Tighter A* estimate on the orthogonal track, and --heuristic-weight

The grid search estimated the remaining distance as a straight line even
when only orthogonal steps exist; Manhattan is the tighter estimate those
moves admit and still never overestimates. --heuristic-weight W (default
1) makes it weighted A*: routes at most W times the shortest (tested).

tests/route/test_real_board_geometry.py

@@ -73,3 +73,24 @@ def test_resolution_one_has_no_halo_so_the_grid_is_unchanged():
     assert GridRouter(board, trace_width=2500, clearance=1500)._halo_offsets == []
     fine = GridRouter(board, trace_width=2500, clearance=1500, resolution=2)
     assert fine.step == 2000 and (1, 0) in fine._halo_offsets and (2, 0) not in fine._halo_offsets
+
+
+def test_heuristic_weight_bounds_route_length():
+    # weighted A* may take a longer route, but never more than W times the shortest
+    places = "(place A 3000 -3000 front 0) (place B 17000 -17000 front 0)"
+
+    def length(weight):
+        result, _, _ = route_dsn_board_exact(
+            parse_dsn(_dsn(f"(component P {places})", "(net N (pins A-1 B-1))")),
+            heuristic_weight=weight,
+        )
+        return sum(
+            math.hypot(q.x - p.x, q.y - p.y)
+            for segs in result.result.wires.values()
+            for _layer, pts in segs
+            for p, q in zip(pts, pts[1:], strict=False)
+        )
+
+    shortest = length(1.0)
+    assert shortest > 0
+    assert length(2.0) <= 2.0 * shortest