Add Cartesian Tree RMQ/LCA implementation with concepts#32
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Introduce `Gen_Cartesian_Tree`, `Gen_Euler_Tour_LCA`, and `Gen_Cartesian_Tree_RMQ` classes for O(1) range queries. This includes the O(n) construction of Cartesian trees using a monotonic stack and the O(1) LCA/RMQ by reducing to Sparse Table over the Euler Tour. Updated CMakeLists files to include the new header, example, and test files. Updated README.md to document the new Cartesian Tree and RMQ features
Refactor: update tpl_cartesian_tree.H with minor fixes
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WalkthroughAdds a Cartesian Tree subsystem (construction, Euler‑tour LCA, RMQ) with examples and tests; introduces a C++20 concepts header Changes
Sequence Diagram(s)sequenceDiagram
participant Client as Client
participant CT as Gen_Cartesian_Tree<T>
participant ET as Gen_Euler_Tour_LCA<T>
participant ST as Sparse_Table
Client->>CT: construct(data)
CT->>CT: build (monotonic stack → parent/children)
CT-->>Client: tree handle
Client->>ET: construct(from tree or data)
ET->>CT: access tree()
CT-->>ET: nodes / parent/children
ET->>ET: build Euler tour (nodes, depths)
ET->>ST: build RMQ on depths
ST-->>ET: RMQ ready
Client->>ET: lca(u,v) or rmq(l,r)
ET->>ST: rmq(depth-range)
ST-->>ET: index of min depth
ET-->>Client: LCA / RMQ result
Estimated code review effort🎯 5 (Critical) | ⏱️ ~120 minutes 🚥 Pre-merge checks | ✅ 3✅ Passed checks (3 passed)
✏️ Tip: You can configure your own custom pre-merge checks in the settings. Comment |
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Pull request overview
This PR introduces a comprehensive implementation of Cartesian Trees and the classic reduction chain RMQ ↔ LCA ↔ Cartesian Tree, confirming that Range Minimum Queries and Lowest Common Ancestor queries are equivalent problems. The implementation includes three main class templates with O(n) tree construction and O(1) query time (after O(n log n) preprocessing for LCA/RMQ).
Changes:
- Added
tpl_cartesian_tree.Hwith three class templates:Gen_Cartesian_Tree(explicit tree with monotonic stack O(n) construction),Gen_Euler_Tour_LCA(O(1) LCA via Euler Tour + Sparse Table), andGen_Cartesian_Tree_RMQ(O(1) static range queries) - Added comprehensive unit tests in
Tests/tpl_cartesian_tree_test.ccwith 598 lines covering edge cases, stress tests, and correctness verification - Added educational example in
Examples/cartesian_tree_example.ccwith four creative scenarios demonstrating the data structures - Updated README.md and documentation files with new section describing Cartesian Trees, LCA, and RMQ
- Fixed redundant initialization in
tpl_segment_tree.H(removed unnecessary loop that re-initialized tree with identity before filling)
Reviewed changes
Copilot reviewed 12 out of 12 changed files in this pull request and generated no comments.
Show a summary per file
| File | Description |
|---|---|
| tpl_cartesian_tree.H | New header implementing Cartesian Tree, Euler Tour LCA, and RMQ with C++20 concepts, Aleph exception macros, and complete Doxygen documentation |
| Tests/tpl_cartesian_tree_test.cc | Comprehensive test suite with 26 test cases covering all three classes, edge cases (empty, single element, sorted), stress tests, and correctness verification |
| Examples/cartesian_tree_example.cc | Educational example with four scenarios demonstrating tree structure, LCA queries, RMQ equivalence, and performance comparison with Sparse Table |
| Tests/CMakeLists.txt | Added tpl_cartesian_tree_test to test programs list |
| Examples/CMakeLists.txt | Added cartesian_tree_example to example programs list |
| CMakeLists.txt | Added tpl_cartesian_tree.H to header list |
| README.md | Added Cartesian Tree section with complexity table, usage examples, and updated range query structures listing |
| README.es.md | Updated Spanish README with new anchor IDs for consistency |
| INSTALL.md | Updated anchor IDs for table of contents consistency |
| INSTALL.es.md | Updated Spanish installation guide anchor IDs |
| tpl_segment_tree.H | Removed redundant identity initialization loop (optimization/cleanup) |
| Doxyfile | Excluded CHANGELOG_v3.md from documentation generation |
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Caution
Some comments are outside the diff and can’t be posted inline due to platform limitations.
