Stage 17 round 6 (#3): drag-reorder rack tiles with a visual gap

Dragging a rack tile and dropping it back on the rack reorders it: the dragged tile is
lifted out (the drag ghost stands in) and the tiles at/after the pointer's drop slot slide
right to open a gap there, so the drop position is visible. On drop the rack and its stable
ids are permuted (reorderIndices, unit-tested). Reorder applies only with no pending tiles,
so it stays a clean permutation; dropping on a board cell still places as before. Server
persistence of the order follows (#4).

ui/src/lib/placement.ts

@@ -106,6 +106,19 @@ export function reset(p: Placement): Placement {
   return { ...p, pending: [] };
 }
 
+/**
+ * reorderIndices returns the permutation of [0, n) that lifts the element at `from` and
+ * drops it at slot `toSlot` among the remaining elements (clamped to a valid slot). It is
+ * applied in parallel to the rack letters and their stable ids when a tile is dragged to a
+ * new rack position.
+ */
+export function reorderIndices(n: number, from: number, toSlot: number): number[] {
+  const order: number[] = [];
+  for (let i = 0; i < n; i++) if (i !== from) order.push(i);
+  order.splice(Math.max(0, Math.min(toSlot, order.length)), 0, from);
+  return order;
+}
+
 /**
  * direction infers the play orientation from the pending tiles: H if they share a row,
  * V if they share a column, null if a single tile (ambiguous) or non-linear (invalid).