Question 8 of 8

Question 8 (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The unit under test is the nested-loop body of GeneratePyramidExample.main (Appendix B, lines 21–31): an outer loop for(i=0; i<=as; i++) containing an inner loop for(j=1; j≤i; j++) that prints a running total y (initialised once, outside both loops, and never reset).

Find. The cyclomatic complexity V(G) of the unit, and a minimal set of V(G) basis-path test cases (each input pair (as, x) plus its exact expected console output) that together execute every independent path through the control-flow graph.

Approach. Draw the flow graph of the nested-loop unit, compute V(G) by both the edge–node formula and the predicate-node formula (they must agree), then derive V(G) independent basis paths by taking a baseline path and flipping one decision outcome at a time, and choose concrete (as, x) inputs that force each path.

1. Build the flow graph and count nodes/edges. Six nodes (1: init; 2: outer test; 3: inner test; 4: inner body; 5: end-of-row println; 6: exit) and seven edges (1→2; 2→3 true; 2→6 false; 3→4 true; 3→5 false; 4→3 back-edge; 5→2 back-edge).
2. Compute V(G) two independent ways. $$V(G) = E - N + 2 = 7 - 6 + 2 = \boxed{3}$$ $$V(G) = 1 + \sum_{\text{predicates}}(\text{out-degree}-1) = 1 + (2-1) + (2-1) = \boxed{3}$$ Both formulas agree at V(G) = 3, so exactly 3 independent basis-path test cases are required.
3. Path 1: outer test fails immediately (nodes 1-2-6). The outer loop body never executes at all — this requires as < 0, since i starts at 0 and i ≤ as must be false on the very first check.
   Input: as = -1, x = 5 → Expected console output: (nothing printed — zero rows)
4. Path 2: outer loop runs, inner test fails on its only visit (nodes 1-2-3-5-2-6). This is forced by as = 0: the single outer iteration has i = 0, so the inner test j ≤ i (i.e. 1 ≤ 0) is false immediately, the inner body never runs, and only the row-ending println("") executes before the outer loop exits.
   Input: as = 0, x = 5 → Expected console output: one blank line
5. Path 3: inner loop body executes at least once (nodes 1-2-3-4-3-5-2-6). This requires an outer iteration with i ≥ 1. Substituting as = 2, x = 1 and tracing by hand: i=0 → inner skipped, blank row; i=1 → inner runs once, prints y=0 then y becomes 1, row = "0\t"; i=2 → inner runs twice, prints y=1 (then y→2) and y=2 (then y→3), row = "1\t2\t".
   Input: as = 2, x = 1 → Expected console output (3 lines):
     (blank)
     0    (tab)
     1    2    (tabs)
   Note that y is declared once before the outer loop and is never reset per row — it is a running total across the ENTIRE pyramid, not a fresh count restarting at 0 on each row, which is why row i=2 continues 1, 2 rather than restarting at 0, 1.