tree_dp_test.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
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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*/
 
 
# include <gtest/gtest.h>
 
# include <limits>
# include <random>
# include <utility>
 
# include <Tree_DP.H>
 
using namespace Aleph;
 
using G = List_Graph<Graph_Node<int>, Graph_Arc<int>>;
 
namespace
{
  Array<size_t>
  brute_sum_distances(const size_t n,
                      const Array<std::pair<size_t, size_t>> & edges)
  {
    Array<Array<size_t>> adj;
    adj.reserve(n);
    for (size_t i = 0; i < n; ++i)
      adj.append(Array<size_t>());
 
    for (size_t i = 0; i < edges.size(); ++i)
      {
        const size_t u = edges[i].first;
        const size_t v = edges[i].second;
        adj(u).append(v);
        adj(v).append(u);
      }
 
    Array<size_t> sums = Array<size_t>::create(n);
    for (size_t src = 0; src < n; ++src)
      {
        Array<size_t> dist = Array<size_t>::create(n);
        for (size_t i = 0; i < n; ++i)
          dist(i) = std::numeric_limits<size_t>::max();
 
        Array<size_t> q;
        q.append(src);
        dist(src) = 0;
 
        for (size_t head = 0; head < q.size(); ++head)
          {
            const size_t u = q[head];
            for (size_t j = 0; j < adj[u].size(); ++j)
              {
                const size_t v = adj[u][j];
                if (dist[v] != std::numeric_limits<size_t>::max())
                  continue;
                dist(v) = dist[u] + 1;
                q.append(v);
              }
          }
 
        size_t sum = 0;
        for (size_t i = 0; i < n; ++i)
          sum += dist[i];
        sums(src) = sum;
      }
    return sums;
  }
} // namespace
 
 
// Helper to build a path tree: 0 -- 1 -- 2 -- ... -- (n-1)
static G build_path(size_t n, Array<G::Node *> & nodes)
{
  G g;
  nodes = Array<G::Node *>::create(n);
  for (size_t i = 0; i < n; ++i)
    nodes(i) = g.insert_node(static_cast<int>(i));
  for (size_t i = 0; i + 1 < n; ++i)
    g.insert_arc(nodes(i), nodes(i + 1), 1);
  return g;
}
 
// Helper to build a star tree: center=0, leaves=1..n-1
static G build_star(size_t n, Array<G::Node *> & nodes)
{
  G g;
  nodes = Array<G::Node *>::create(n);
  for (size_t i = 0; i < n; ++i)
    nodes(i) = g.insert_node(static_cast<int>(i));
  for (size_t i = 1; i < n; ++i)
    g.insert_arc(nodes(0), nodes(i), 1);
  return g;
}
 
 
// ── Subtree sizes ─────────────────────────────────────────────────
 
TEST(TreeDP, SubtreeSizes_Path)
{
  Array<G::Node *> nodes;
  auto g = build_path(5, nodes);
  // Root at node 0: 0-1-2-3-4
  // subtree(0) = 5, subtree(1) = 4, ..., subtree(4) = 1
  auto sizes = tree_subtree_sizes(g, nodes(0));
  EXPECT_EQ(sizes.size(), 5u);
 
  // Find the ids. Use Tree_DP to get the mapping.
  Gen_Tree_DP<G, size_t> dp(g, nodes(0),
    [](auto *) -> size_t { return 1; },
    [](auto *, const size_t & a, auto *, const size_t & c) -> size_t {
      return a + c;
    });
 
  for (size_t i = 0; i < 5; ++i)
    EXPECT_EQ(dp.value(nodes(i)), 5 - i)
      << "Subtree of node " << i;
}
 
TEST(TreeDP, SubtreeSizes_Star)
{
  Array<G::Node *> nodes;
  auto g = build_star(5, nodes);
  // Root at center: subtree(center) = 5, subtree(leaf) = 1
  Gen_Tree_DP<G, size_t> dp(g, nodes(0),
    [](auto *) -> size_t { return 1; },
    [](auto *, const size_t & a, auto *, const size_t & c) -> size_t {
      return a + c;
    });
 