⚠️ Outside diff range comments (1)
README.md (1)
1924-1928:⚠️ Potential issue | 🟡 MinorDefine
itemsbeforepfor_eachto keep the example buildable.
itemsis not declared in this snippet, so the example won’t compile as-is. Add a container declaration (e.g.,DynList<Item> items = {...};) or reuse an existing one.🔧 Suggested patch
- // Parallel for_each: apply operation to all elements - pfor_each(items, [](Item& item) { + // Parallel for_each: apply operation to all elements + DynList<Item> items = {/* ... */}; + pfor_each(items, [](Item& item) { item.expensive_process(); });
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Improve performance by caching child nodes in Euler tour LCA and adding path stack capacity to RB-tree. Also, clarify doxygen comments.
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Actionable comments posted: 1
🤖 Fix all issues with AI agents
In `@README.md`:
- Around line 768-779: Remove the misleading footnote line "* Amortized **
Expected (randomized)" that follows the RMQ ←→ LCA ←→ Cartesian Tree table in
README.md; this footnote does not apply to the deterministic classes
Gen_Cartesian_Tree, Gen_Euler_Tour_LCA, and Gen_Cartesian_Tree_RMQ, so delete
that footnote text to avoid confusion and leave the table rows and headings
unchanged.
🧹 Nitpick comments (3)
tpl_tdRbTreeRk.H (2)
240-284: Stack push has no runtime bounds check — safe by invariant, but fragile under corruption.The
static_assertat line 106 guaranteesPATH_STACK_CAPACITY≥ worst-case RB height for the platform'ssize_t, sostack_lencannot exceed capacity for a valid tree. However, there is no runtime guard (assert(stack_len < PATH_STACK_CAPACITY)) beforestack[stack_len++]at lines 249 and 284 (and similarly at 321/353/637/660). A debug-mode assertion would catch corruption scenarios (cycles or exceeded height) before silent buffer overwrite.Consider adding a defensive assert:
🛡️ Suggested defensive assert
- stack[stack_len++] = p; + assert(stack_len < PATH_STACK_CAPACITY); + stack[stack_len++] = p;Apply similarly at all push sites (lines 249, 284, 321, 353, 637, 660).
837-863:remove()falls back to O(n)updateCountRecdespite collecting a path stack.The stack collected in
searchAndColorRedis unused —remove()always callsupdateCountRec(root)(O(n)) at line 859. The commit message mentions adding path-stack capacity for rank updates, suggesting the intent was O(log n) count maintenance. If this fallback is intentional for safety after complex swaps inremoveAndRendLeafRed, a brief comment explaining why the stack-based update is insufficient here (and when/if it will be revisited) would help future readers.tpl_cartesian_tree.H (1)
656-693: Consider extracting the repeated constructor body into a private helper.All five
Gen_Euler_Tour_LCAconstructors have identical bodies (build_euler_tour(); build_sparse_table();). While not a bug, the same pattern repeats acrossGen_Cartesian_Tree_RMQ. A privateinit()method wouldn't reduce the constructor count but would centralize the build sequence if it ever changes.
Refactor README.md to improve readability and consistency. Updates included: - Removed redundant HTML anchor `name` attributes. - Standardized section headings and code block formatting. - Added comprehensive examples for various data structures and algorithms. - Updated tables and diagrams for clarity.
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Actionable comments posted: 4
🤖 Fix all issues with AI agents
In `@scripts/ci_header_doc_coverage.rb`:
- Line 1: The script starting with the shebang "#!/usr/bin/env ruby" lacks
execute permission; make it executable so CI can invoke it directly by running
chmod +x on scripts/ci_header_doc_coverage.rb (ensure the file's mode is updated
in the repo/commit so CI sees the executable bit).
