docs: align doc variable names with code (#253)

* docs: align doc variable names with code

Doc comments referenced le/ri while the actual parameters and loop variables are named l/r. Also fix the functional graph doc to name the returned childs member, correct the find_substr comment, and reformat the cart_k_ary_tree example block.

* [auto-verifier] verify commit 28b17cf

---------

Co-authored-by: GitHub <noreply@github.com>

Author: cameroncuster

.verify-helper/timestamps.remote.json

@@ -35,7 +35,7 @@
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2026-07-07 10:02:09 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2026-07-06 13:10:16 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2026-07-06 13:10:16 -0700",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2026-07-09 23:01:31 -0500",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2026-07-10 20:39:22 -0700",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2026-07-10 20:39:22 -0700",
@@ -74,11 +74,11 @@
 "tests/library_checker_aizu_tests/graphs/strongly_connected_components_aizu.test.cpp": "2026-07-19 15:46:31 -0700",
 "tests/library_checker_aizu_tests/graphs/strongly_connected_components_lib_checker.test.cpp": "2026-07-19 15:46:31 -0700",
 "tests/library_checker_aizu_tests/graphs/two_edge_components.test.cpp": "2026-07-07 12:06:00 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/count_paths.test.cpp": "2026-07-19 15:46:31 -0700",
+"tests/library_checker_aizu_tests/handmade_tests/count_paths.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/dsu.test.cpp": "2026-07-07 12:06:00 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2026-07-19 15:46:31 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/fib_matrix_expo.test.cpp": "2026-07-07 12:06:00 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/functional_graph.test.cpp": "2026-07-07 12:06:00 -0700",
+"tests/library_checker_aizu_tests/handmade_tests/functional_graph.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/hilbert_mos.test.cpp": "2026-07-10 20:39:22 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/kd_bit.test.cpp": "2026-07-07 12:06:00 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/kth_par.test.cpp": "2026-07-10 20:39:22 -0700",
@@ -89,13 +89,13 @@
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2026-07-07 12:06:00 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2026-07-12 12:50:20 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2026-07-12 12:50:20 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2026-07-07 12:06:00 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_midpoint.test.cpp": "2026-07-07 09:17:02 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/xor_basis_walk.test.cpp": "2026-07-07 12:06:00 -0700",
 "tests/library_checker_aizu_tests/loops/chooses.test.cpp": "2026-07-06 13:10:16 -0700",
-"tests/library_checker_aizu_tests/loops/quotients.test.cpp": "2026-07-06 13:10:16 -0700",
+"tests/library_checker_aizu_tests/loops/quotients.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/loops/submasks.test.cpp": "2026-07-08 09:28:48 -0700",
 "tests/library_checker_aizu_tests/loops/supermasks.test.cpp": "2026-07-06 13:10:16 -0700",
 "tests/library_checker_aizu_tests/math/binary_matrix_mult.test.cpp": "2026-07-06 13:10:16 -0700",
@@ -111,24 +111,24 @@
 "tests/library_checker_aizu_tests/math/tetration.test.cpp": "2026-07-10 20:39:22 -0700",
 "tests/library_checker_aizu_tests/math/totient.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2026-07-07 12:06:00 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2026-07-07 12:06:00 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2026-07-08 09:28:48 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/strings/lcp_query_zfunc.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/strings/lcp_query_zfunc.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/strings/lcs_dp.test.cpp": "2026-07-19 15:32:29 -0700",
 "tests/library_checker_aizu_tests/strings/lcs_queries.test.cpp": "2026-07-19 15:32:29 -0700",
 "tests/library_checker_aizu_tests/strings/lcs_queries_merge_sort_tree.test.cpp": "2026-07-19 15:32:29 -0700",
 "tests/library_checker_aizu_tests/strings/manacher.test.cpp": "2026-07-19 15:32:29 -0700",
-"tests/library_checker_aizu_tests/strings/multi_matching_bs.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/strings/multi_matching_bs.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/strings/prefix_function.test.cpp": "2026-07-06 13:10:16 -0700",
-"tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2026-07-19 15:32:29 -0700",
-"tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2026-07-12 12:50:20 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2026-07-06 13:10:16 -0700",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2026-07-07 12:06:00 -0700",
@@ -142,12 +142,12 @@
 "tests/library_checker_aizu_tests/trees/hld_lib_checker_path.test.cpp": "2026-07-10 20:39:22 -0700",
 "tests/library_checker_aizu_tests/trees/hld_lib_checker_subtree_edges.test.cpp": "2026-07-10 20:39:22 -0700",
 "tests/library_checker_aizu_tests/trees/hld_lib_checker_subtree_nodes.test.cpp": "2026-07-10 20:39:22 -0700",
-"tests/library_checker_aizu_tests/trees/kth_path_hagerup.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/trees/kth_path_hagerup.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/trees/kth_path_ladder.test.cpp": "2026-07-09 23:01:31 -0500",
 "tests/library_checker_aizu_tests/trees/kth_path_linear.test.cpp": "2026-07-10 20:39:22 -0700",
-"tests/library_checker_aizu_tests/trees/kth_path_tree_lift.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2026-07-12 12:50:20 -0700",
-"tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2026-07-12 12:50:20 -0700",
+"tests/library_checker_aizu_tests/trees/kth_path_tree_lift.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2026-08-17 17:35:30 -0700",
+"tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2026-08-17 17:35:30 -0700",
 "tests/library_checker_aizu_tests/trees/shallowest_aizu_tree_height.test.cpp": "2026-07-19 15:46:31 -0700",
 "tests/library_checker_aizu_tests/trees/shallowest_lib_checker_tree_path_composite.test.cpp": "2026-07-19 15:46:31 -0700",
 "tests/library_checker_aizu_tests/trees/subtree_isomorphism.test.cpp": "2026-07-19 15:46:31 -0700"

