splay-tree.cc

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
#include <algorithm>
#include <vector>
 
#include <gtest/gtest.h>
 
#include <tpl_splay_tree.H>
 
using namespace Aleph;
 
namespace
{
  template <class Node>
  size_t count_nodes(Node * root) noexcept
  {
    if (root == Node::NullPtr)
      return 0;
    return 1 + count_nodes(LLINK(root)) + count_nodes(RLINK(root));
  }
 
  template <class Node>
  std::vector<typename Node::key_type> inorder_keys(Node * root)
  {
    std::vector<typename Node::key_type> keys;
    if (root == Node::NullPtr)
      return keys;
 
    auto left = inorder_keys(LLINK(root));
    keys.insert(keys.end(), left.begin(), left.end());
    keys.push_back(KEY(root));
    auto right = inorder_keys(RLINK(root));
    keys.insert(keys.end(), right.begin(), right.end());
    return keys;
  }
 
  template <class Tree>
  void assert_valid_tree(Tree & tree)
  {
    ASSERT_TRUE(tree.verify()) << "BST invariant violated";
  }
 
  template <class Tree>
  struct NodePool
  {
    using Node = typename Tree::Node;
    std::vector<Node *> allocated;
 
    Node * make(typename Node::key_type k)
    {
      auto * p = new Node(k);
      allocated.push_back(p);
      return p;
    }
 
    void forget(Node * p) noexcept
    {
      for (auto & q : allocated)
        if (q == p)
          {
            q = nullptr;
            return;
          }
    }
 
    ~NodePool()
    {
      for (auto * p : allocated)
        delete p;
    }
  };
 
  struct StatefulLess
  {
    bool use_abs = false;
 
    StatefulLess() = default;
    explicit StatefulLess(bool b) : use_abs(b) {}
 
    bool operator()(int a, int b) const
    {
      if (use_abs)
        {
          a = std::abs(a);
          b = std::abs(b);
        }
      return a < b;
    }
  };
 
} // namespace
 
TEST(SplayTree, EmptyTreeProperties)
{
  Splay_Tree<int> tree;
  EXPECT_EQ(tree.getRoot(), Splay_Tree<int>::Node::NullPtr);
  EXPECT_EQ(tree.search(42), nullptr);
  EXPECT_EQ(tree.remove(42), nullptr);
  EXPECT_TRUE(tree.verify());
}
 
TEST(SplayTree, InsertSingleElementBecomesRoot)
{
  using Tree = Splay_Tree<int>;
  using Node = Tree::Node;
 
  Tree tree;
  NodePool<Tree> pool;
 
  auto * p = pool.make(7);
  EXPECT_EQ(tree.insert(p), p);
  EXPECT_EQ(tree.getRoot(), p);
  assert_valid_tree(tree);
  EXPECT_EQ(count_nodes<Node>(tree.getRoot()), 1u);
}
 
TEST(SplayTree, InsertRejectsDuplicates)
{
  using Tree = Splay_Tree<int>;
  using Node = Tree::Node;
 
  Tree tree;
  NodePool<Tree> pool;
 
  auto * p1 = pool.make(10);
  EXPECT_EQ(tree.insert(p1), p1);
 
  auto * p2 = pool.make(10);
  EXPECT_EQ(tree.insert(p2), nullptr);
 
  assert_valid_tree(tree);
  EXPECT_EQ(count_nodes<Node>(tree.getRoot()), 1u);
}
 
TEST(SplayTree, InsertDupAllowsDuplicates)
{
  using Tree = Splay_Tree<int>;
  using Node = Tree::Node;
 
  Tree tree;
  NodePool<Tree> pool;
 
  for (int i = 0; i < 5; ++i)
    ASSERT_NE(tree.insert_dup(pool.make(42)), nullptr);
 
  assert_valid_tree(tree);
  EXPECT_EQ(count_nodes<Node>(tree.getRoot()), 5u);
 
  auto keys = inorder_keys(tree.getRoot());
  EXPECT_EQ(keys, (std::vector<int>{42, 42, 42, 42, 42}));
}
 