- Around line 177-179: sanitize_for_braces currently only removes // comments so
braces inside block comments or string literals still affect brace_depth; update
sanitize_for_braces to also strip block comment fragments (/* ... */) and remove
string literal contents (both single and double quotes, handling escaped quotes)
from the input line before returning it so brace counting ignores braces inside
comments and strings; ensure the function accounts for block comment start/end
that may occur on the same line and safely returns a cleaned line used by the
brace_depth logic.
- Around line 263-265: The access-specifier regex in the condition that updates
class_stack.last[:access] (the stripped.match call) is too strict and fails on
lines with trailing comments or extra whitespace; change the regex used in the
(m = stripped.match(...)) expression to allow optional trailing whitespace and
comments after the colon (e.g., accept anything like "public: // comment" or
"protected: "), so that class_stack.last[:access] is correctly set when access
specifiers have trailing content.
- Around line 92-116: The parse_added_lines method miscounts when encountering
Git's "\ No newline at end of file" marker because that line falls into the else
branch and increments cur_new; update parse_added_lines to detect that marker
(e.g., line.strip == '\\ No newline at end of file' or starts_with?('\\ No
newline')) and skip it (do not increment cur_new) so hunk destination line
numbering remains correct; modify the logic around the else branch in
parse_added_lines to treat that marker like a metadata line and continue without
changing cur_new.
🧹 Nitpick comments (3)
scripts/ci_header_doc_coverage.rb (3)
379-389: First file analysis failure aborts the entire run.The
rescueon Line 386 returns1immediately, so a single unparseable header (e.g., encoding issue) will skip coverage checking for all remaining files. Consider collecting errors and continuing, then failing at the end, so the developer sees the full picture.
201-218: Regex may fail on multi-line or complex signatures.The regex on Line 205-206 expects the entire function signature (params, qualifiers, trailing return) on a single line. Declarations split across lines (common in heavily-templated C++ code) will be silently missed. This is acceptable for a heuristic scanner, but documenting the single-line assumption in a comment would help future maintainers.
75-83: Clarify the diff range reference for better portability.The fetch refspec
"#{base}:#{base}"(line 81) creates a local branch, but line 82 returns"origin/#{base}...HEAD"referencing the remote-tracking ref. This works in the current CI setup becausefetch-depth: 0ensuresorigin/<base>already exists, but the code is unclear and would break with shallow clones or different checkout configurations.Either use the local ref that the fetch creates, or explicitly fetch into the remote-tracking namespace:
Option A: use the local ref
- run!(['git', 'fetch', '--no-tags', '--prune', 'origin', "#{base}:#{base}"]) - "origin/#{base}...HEAD" + run!(['git', 'fetch', '--no-tags', '--prune', 'origin', "#{base}:#{base}"]) + "#{base}...HEAD"Option B: explicitly fetch into the remote-tracking namespace
- run!(['git', 'fetch', '--no-tags', '--prune', 'origin', "#{base}:#{base}"]) - "origin/#{base}...HEAD" + run!(['git', 'fetch', '--no-tags', '--prune', 'origin', "+refs/heads/#{base}:refs/remotes/origin/#{base}"]) + "origin/#{base}...HEAD"
Refactor CI scripts for better maintainability and add detailed Doxygen comments to tpl_cartesian_tree.H. This includes fixing git fetch commands in multiple CI scripts and enhancing docstring parsing in ci_header_doc_coverage.rb.
| <a id="readme-es-contenido"></a> | ||
| ## Contenido {#readme-es-contenido} | ||
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These headings include Doxygen-style {#...} anchor syntax, but the file already adds explicit <a id="..."> anchors above, so {#...} will be rendered as literal text on GitHub. Consider removing the {#...} fragments (or switching fully to HTML anchors) to keep the README clean on GitHub while preserving stable links.
| ## Table of Contents {#install-table-of-contents} | ||
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| - [Prerequisites](#install-prerequisites) |
There was a problem hiding this comment.
The {#install-...} anchor fragments in headings are likely to render as literal text in GitHub Markdown. Consider switching these headings to the same pattern used in README.md (explicit <a id="..."> anchors + plain headings) or removing {#...} to keep the rendered INSTALL guide clean.
