construct huffman table directly on reversed elements

Change-Id: Ic42b6b1c03f10077d19d49a9e6544214834ba42f

huffman/src/detail/table_node.hpp

@@ -114,30 +114,36 @@ class table_node : public encoding<Symbol>
     return init_.node_size;
   }
   /// "Joins" two `table_node`s
-  /// @param lhs left table_node
   /// @param rhs right table_node
-  /// @pre `&lhs + lhs.node_size() == &rhs`
+  /// @param lhs left table_node
+  /// @pre `&rhs - rhs.node_size() == &lhs`
+  ///
+  /// Logically "join" `rhs` with the next adjacent node `lhs` "creating" an
+  /// internal node. This adds the frequency of `lhs` to `rhs`, left pads all
+  /// the codes of the internal nodes of `rhs` with 0s and left pads all the
+  /// code of the internal nodes of `lhs` with 1s.
   ///
-  /// Logically "join" `lhs` with the next adjacent node `rhs` "creating" an
-  /// internal node. This adds the frequency of `rhs` to `lhs`, left pads all
-  /// the codes of the internal nodes of `lhs` with 0s and left pads all the
-  /// code of the internal nodes of `rhs` with 1s.
+  /// @attention This is intended to be used with a reversed view of table
+  ///     elements.
   ///
-  friend constexpr auto join(table_node& lhs, table_node& rhs) -> void
+  friend constexpr auto join_reversed(table_node& rhs, table_node& lhs) -> void
   {
-    assert(
-        &lhs + lhs.node_size() == &rhs and "`lhs` and `rhs` are not adjacent");
+    assert(&rhs == &lhs + rhs.node_size() and  //
+           "`rhs` and `lhs` are not adjacent");
 
     const auto left_pad_with = [](auto b) {
       return [b](table_node& n) { b >> static_cast<code&>(n); };
     };
 
-    std::for_each(&lhs, &rhs, left_pad_with(bit{0}));
-    std::for_each(&rhs, &rhs + rhs.node_size(), left_pad_with(bit{1}));
+    std::for_each(&lhs + 1, &rhs + 1, left_pad_with(bit{0}));
+    std::for_each(
+        &lhs + (1 - static_cast<std::ptrdiff_t>(lhs.node_size())),
+        &lhs + 1,
+        left_pad_with(bit{1}));
 
     // NOLINTBEGIN(cppcoreguidelines-pro-type-union-access)
-    lhs.init_.frequency += rhs.frequency();
-    lhs.init_.node_size += rhs.node_size();
+    rhs.init_.frequency += lhs.frequency();
+    rhs.init_.node_size += lhs.node_size();
     // NOLINTEND(cppcoreguidelines-pro-type-union-access)
   }
 

huffman/src/table.hpp

@@ -69,18 +69,20 @@ class table
 
   constexpr auto encode_symbols() -> void
   {
+    auto reversed = std::views::reverse(table_);
+
     // precondition, audit
-    assert(std::ranges::is_sorted(table_));
+    assert(std::ranges::is_sorted(reversed));
 
-    const auto total_size = table_.size();
-    auto first = table_.begin();
-    const auto last = table_.end();
+    const auto total_size = reversed.size();
+    auto first = reversed.begin();
+    const auto last = reversed.end();
 
     while (first->node_size() != total_size) {
-      join(first[0], first[to_index(first->node_size())]);
+      join_reversed(first[0], first[to_index(first->node_size())]);
 
-      const auto has_higher_freq = [f = first->frequency()](const auto& n) {
-        return n.frequency() > f;
+      const auto has_higher_freq = [&first](const auto& n) {
+        return n.frequency() > first->frequency();
       };
 
       auto lower = first + to_index(first->node_size());
@@ -105,25 +107,26 @@ class table
       return;
     }
 
-    std::ranges::sort(table_);
+    auto reversed = std::views::reverse(table_);
+
+    std::ranges::sort(reversed);
 
     // precondition
     assert(
         std::ranges::unique(
-            table_, {}, [](const auto& elem) { return elem.symbol; })
+            reversed, {}, [](const auto& elem) { return elem.symbol; })
             .empty() and
         "a `table` cannot contain duplicate symbols");
 
     const auto frequencies = std::views::transform(
-        table_, [](const auto& elem) { return elem.frequency(); });
+        reversed, [](const auto& elem) { return elem.frequency(); });
     [[maybe_unused]] const auto total_freq =
         std::accumulate(std::cbegin(frequencies), std::cend(frequencies), 0UZ);
 
     encode_symbols();
 
     // postcondition
-    assert(total_freq == table_.front().frequency());
-    std::ranges::reverse(table_);
+    assert(total_freq == reversed.front().frequency());
   }
 
   constexpr auto set_skip_fields() -> void