  EXPECT_EQ(dp.value(nodes(0)), 5u);
  for (size_t i = 1; i < 5; ++i)
    EXPECT_EQ(dp.value(nodes(i)), 1u);
}
 
TEST(TreeDP, SubtreeSizes_SingleNode)
{
  G g;
  auto n = g.insert_node(0);
  auto sizes = tree_subtree_sizes(g, n);
  EXPECT_EQ(sizes.size(), 1u);
  EXPECT_EQ(sizes[0], 1u);
}
 
 
// ── Max distance (eccentricity via rerooting) ─────────────────────
 
TEST(TreeDP, MaxDistance_Path)
{
  Array<G::Node *> nodes;
  auto g = build_path(5, nodes);
  // Path 0-1-2-3-4: max distance from each node
  // node 0: max dist = 4
  // node 1: max dist = 3
  // node 2: max dist = 2
  // node 3: max dist = 3
  // node 4: max dist = 4
  auto dists = tree_max_distance(g, nodes(0));
 
  Gen_Reroot_DP<G, size_t> dp(g, nodes(0),
    size_t(0),
    [](auto *) -> size_t { return 0; },
    [](const size_t & a, const size_t & b) -> size_t {
      return std::max(a, b);
    },
    [](auto *, auto *, const size_t & v) -> size_t { return v + 1; });
 
  EXPECT_EQ(dp.value(nodes(0)), 4u);
  EXPECT_EQ(dp.value(nodes(1)), 3u);
  EXPECT_EQ(dp.value(nodes(2)), 2u);
  EXPECT_EQ(dp.value(nodes(3)), 3u);
  EXPECT_EQ(dp.value(nodes(4)), 4u);
}
 
TEST(TreeDP, MaxDistance_Star)
{
  Array<G::Node *> nodes;
  auto g = build_star(5, nodes);
  // Star with 5 nodes: center distance = 1, leaves distance = 2
  Gen_Reroot_DP<G, size_t> dp(g, nodes(0),
    size_t(0),
    [](auto *) -> size_t { return 0; },
    [](const size_t & a, const size_t & b) -> size_t {
      return std::max(a, b);
    },
    [](auto *, auto *, const size_t & v) -> size_t { return v + 1; });
 
  EXPECT_EQ(dp.value(nodes(0)), 1u);
  for (size_t i = 1; i < 5; ++i)
    EXPECT_EQ(dp.value(nodes(i)), 2u);
}
 
 
// ── Sum of distances (rerooting) ──────────────────────────────────
 
TEST(TreeDP, SumOfDistances_Path)
{
  Array<G::Node *> nodes;
  auto g = build_path(4, nodes);
  // Path 0-1-2-3
  // sum_dist(0) = 0+1+2+3 = 6
  // sum_dist(1) = 1+0+1+2 = 4
  // sum_dist(2) = 2+1+0+1 = 4
  // sum_dist(3) = 3+2+1+0 = 6
  auto dists = tree_sum_of_distances(g, nodes(0));
 
  using P = std::pair<size_t, size_t>;
  Gen_Reroot_DP<G, P> dp(g, nodes(0),
    P{0, 0},
    [](auto *) -> P { return {1, 0}; },
    [](const P & a, const P & b) -> P {
      return {a.first + b.first, a.second + b.second};
    },
    [](auto *, auto *, const P & v) -> P {
      return {v.first, v.second + v.first};
    });
 
  EXPECT_EQ(dp.value(nodes(0)).second, 6u);
  EXPECT_EQ(dp.value(nodes(1)).second, 4u);
  EXPECT_EQ(dp.value(nodes(2)).second, 4u);
  EXPECT_EQ(dp.value(nodes(3)).second, 6u);
}
 