library/graphs/uncommon/functional_graph_processor.hpp

@@ -8,7 +8,7 @@
 //!   bool is_on_cycle = (v == root);
 //! @endcode
 //! root = first reachable node on cycle from v
-//! t[v].childs = forest of reversed edges not in cycles
+//! childs = forest of reversed edges not in cycles
 //! @time O(n)
 //! @space O(n)
 auto func_graph(const vi& a) {

library/loops/quotients.hpp

@@ -1,10 +1,10 @@
 #pragma once
 //! https://github.com/tfg50/Competitive-Programming/blob/master/Biblioteca/Math/DivisionTrick.cpp
-//! i-th iteration gives an interval [le_i, ri_i]:
-//!   - for all i in [le_i, ri_i]: n / i is the same
-//!   - le_0 = 1
-//!   - ri_last = n
-//!   - ri_i + 1 = le_(i+1)
+//! i-th iteration gives an interval [l_i, r_i]:
+//!   - for all i in [l_i, r_i]: n / i is the same
+//!   - l_0 = 1
+//!   - r_last = n
+//!   - r_i + 1 = l_(i+1)
 //! @time O(sqrt(n))
 //! @space O(1)
 for (ll l = 1, r; l <= n && (r = n / (n / l)); l = r + 1) 

library/monotonic_stack/cartesian_binary_tree.hpp

@@ -2,8 +2,8 @@
 #include "monotonic_stack.hpp"
 //! @code
 //!   // right-most min is root
-//!   auto le = mono_st(a, less());
-//!   auto p = cart_binary_tree(le);
+//!   auto l = mono_st(a, less());
+//!   auto p = cart_binary_tree(l);
 //!
 //!   // less_equal() -> left-most min is root
 //!   // greater() -> right-most max is root

library/monotonic_stack/cartesian_k_ary_tree.hpp

@@ -20,11 +20,10 @@
 //! p[5] = 9
 //!
 //! @code
-//!     auto le = mono_st(a, less()), p =
-//!     cart_k_ary_tree(a, le); // min cart tree auto le =
-//!     mono_st(a, greater()), p = cart_k_ary_tree(a, le);
-//!     // max cart tree bool is_node = (p[i] < i || a[i]
-//!     != a[p[i]]);
+//!   auto l = mono_st(a, less());    // min cart tree
+//!   auto l = mono_st(a, greater()); // max cart tree
+//!   auto p = cart_k_ary_tree(a, l);
+//!   bool is_node = (p[i] < i || a[i] != a[p[i]]);
 //! @endcode
 //!
 //! @param a,l array and its left-monotonic stack

library/monotonic_stack/monotonic_range.hpp

@@ -1,12 +1,12 @@
 #pragma once
 #include "monotonic_stack.hpp"
 //! @code
-//!   vector<int> le = mono_st(a, less()),
-//!     ri = mono_range(le);
+//!   vector<int> l = mono_st(a, less()),
+//!     r = mono_range(l);
 //!   // less_equal(), greater(), greater_equal()
 //! @endcode
 //! when cmp == less():
-//!   a[le[i]] < a[i] >= a[ri[i]]
+//!   a[l[i]] < a[i] >= a[r[i]]
 //! @time O(n)
 //! @space O(n)
 vi mono_range(const vi& l) {

library/monotonic_stack/monotonic_stack.hpp

@@ -1,10 +1,10 @@
 #pragma once
 //! @code
-//!   vector<int> le = mono_st(a, less());
+//!   vector<int> l = mono_st(a, less());
 //!   // less_equal(), greater(), greater_equal()
 //! @endcode
 //! when cmp == less():
-//!   a[le[i]] < a[i]
+//!   a[l[i]] < a[i]
 //! @time O(n)
 //! @space O(n)
 vi mono_st(const auto& a, const auto& cmp) {

library/strings/suffix_array/find/find_substring.hpp

@@ -8,7 +8,7 @@
 //! requires s_l < n
 //! for all i in [sa_le,sa_ri): s.substr(s_l,s_r-s_l)
 //!   == s.substr(sa[i],s_r-s_l)
-//!   - `r-l` is the # of matches of
+//!   - `sa_ri-sa_le` is the # of matches of
 //!       s.substr(s_l, s_r - s_l) in s.
 //! @time O(log(|s|))
 //! @space O(1)