Exercise 1: DFS-Based Topological Sort of X-Y, X-Z, Y-W, Z-W — Possible Solution
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GIVEN
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Edges: X->Y, X->Z, Y->W, Z->W

STEP 1: DFS FROM X, TRACKING FINISH ORDER
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Visit X (gray). First neighbor: Y.

Visit Y (gray). Its only neighbor is W. Visit W.

Visit W (gray). W has no outgoing edges, so it finishes
immediately - mark W black, push W onto the finish stack.
  Finish stack so far: [W]

Back at Y: no more neighbors to explore. Y finishes - mark Y
black, push Y.
  Finish stack so far: [W, Y]

Back at X: next neighbor is Z. Visit Z.

Visit Z (gray). Its only neighbor is W, which is already black
(fully finished) - skip it, no need to revisit. Z finishes - mark
Z black, push Z.
  Finish stack so far: [W, Y, Z]

Back at X: no more neighbors. X finishes - mark X black, push X.
  Finish stack so far: [W, Y, Z, X]

STEP 2: REVERSE THE FINISH STACK
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Finish stack:      [W, Y, Z, X]
Reversed (answer): [X, Z, Y, W]

RESULT
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A valid topological order is: X, Z, Y, W

Checking every edge points forward in this order: X->Y (X before
Y, correct), X->Z (X before Z, correct), Y->W (Y before W,
correct), Z->W (Z before W, correct). All four edges point
forward, confirming this is a valid topological order.

WHY THIS WORKS AS AN ANSWER
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The DFS-based method from this chapter is applied exactly as
specified - each vertex is pushed onto the finish stack only once
every one of its outgoing edges has been fully explored, an
already-finished (black) vertex is correctly skipped rather than
re-explored, and the final answer is obtained by reversing the
raw finish-order stack rather than reading it directly.