TEST(SplayTree, SearchFindsExistingKeyAndSplaysToRoot)
{
  using Tree = Splay_Tree<int>;
 
  Tree tree;
  NodePool<Tree> pool;
 
  for (int k : {5, 3, 7, 1, 4, 6, 8})
    tree.insert(pool.make(k));
 
  auto * found = tree.search(4);
  ASSERT_NE(found, nullptr);
  EXPECT_EQ(KEY(found), 4);
  EXPECT_EQ(tree.getRoot(), found);
 
  assert_valid_tree(tree);
}
 
TEST(SplayTree, SearchMissingSplaysToExtreme)
{
  using Tree = Splay_Tree<int>;
 
  Tree tree;
  NodePool<Tree> pool;
 
  for (int k : {1, 3, 5})
    tree.insert(pool.make(k));
 
  EXPECT_EQ(tree.search(0), nullptr);
  ASSERT_NE(tree.getRoot(), Tree::Node::NullPtr);
  EXPECT_EQ(KEY(tree.getRoot()), 1);
 
  EXPECT_EQ(tree.search(6), nullptr);
  ASSERT_NE(tree.getRoot(), Tree::Node::NullPtr);
  EXPECT_EQ(KEY(tree.getRoot()), 5);
 
  assert_valid_tree(tree);
}
 
TEST(SplayTree, SearchOrInsertDoesNotInsertDuplicate)
{
  using Tree = Splay_Tree<int>;
  using Node = Tree::Node;
 
  Tree tree;
  NodePool<Tree> pool;
 
  auto * p1 = pool.make(10);
  EXPECT_EQ(tree.search_or_insert(p1), p1);
 
  auto * p2 = pool.make(10);
  auto * ret2 = tree.search_or_insert(p2);
  EXPECT_EQ(ret2, p1);
 
  assert_valid_tree(tree);
  EXPECT_EQ(count_nodes<Node>(tree.getRoot()), 1u);
}
 
TEST(SplayTree, RemoveExistingKeyDetachesNode)
{
  using Tree = Splay_Tree<int>;
  using Node = Tree::Node;
 
  Tree tree;
  NodePool<Tree> pool;
 
  for (int k : {1, 2, 3, 4, 5})
    tree.insert(pool.make(k));
 
  Node * removed = tree.remove(3);
  ASSERT_NE(removed, nullptr);
  EXPECT_EQ(KEY(removed), 3);
  EXPECT_EQ(LLINK(removed), Node::NullPtr);
  EXPECT_EQ(RLINK(removed), Node::NullPtr);
 
  pool.forget(removed);
  delete removed;
 
  EXPECT_EQ(tree.search(3), nullptr);
  assert_valid_tree(tree);
 
  auto keys = inorder_keys(tree.getRoot());
  EXPECT_EQ(keys, (std::vector<int>{1, 2, 4, 5}));
}
 
TEST(SplayTree, RemoveSplaysMaxOfLeftSubtree)
{
  using Tree = Splay_Tree<int>;
  using Node = Tree::Node;
 
  Tree tree;
  NodePool<Tree> pool;
 
  for (int k : {1, 2, 3, 4, 5})
    tree.insert(pool.make(k));
 
  Node * removed = tree.remove(5);
  ASSERT_NE(removed, nullptr);
  pool.forget(removed);
  delete removed;
 
  ASSERT_NE(tree.getRoot(), Node::NullPtr);
  EXPECT_EQ(KEY(tree.getRoot()), 4);
  assert_valid_tree(tree);
}
 
TEST(SplayTree, StatefulComparatorAffectsEquality)
{
  using Tree = Splay_Tree<int, StatefulLess>;
  using Node = Tree::Node;
 
  Tree tree(StatefulLess(true));
  NodePool<Tree> pool;
 
  auto * p = pool.make(1);
  tree.insert(p);
 
  Node * found = tree.search(-1);
  ASSERT_NE(found, nullptr);
  EXPECT_EQ(found, p);
  EXPECT_EQ(tree.getRoot(), p);
  assert_valid_tree(tree);
}