Past exam of the computer science course of the University of Oxford / 2015 / Object oriented programming / 3 / b

Let brick $i$ have positive integer width $w_i$. Regard its horizontal occupied region as $[x_i,x_i+w_i)$ and its vertical occupied region as $[y_i,y_i+1)$. These half-open interval conventions allow adjoining bricks to touch without overlapping. Since the vertical coordinates are integers, two bricks can overlap only when they are on the same row. A suitable predicate isPositive widths and nonnegative integer heights are the underlying domain conditions for a wall built on the baseplate. Distinct members of the set are compared even if their Brick references happen to be identical: one brick specification can describe several placements. Testing object identity alone would miss two overlapping placements of the same specification.

For example, width-two bricks beginning at 0 and 2 on the same row satisfy the predicate; beginnings at 0 and 1 do not. The non-strict separation inequalities are essential because touching edges are permitted.