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Actionable comments posted: 4
🤖 Fix all issues with AI agents
In `@ah-concepts.H`:
- Around line 33-44: Update the file-level Doxygen header in ah-concepts.H to
state that four concepts are defined instead of three and list them:
BinaryPredicate, StrictWeakOrder, EqualityComparator, and BSTPolicy; locate the
top-of-file comment that currently describes "three concepts" and change the
count and the short bulleted description to include BSTPolicy so the summary
accurately reflects all defined concepts and remains concise.
In `@Examples/cartesian_tree_example.cc`:
- Around line 58-66: Add the missing standard headers to the top-of-file
includes so uses of std::string, std::pair and std::min are portable: include
<string> to cover std::string, include <utility> (or <tuple>) to cover
std::pair, and include <algorithm> to cover std::min; update the include block
that currently has tpl_cartesian_tree.H, tpl_sparse_table.H and the
iostream/vector headers to also `#include` these three standard headers.
- Around line 183-188: Replace the std::vector usage with an Aleph container
(e.g., aleph::Array<int> or aleph::DynList<int>) and pass that to
Cartesian_Tree_RMQ<int> and Sparse_Table<int>; update the variable declaration
(replace "std::vector<int> data = {...}" with an Aleph container initialized
with the same elements), ensure the appropriate Aleph container header is
included and/or aleph namespace is used, and leave the Cartesian_Tree_RMQ<int>
ct_rmq(data) and Sparse_Table<int> sparse(data) calls unchanged so they receive
the Aleph container directly.
In `@tpl_cartesian_tree.H`:
- Around line 198-206: Add the missing Doxygen tags for the new public APIs:
update the Gen_Cartesian_Tree(const Array<T>&, Comp) constructor (and the
initializer_list / DynList / num overloads) and the public constructors in
Gen_Euler_Tour_LCA and Gen_Cartesian_Tree_RMQ to include `@brief`, `@param` for each
parameter, `@throws` (e.g., bad_alloc or invalid_argument if empty/invalid input),
and explicit time/space complexity notes (big-O for construction and memory),
keeping the wording consistent with existing header docs and applying the same
tags/format across all new public member functions so Doxygen emits no warnings.
🧹 Nitpick comments (1)
scripts/ci_header_doc_coverage.rb (1)
273-383: Consider extracting helper methods to reduce complexity.RuboCop flags this function with high cyclomatic complexity (32/7). While acceptable for a CI heuristic script, consider extracting the class/struct detection (lines 293-314), access specifier handling (lines 316-319), concept detection (lines 321-334), and function-like declaration detection (lines 336-351) into separate helper methods for maintainability.
| /** @file ah-concepts.H | ||
| * @brief C++20 concepts for constraining comparison functors. | ||
| * | ||
| * Defines three concepts used throughout Aleph-w to constrain | ||
| * template parameters that act as binary predicates: | ||
| * | ||
| * - **BinaryPredicate<F, T>** — base concept: `f(a, b)` returns | ||
| * something convertible to `bool`. | ||
| * - **StrictWeakOrder<F, T>** — wraps `std::strict_weak_order<F, T, T>` | ||
| * for BST comparators. | ||
| * - **EqualityComparator<F, T>** — wraps `std::equivalence_relation<F, T, T>` | ||
| * for hash table equality comparators. |
There was a problem hiding this comment.
Fix the file-level doc to reflect four concepts.
It currently says “three concepts” but BSTPolicy is also defined.
✏️ Suggested doc update
- * Defines three concepts used throughout Aleph-w to constrain
+ * Defines four concepts used throughout Aleph-w to constrain
@@
- * - **EqualityComparator<F, T>** — wraps `std::equivalence_relation<F, T, T>`
- * for hash table equality comparators.
+ * - **EqualityComparator<F, T>** — wraps `std::equivalence_relation<F, T, T>`
+ * for hash table equality comparators.
+ * - **BSTPolicy<T, Key>** — checks that tree policies expose the DynSetTree
+ * API surface.As per coding guidelines, "Keep Doxygen descriptions concise but complete".
