A lower bound on the errors the rest of the pattern must cost

A lower bound on the errors the rest of the pattern must cost

The pattern "atgaattcatgagtga" against 3,000 characters. The step line is D — computed in one pass by extending the pattern in an index of the reversed text and counting the points where the interval empties, since a piece occurring nowhere must hold an error. The upper line is the least number of errors any alignment of that prefix really needs, from the quadratic table. D never exceeds it, which is what makes pruning on it safe; it falls one short at position 14, which is pruning left unclaimed. The bound cost 72 rank operations and 1 resets.

Drawn at 700 × 430, wide on the page. Everything above is what error-bound returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

4 essays call error-bound. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.