scc: speed up iterative DFS by dropping tuple-based stack simulation

[shakayami]

Summary

• The previous scc() simulated recursion by pushing (v, bef, t) tuples onto a stack — up to two tuple allocations per edge, plus duplicate pushes when multiple frontier nodes shared an undiscovered neighbor (detected and discarded later at pop time).
• Replaced it with the standard "one frame per active vertex + resumable edge-iterator index" iterative DFS, so each vertex is pushed at most once and each edge is scanned exactly once. Also flattened the nested dfs() closure into the main function body to avoid LOAD_DEREF overhead on low/Ord/visited.
• Output is byte-for-byte identical to the previous implementation (verified below) — no behavior change, no API change.

Why

Reported that stuffing tuples onto the stack looked like the bottleneck in scc(); profiling/benchmarking confirmed it.

Test plan

• python3 -m unittest discover -s tests — all 146 existing tests pass (including two_sat.py, which depends on scc)
• Randomized differential test: 3500+ random graphs (up to 60 vertices/200 edges, and smaller dense graphs) comparing old vs. new implementation output — 0 mismatches
• Benchmarked old vs. new on larger graphs:
  • random n=200000, m=200000: 2.24x faster
  • random n=100000, m=400000: 1.29x faster
  • random n=50000, m=500000: 1.87x faster
  • chain n=200000: 1.38x faster
  • big single cycle n=300000: 2.31x faster
  • fan-in heavy DAG n=4000, m=100000: 1.21x faster
• Repo's existing benchmarks/workloads.py already includes an scc workload for the perf-comparison CI

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Generated by Claude Code

[github-actions]

📊 Performance Benchmark Results

⏱️ Execution time (mean, lower is better)

Benchmark	Base	PR	Delta
acl_math	2.032s	2.013s	-0.9%
acl_string	247.57ms	249.11ms	+0.6%
convolution	921.48ms	954.50ms	+3.6%
dsu	705.78ms	711.16ms	+0.8%
fenwicktree	1.243s	1.211s	-2.5% ✅
fps	604.20ms	626.61ms	+3.7%
lazysegtree	2.576s	2.512s	-2.5% ✅
maxflow	838.78ms	880.46ms	+5.0%
mincostflow	47.00ms	48.41ms	+3.0%
prime_fact	2.098s	2.078s	-1.0%
scc	470.20ms	411.38ms	-12.5% ✅
segtree	830.66ms	815.03ms	-1.9% ✅
two_sat	1.542s	1.516s	-1.7% ✅

💾 Peak memory (lower is better)

Benchmark	Base	PR	Delta
acl_math	4.9KiB	4.9KiB	+0.0%
acl_string	13.5MiB	13.5MiB	+0.0%
convolution	16.1MiB	16.1MiB	+0.0%
dsu	40.4MiB	40.4MiB	+0.0%
fenwicktree	8.9MiB	8.9MiB	+0.0%
fps	3.9MiB	3.9MiB	+0.0%
lazysegtree	9.8MiB	9.8MiB	+0.0%
maxflow	97.0MiB	97.0MiB	+0.0%
mincostflow	16.3MiB	16.3MiB	+0.0%
prime_fact	8.5KiB	8.5KiB	+0.0%
scc	32.7MiB	25.1MiB	-23.4% ✅
segtree	6.0MiB	6.0MiB	+0.0%
two_sat	174.0MiB	174.0MiB	+0.0%

_{Base = target branch, PR = this branch. Negative delta = improvement. ✅ improvement ≥ 1%, ⚠️ regression > 5%. "n/a" base entries mean the target branch has no benchmark suite yet.}