What does a clue of 0 mean?

Every digit that could sit between the 1 and the 9 is at least 2, so even a single sandwiched cell would push the sum to 2 or more. The only way the sum can be exactly 0 is for the sandwich to be empty - The 1 and 9 must occupy consecutive cells. Note that the order is free: 1-then-9 and 9-then-1 both satisfy the clue, so a 0 clue tells you that they touch, not which comes first. In a nine-cell line there are only eight adjacent pairs of cells, so the search space collapses immediately.

Treat the 1 and 9 of a 0-clue line as a glued domino and test where the domino fits. Box constraints do most of the work: if box 1 already contains a 9, no domino cell inside box 1 may hold that line's 9. Crossing clues help too - If a column's clue forces its 1 far from a row's candidate domino positions, those positions die. Each elimination removes two cells at once, which is why 0 clues crack open faster than any other clue. The moment you place either the 1 or the 9 in that line, the partner digit is forced into an adjacent cell - Usually uniquely, once row and box exclusions are applied.

Puzzles often include 0 clues on intersecting lines. A row 0-clue and a column 0-clue that cross create a strong interaction: if the shared cell held the row's 1, the column would need its 9 directly above or below, and both placements can be tested against the boxes in seconds. Always resolve 0-clue lines first and revisit them after every few placements - They keep paying out as the grid fills in.