📝 Committable suggestion
‼️ IMPORTANT
Carefully review the code before committing. Ensure that it accurately replaces the highlighted code, contains no missing lines, and has no issues with indentation. Thoroughly test & benchmark the code to ensure it meets the requirements.
| /** @file ah-concepts.H | |
| * @brief C++20 concepts for constraining comparison functors. | |
| * | |
| * Defines three concepts used throughout Aleph-w to constrain | |
| * template parameters that act as binary predicates: | |
| * | |
| * - **BinaryPredicate<F, T>** — base concept: `f(a, b)` returns | |
| * something convertible to `bool`. | |
| * - **StrictWeakOrder<F, T>** — wraps `std::strict_weak_order<F, T, T>` | |
| * for BST comparators. | |
| * - **EqualityComparator<F, T>** — wraps `std::equivalence_relation<F, T, T>` | |
| * for hash table equality comparators. | |
| /** `@file` ah-concepts.H | |
| * `@brief` C++20 concepts for constraining comparison functors. | |
| * | |
| * Defines four concepts used throughout Aleph-w to constrain | |
| * template parameters that act as binary predicates: | |
| * | |
| * - **BinaryPredicate<F, T>** — base concept: `f(a, b)` returns | |
| * something convertible to `bool`. | |
| * - **StrictWeakOrder<F, T>** — wraps `std::strict_weak_order<F, T, T>` | |
| * for BST comparators. | |
| * - **EqualityComparator<F, T>** — wraps `std::equivalence_relation<F, T, T>` | |
| * for hash table equality comparators. | |
| * - **BSTPolicy<T, Key>** — checks that tree policies expose the DynSetTree | |
| * API surface. |
🤖 Prompt for AI Agents
In `@ah-concepts.H` around lines 33 - 44, Update the file-level Doxygen header in
ah-concepts.H to state that four concepts are defined instead of three and list
them: BinaryPredicate, StrictWeakOrder, EqualityComparator, and BSTPolicy;
locate the top-of-file comment that currently describes "three concepts" and
change the count and the short bulleted description to include BSTPolicy so the
summary accurately reflects all defined concepts and remains concise.
| # include <tpl_cartesian_tree.H> | ||
| # include <tpl_sparse_table.H> | ||
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| # include <iostream> | ||
| # include <iomanip> | ||
| # include <chrono> | ||
| # include <random> | ||
| # include <vector> | ||
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Add missing standard headers for std::string, std::min, and std::pair.
These symbols are used throughout the file (lines 93, 97–98, 196, 201 for std::string; line 263 for std::pair; line 295 for std::min) and relying on transitive includes is non-portable and fragile.
🔧 Proposed fix
# include <tpl_cartesian_tree.H>
# include <tpl_sparse_table.H>
+# include <algorithm>
# include <iostream>
# include <iomanip>
# include <chrono>
# include <random>
+# include <string>
+# include <utility>
# include <vector>📝 Committable suggestion
‼️ IMPORTANT
Carefully review the code before committing. Ensure that it accurately replaces the highlighted code, contains no missing lines, and has no issues with indentation. Thoroughly test & benchmark the code to ensure it meets the requirements.
| # include <tpl_cartesian_tree.H> | |
| # include <tpl_sparse_table.H> | |
| # include <iostream> | |
| # include <iomanip> | |
| # include <chrono> | |
| # include <random> | |
| # include <vector> | |
| # include <tpl_cartesian_tree.H> | |
| # include <tpl_sparse_table.H> | |
| # include <algorithm> | |
| # include <iostream> | |
| # include <iomanip> | |
| # include <chrono> | |
| # include <random> | |
| # include <string> | |
| # include <utility> | |
| # include <vector> |
🤖 Prompt for AI Agents
In `@Examples/cartesian_tree_example.cc` around lines 58 - 66, Add the missing
standard headers to the top-of-file includes so uses of std::string, std::pair
and std::min are portable: include <string> to cover std::string, include
<utility> (or <tuple>) to cover std::pair, and include <algorithm> to cover
std::min; update the include block that currently has tpl_cartesian_tree.H,
tpl_sparse_table.H and the iostream/vector headers to also `#include` these three
standard headers.
