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   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License, version 2.0,
   as published by the Free Software Foundation.

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   documentation.  The authors of MySQL hereby grant you an additional
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   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License, version 2.0, for more details.

   You should have received a copy of the GNU General Public License
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#include "sql/join_optimizer/online_cycle_finder.h"

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <numeric>
#include <unordered_map>
#include <utility>

#include "sql/mem_root_array.h"
#include "sql/sql_array.h"

struct MEM_ROOT;

OnlineCycleFinder::OnlineCycleFinder(MEM_ROOT *mem_root, int num_vertices)
    : m_order(Bounds_checked_array<int>::Alloc(mem_root, num_vertices)),
      m_position_of_node(
          Bounds_checked_array<int>::Alloc(mem_root, num_vertices)),
      m_visited(Bounds_checked_array<bool>::Alloc(mem_root, num_vertices)),
      m_to_shift(mem_root),
      m_edges(mem_root) {
  std::iota(m_order.begin(), m_order.end(), 0);
  std::iota(m_position_of_node.begin(), m_position_of_node.end(), 0);
  std::fill(m_visited.begin(), m_visited.end(), false);
}

bool OnlineCycleFinder::EdgeWouldCreateCycle(int a_idx, int b_idx) {
  assert(a_idx >= 0);
  assert(static_cast<size_t>(a_idx) < m_order.size());
  assert(b_idx >= 0);
  assert(static_cast<size_t>(b_idx) < m_order.size());
  if (a_idx == b_idx) {
    return true;
  }
  int const pos_of_a = m_position_of_node[a_idx];
  int const pos_of_b = m_position_of_node[b_idx];
  if (pos_of_a < pos_of_b) {
    // Already in the topologically desired order,
    // so we don't need to do any checks.
  } else {
    // We have B first, then A. This is the opposite of what we want.
    // See if we are allowed to move B to the right, by doing a depth-first
    // search. The DFS has two purposes:
    //
    //  1. It finds everything that must come after B, transitively
    //     (and marks it as visited).
    //  2. It sees if A is reachable from B (if so, we have a cycle).
    //
    // As an optimization, we only need to care about the nodes between
    // B and A; all the nodes that are after A won't be affected by moving
    // B to A's immediate right.
    std::fill(m_visited.begin(), m_visited.end(), false);
    if (DepthFirstSearch(b_idx, pos_of_a + 1, /*node_idx_to_avoid=*/a_idx)) {
      // Found a cycle.
      return true;
    }

    // Everything seen during the DFS must be moved to the right,
    // together with B, since it still needs to stay after B.
    MoveAllMarked(pos_of_b, pos_of_a + 1);
  }
  return false;
}

bool OnlineCycleFinder::AddEdge(int a_idx, int b_idx) {
  if (EdgeWouldCreateCycle(a_idx, b_idx)) {
    return true;
  }
  m_edges.emplace(a_idx, b_idx);
  return false;
}

bool OnlineCycleFinder::DepthFirstSearch(int node_idx, int upper_bound,
                                         int node_idx_to_avoid) {
  if (node_idx == node_idx_to_avoid) {
    // This node can reach A, so it must be to the left of A.
    // But our search started from B, which means that the node
    // needs to be to the right of B, ie. B < N < A.
    // But we're trying to add A < B, so we have a cycle.
    return true;
  }

  if (m_visited[node_idx]) {
    // Already seen through some other path; e.g., if we have X-Y and X-Z-Y,
    // we can just ignore Y the second time.
    return false;
  }
  if (m_position_of_node[node_idx] >= upper_bound) {
    // This node comes after A, so we don't care;
    // moving A before B won't affect it negatively.
    // (And we know we also cannot reach A.)
    return false;
  }

  m_visited[node_idx] = true;
  auto first_and_last = m_edges.equal_range(node_idx);
  for (auto dest_node_it = first_and_last.first;
       dest_node_it != first_and_last.second; ++dest_node_it) {
    int const dest_node_idx = dest_node_it->second;
    assert(m_position_of_node[dest_node_idx] > m_position_of_node[node_idx]);
    if (DepthFirstSearch(dest_node_idx, upper_bound, node_idx_to_avoid)) {
      // We found a cycle, so abort.
      return true;
    }
  }
  return false;
}

void OnlineCycleFinder::MoveAllMarked(int start_pos, int new_pos) {
  m_to_shift.clear();

  for (int i = start_pos; i < new_pos; ++i) {
    int const node_idx = m_order[i];
    if (m_visited[node_idx]) {
      // Needs to move to the right (after upper_bound).
      m_to_shift.push_back(node_idx);
    } else {
      // Not involved, so just leave it where it is, relatively speaking.
      Allocate(node_idx, i - m_to_shift.size());
    }
  }

  for (size_t i = 0; i < m_to_shift.size(); ++i) {
    Allocate(m_to_shift[i], new_pos + i - m_to_shift.size());
  }
}

void OnlineCycleFinder::DeleteEdge(int a_idx, int b_idx) {
  auto [begin, end] = m_edges.equal_range(a_idx);
  for (auto it = begin; it != end; ++it) {
    if (it->second == b_idx) {
      m_edges.erase(it);
      return;
    }
  }
  assert(false);
}