 
// ── Error handling ────────────────────────────────────────────────
 
TEST(TreeDP, NotATree)
{
  // Create a graph with a cycle
  G g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  g.insert_arc(n0, n1, 1);
  g.insert_arc(n1, n2, 1);
  g.insert_arc(n2, n0, 1); // creates cycle
 
  EXPECT_THROW(tree_subtree_sizes(g, n0), std::domain_error);
}
 
TEST(TreeDP, DisconnectedGraph)
{
  G g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  auto n3 = g.insert_node(3);
  g.insert_arc(n0, n1, 1);
  g.insert_arc(n2, n3, 1);
  EXPECT_THROW(tree_subtree_sizes(g, n0), std::domain_error);
}
 
TEST(TreeDP, RootNotInGraph)
{
  G g1;
  auto r1 = g1.insert_node(1);
  (void) r1;
 
  G g2;
  auto external_root = g2.insert_node(42);
  EXPECT_THROW(tree_subtree_sizes(g1, external_root), std::domain_error);
}
 
TEST(TreeDP, ParallelEdgesAreIgnored)
{
  G g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  g.insert_arc(n0, n1, 1);
  g.insert_arc(n0, n1, 1); // duplicate edge
  g.insert_arc(n1, n2, 1);
 
  Gen_Tree_DP<G, size_t> dp(g, n0,
    [](auto *) -> size_t { return 1; },
    [](auto *, const size_t & a, auto *, const size_t & c) -> size_t {
      return a + c;
    });
 
  EXPECT_EQ(dp.value(n0), 3u);
  EXPECT_EQ(dp.value(n1), 2u);
  EXPECT_EQ(dp.value(n2), 1u);
}
 
TEST(TreeDP, BinaryTree)
{
  //       0
  //      / |
  //     1   2
  //    / |
  //   3   4
  G g;
  auto n0 = g.insert_node(0);
  auto n1 = g.insert_node(1);
  auto n2 = g.insert_node(2);
  auto n3 = g.insert_node(3);
  auto n4 = g.insert_node(4);
  g.insert_arc(n0, n1, 1);
  g.insert_arc(n0, n2, 1);
  g.insert_arc(n1, n3, 1);
  g.insert_arc(n1, n4, 1);
 
  Gen_Tree_DP<G, size_t> dp(g, n0,
    [](auto *) -> size_t { return 1; },
    [](auto *, const size_t & a, auto *, const size_t & c) -> size_t {
      return a + c;
    });
 
  EXPECT_EQ(dp.value(n0), 5u);
  EXPECT_EQ(dp.value(n1), 3u);
  EXPECT_EQ(dp.value(n2), 1u);
  EXPECT_EQ(dp.value(n3), 1u);
  EXPECT_EQ(dp.value(n4), 1u);
}
 
TEST(TreeDP, RandomSumOfDistancesVsBfs)
{
  std::mt19937 rng(20260226);
 
  for (int trial = 0; trial < 80; ++trial)
    {
      const size_t n = 2 + rng() % 40;
      G g;
      Array<G::Node *> nodes = Array<G::Node *>::create(n);
      for (size_t i = 0; i < n; ++i)
        nodes(i) = g.insert_node(static_cast<int>(i));
 
      Array<std::pair<size_t, size_t>> edges;
      edges.reserve(n - 1);
      for (size_t i = 1; i < n; ++i)
        {
          const size_t p = static_cast<size_t>(rng() % i);
          g.insert_arc(nodes(p), nodes(i), 1);
          edges.append(std::make_pair(p, i));
        }
 
      const auto brute = brute_sum_distances(n, edges);
      const auto fast = tree_sum_of_distances(g, nodes(0));
 
      Gen_Tree_DP<G, size_t> map(g, nodes(0),
        [](auto *) -> size_t { return 1; },
        [](auto *, const size_t & a, auto *, const size_t & c) -> size_t {
          return a + c;
        });
 
      for (size_t i = 0; i < n; ++i)
        {
          const size_t id = map.id_of(nodes(i));
          EXPECT_EQ(fast[id], brute[i])
            << "trial=" << trial << " node=" << i;
        }
    }
}