| std::vector<int> data = {5, 2, 4, 7, 1, 3, 6, 8, 0, 9}; | ||
| std::cout << "Array: {5, 2, 4, 7, 1, 3, 6, 8, 0, 9}\n\n"; | ||
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| Cartesian_Tree_RMQ<int> ct_rmq(data); | ||
| Sparse_Table<int> sparse(data); | ||
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# Look for more constructors in tpl_cartesian_tree.H (around the constructor definitions)
sed -n '100,400p' tpl_cartesian_tree.H | grep -B 5 -A 10 "^ \(explicit \)\?Gen_Cartesian_Tree"Repository: lrleon/Aleph-w
Length of output: 2926
🏁 Script executed:
# Search for all constructors in tpl_sparse_table.H
sed -n '1,600p' tpl_sparse_table.H | grep -A 15 "Construct\|^ Gen_Sparse_Table"Repository: lrleon/Aleph-w
Length of output: 4329
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# Look at tpl_array.H to see if Array can be constructed from std::vector
sed -n '1,200p' tpl_array.H | head -150Repository: lrleon/Aleph-w
Length of output: 5199
Replace std::vector with Aleph containers in examples.
Both Cartesian_Tree_RMQ and Sparse_Table constructors accept Array<T> and DynList<T> directly. Use these Aleph containers instead of std::vector in the example code at lines 183–188 and 238–264 to follow the project's coding guidelines: "ALWAYS use Aleph containers when an equivalent exists; Standard library containers are ONLY permitted when no Aleph equivalent is available."
🤖 Prompt for AI Agents
In `@Examples/cartesian_tree_example.cc` around lines 183 - 188, Replace the
std::vector usage with an Aleph container (e.g., aleph::Array<int> or
aleph::DynList<int>) and pass that to Cartesian_Tree_RMQ<int> and
Sparse_Table<int>; update the variable declaration (replace "std::vector<int>
data = {...}" with an Aleph container initialized with the same elements),
ensure the appropriate Aleph container header is included and/or aleph namespace
is used, and leave the Cartesian_Tree_RMQ<int> ct_rmq(data) and
Sparse_Table<int> sparse(data) calls unchanged so they receive the Aleph
container directly.
| /** @brief Construct from an Array\<T\>. | ||
| * @param values source array. | ||
| * @param c comparator (default-constructed). | ||
| */ | ||
| Gen_Cartesian_Tree(const Array<T> & values, Comp c = Comp()) | ||
| : data_(values), root_(NONE), n_(values.size()), comp_(c) | ||
| { | ||
| init_and_build(); | ||
| } |
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Fill in required Doxygen tags for the new public APIs.
Several new public constructors/accessors (e.g., this Array ctor, plus the initializer_list/DynList/num overloads here and the public ctors in Gen_Euler_Tour_LCA/Gen_Cartesian_Tree_RMQ) are missing explicit @throws and time/space complexity notes. This violates the header doc rules and can trip the doc-coverage gate. Please add the missing tags consistently across the public API surface.
📝 Example adjustment (apply similarly to the other public APIs)
- /** `@brief` Construct from an Array<T>.
- * `@param` values source array.
- * `@param` c comparator (default-constructed).
- */
+ /** `@brief` Construct from an Array<T>.
+ * `@param` values source array.
+ * `@param` c comparator (default-constructed).
+ * `@throws` std::bad_alloc if internal arrays cannot be allocated.
+ * `@note` Complexity: O(n) time and O(n) space.
+ */As per coding guidelines, “All public member functions must have @brief description, @param for each parameter, @return if applicable, @throws if applicable, and time/space complexity in documentation” and “Doxygen must generate no warnings for changed files.”
🤖 Prompt for AI Agents
In `@tpl_cartesian_tree.H` around lines 198 - 206, Add the missing Doxygen tags
for the new public APIs: update the Gen_Cartesian_Tree(const Array<T>&, Comp)
constructor (and the initializer_list / DynList / num overloads) and the public
constructors in Gen_Euler_Tour_LCA and Gen_Cartesian_Tree_RMQ to include `@brief`,
`@param` for each parameter, `@throws` (e.g., bad_alloc or invalid_argument if
empty/invalid input), and explicit time/space complexity notes (big-O for
construction and memory), keeping the wording consistent with existing header
docs and applying the same tags/format across all new public member functions so
Doxygen emits no warnings.
Summary by CodeRabbit
Release Notes
New Features
Tests
Documentation
Improvements