fixed index into the variable-length array stays a single value per
+   // entry and falls back to the alternate when the index is out of range.
+   // This is the documented Alt$(arr[i], default) use case and must not be
+   // turned into a zero-instance (dropped) entry.
+   {
+      TTreeFormula form("form", "Alt$(x[2],-1)", &t);
+      const std::vector<std::vector<double>> expected{{3}, {6}, {-1}, {-1}}; // x[2] only exists for n==3
+      for (Long64_t entry = 0; entry < t.GetEntries(); ++entry)
+         EXPECT_EQ(evalAll(t, form, entry), expected[entry]) << "entry " << entry;
+   }
+}
+
+// Companion to AltDollarVariableArray: when Alt$ is combined with another array
+// that drives the iteration, the alternate must pad the shorter array rather
+// than shrinking the loop. See the TTree::Draw documentation for Alt$.
+TEST(TTreeFormulaRegressions, AltDollarPadsShorterArray)
+{
+   TTree t("t", "t");
+   Int_t n1 = 3, n2 = 2;
+   Float_t a1[3]{10, 20, 30};
+   Float_t a2[3]{1, 2, 3};
+   t.Branch("n1", &n1);
+   t.Branch("n2", &n2);
+   t.Branch("a1", &a1, "a1[n1]/F");
+   t.Branch("a2", &a2, "a2[n2]/F");
+   t.Fill();
+
+   // The loop is driven by a1 (3 elements); Alt$(a2,0) yields a2[0],a2[1],0.
+   TTreeFormula form("form", "a1+Alt$(a2,0)", &t);
+   t.LoadTree(0);
+   ASSERT_EQ(form.GetNdata(), 3);
+   const std::vector<double> expected{11, 22, 30};
+   for (Int_t i = 0; i < 3; ++i)
+      EXPECT_FLOAT_EQ(form.EvalInstance(i), expected[i]) << "instance " << i;
+}
+
 // https://github.com/root-project/root/issues/20249
 TEST(TTreeScan, TTreeGetBranchOfFriendTChain)
 {