GH-38149: [C++][Parquet] Avoid rebuilding column paths during schema initialization

[namtran1812]

Rationale for this change

SchemaDescriptor::BuildTree currently constructs each leaf's dot-separated path through node->path()->ToDotString(). For wide schemas, this repeatedly walks parent links and creates temporary path and string objects for every leaf during schema initialization.

This change reduces that overhead. It is relevant to the wide-schema metadata costs discussed in #38149, although it does not eliminate full-schema metadata deserialization or fully resolve selective column reads.

What changes are included in this PR?

• Build the dot-separated column path incrementally while traversing the schema tree instead of reconstructing it independently for every leaf.
• Insert the constructed path directly into leaf_to_idx_.
• Preserve existing nested-path and duplicate-path lookup semantics.
• Add a regression test verifying that duplicate paths are still disambiguated by node identity.
• Extend ReadFileMetadata benchmarks with 5K, 10K, 20K, and 50K-column single-row-group cases.

Local benchmark results (median wall time):

Columns	Before	After	Improvement
1,000	0.907 ms	0.771 ms	15.1%
5,000	4.619 ms	3.936 ms	14.8%
10,000	9.369 ms	8.017 ms	14.4%
20,000	18.951 ms	16.213 ms	14.4%
50,000	47.894 ms	42.542 ms	11.2%

The 50K-column case showed higher variance than the smaller cases. Across these measurements, metadata-read time improved by approximately 11–15%.

Are these changes tested?

Yes.

• parquet-schema-test: 44/44 tests passed.
• Added TestSchemaDescriptor.ColumnIndexDuplicatePath to cover duplicate-path identity lookup.
• git diff --check passes.
• The updated metadata benchmark was built and run locally across 1K–50K-column schemas.

Are there any user-facing changes?

No. This is an internal Parquet schema initialization optimization with no intended public API or behavioral changes.

Was AI used for this PR?

AI was used to assist with implementation analysis, review, testing strategy, and drafting the PR description. The changes and benchmark/test results were reviewed and validated locally before submission.

PR code and description written by:

• Human
• AI

Reviewed before submission by:

• Human
• AI
• Not reviewed

• GitHub Issue: [C++][Parquet] Slow column reading from multi-column parquet files #38149

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See also:

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• Contribution Guidelines - Contributing Overview

[github-actions]

⚠️ GitHub issue #38149 has been automatically assigned in GitHub to PR creator.