Task: Join Order Enumeration

This task is part of feature #18249 illustrating join order enumeration for Q5 using a Join Ranking, where higher ranks indicate earlier execution. It assumes ranks are precomputed and focuses solely on enumeration and pruning. Rank computation and pruning strategies will be described in separated tickets

## Enumeration Examples

Figure 2 shows three joins ranked 4, one ranked 3, and two ranked 2. The three rank-4 joins are selected first in the join order, initiating three in-progress plans as illustrated in Figure 3. In these examples, we assume the join output remains sorted on the join key if the larger input is already sorted. This reflects the behavior of merge joins, which preserve sort order. Hash joins, on the other hand, do not generally guarantee output order, though some engines may preserve probe-side order in specific cases.

Figure 2: Join Graph Annotated with Join Ranked

After a join is selected, remaining join ranks are recalculated using updated properties and may change from earlier values.

Figure 3: Level-1 Partial Plans

In this enumeration scheme/examples, join type matters: if inputs are sorted, both merge and hash joins are considered; otherwise, only hash joins are used. As a result, the three plans above expand into five plans shown in Figure 4.

Figure 4: Level-1 Partial Plans with Join Type Selection

To avoid plan space explosion during enumeration, we retain at most two plans after each step. A pruning strategy is applied to discard less promising options. We'll cover pruning later; for now, we assume it eliminates plans (1.2) and (2), as shown in Figure 5.

Figure 5: Level-1 Partial Plans After Join Type Selection and Pruning

Similarly, the remaining level-1 partial plans (1.1) and (3) generate three level-2 plans, as shown in Figure 6.

Figure 6: Level-2 Partial Plans

Then plan (3.1) is pruned because it shares the same structure as plan (1.1.1).

Figure 7: Level-2 Partial Plans After Pruning

Continuing, level-2 plans (1.1.1) and (3.2) each contain a single highest-ranked join (rank 3), resulting in two level-3 plans shown in Figure 8.

Figure 8: Level-3 Partial Plans

Continuing, Figures 9 and 10 show the level-4 plans before and after pruning, respectively.

Figure 9: Level-4 Partial Plans

Figure10: Level-4 Partial Plans after Pruning

Finally, Figure 11 shows the two final-level plans, with plan (3.2.1.1.1) selected as the best.

Figure11: Final-level Plans

## Enumeration Summary

As shown, the enumeration process depends on three customizable components:
- A join ranking strategy, which can vary and be tailored as needed
- A pruning mechanism, which can also be adapted
- An option to include or exclude join types (i.e., physical plans) during enumeration

This suggests we can design a flexible enumeration framework that avoids relying on fixed join rankings or pruning strategies.

The issue names no files, tests, or entry points. Start by locating DataFusion's join-planning code and reading how join plans are currently enumerated. Done means a flexible framework supports configurable join ranking, pruning, and physical join-type selection as described in the examples.

Written by the indexing model from the issue text.