faster implementation of method sage.graphs.generators.families.BalancedTree

[dcoudert]

We propose a direct implementation of the graph generator BalancedTree that is faster than the previous method using networkx.

Before (using networkx)

sage: %timeit G = graphs.BalancedTree(3, 5)
550 µs ± 1.17 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
sage: %timeit G = graphs.BalancedTree(3, 7)
5.33 ms ± 37.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
sage: %timeit G = graphs.BalancedTree(4, 5)
2.13 ms ± 18.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
sage: %timeit G = graphs.BalancedTree(4, 7)
54.5 ms ± 278 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

With this PR

sage: %timeit G = graphs.BalancedTree(3, 5)
157 µs ± 809 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
sage: %timeit G = graphs.BalancedTree(3, 7)
1.44 ms ± 4.94 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
sage: %timeit G = graphs.BalancedTree(4, 5)
569 µs ± 6.78 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
sage: %timeit G = graphs.BalancedTree(4, 7)
9.52 ms ± 61.6 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit e8f0782; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[tscrim]

All of these changes can be ignored if you prefer as they are either tangential or micro-optimizations. Once changed or ignored, you can set a positive review.

[dcoudert]

I have implemented all proposed changes. Thanks.

[tscrim]

Thank you.