Exercise 2: Choosing a Representation for a 200-Vertex Sparse Graph — Possible Solution
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GIVEN
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V = 200 vertices, E = 190 edges.

STEP 1: ADJACENCY MATRIX SPACE
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V^2 = 200 x 200 = 40,000 cells

STEP 2: ADJACENCY LIST SPACE
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V + 2E = 200 + (2 x 190) = 200 + 380 = 580 entries

STEP 3: THE RATIO
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40,000 / 580 ~= 69.0

The adjacency matrix would need roughly 69 times more space than the
adjacency list for this graph.

WHICH REPRESENTATION TO CHOOSE
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With only 190 edges against a possible maximum of roughly 19,900
edges for 200 vertices (200 x 199 / 2), this graph is clearly sparse -
each vertex connects, on average, to fewer than 2 other vertices out
of 199 possible ones. Per this chapter's own sparse-vs-dense guidance,
the adjacency list is the clear choice here: it uses dramatically less
space (580 vs. 40,000 entries) AND is at least as fast for the
neighbor-listing operations that traversal algorithms (Chapter 3
onward) rely on most heavily. There's no real advantage to the
matrix's O(1) edge-lookup speed unless that specific operation is
needed unusually often.

WHY THIS WORKS AS AN ANSWER
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Both space figures are computed directly from this chapter's own
formulas, the ratio is stated explicitly, and the representation
choice is justified by applying this chapter's own sparse-vs-dense
reasoning to the actual numbers rather than picking one representation
by default.