aocpp/dlx/src/dlx.cpp

// See http://en.wikipedia.org/wiki/Dancing_Links.

#include "dlx.hpp"

#include <limits>

using namespace dlx;

#define F(i,n) for(int i = 0; i < n; i++)

#define C(i,n,dir) for(cell_ptr i = (n)->dir; i != n; i = i->dir)

Dlx::Dlx() {
  root_ = Cell::ColNew();
  root_->LR_self();
}

Dlx::~Dlx() {
  for (auto const row : rtab_) {
    if (row) {
      Cell* next;
      for (auto cursor = row->R; cursor != row; cursor = next) {
        next = cursor->R;
        delete cursor;
      }
      delete row;
    }
  }
  for (auto const col : ctab_) {
    if (col) { delete col; }
  }
  delete root_;
}

auto Dlx::Rows() const -> std::size_t { return rtab_.size(); }
auto Dlx::Cols() const -> std::size_t { return ctab_.size(); }

auto Dlx::AddCol() -> void {
  auto c = Cell::ColNew();
  c->LR_insert(root_);
  c->n = Cols();
  ctab_.push_back(c);
}

auto Dlx::AddRow() -> void {
  rtab_.push_back(nullptr);
}
auto Dlx::AllocCol(std::size_t n) -> void {
  while(Cols() <= n) AddCol();
}

auto Dlx::AllocRow(std::size_t n) -> void {
  while(Rows() <= n) AddRow();
}


auto Dlx::MarkOptional(std::size_t col) -> void {
  AllocCol(col);
  auto c = ctab_[col];
  // Prevent undeletion by self-linking.
  c->LR_delete();
  c->LR_self();
}


auto Dlx::Set(std::size_t row, std::size_t col) -> void {
  // We don't bother sorting. DLX works fine with jumbled rows and columns.
  // We just have to watch out for duplicates. (Actually, I think the DLX code
  // works even with duplicates, though it would be inefficient.)
  //
  // For a given column, the UD list is ordered in the order that dlx_set()
  // is called, not by row number. Similarly for a given row and its LR list.
  AllocRow(row);
  AllocCol(col);
  auto c = ctab_[col];

  auto const new1 = [&]() -> Cell* {
    auto n = new Cell;
    n->n = row;
    n->c = c;
    c->s++;
    n->UD_insert(c);
    return n;
  };
  
  auto & r = rtab_[row];
  
  if (!r) {
    r = new1();
    r->LR_self();
    return;
  }

  // Ignore duplicates.
  if (r->c->n == col) return;

  for (auto cursor = r->R; cursor != r; cursor = cursor->R) {
    if (cursor->c->n == col) return;
  }

  // Otherwise insert at end of LR list.
  new1()->LR_insert(r);
}

auto Dlx::PickRow(std::size_t i) -> int {
  auto r = rtab_.at(i);
  if (!r) return 0;  // Empty row.
  r->c->CoverCol();
  for (auto j = r->R; j != r; j = j->R) {
    j->c->CoverCol();
  }

  return 0;
}


auto Dlx::RemoveRow(std::size_t i) -> int {
  auto & r = rtab_.at(i);
  if (!r) return 0;  // Empty row.
  r->UD_delete();
  r->c->s--;
  for (auto j = r->R; j != r; j = j->R) {
    j->UD_delete();
    j->c->s--;
  }
  r = nullptr;
  return 0;
}

auto Dlx::Solve(
  std::function<void(std::size_t, std::size_t, std::size_t)> try_cb,
  std::function<void()> undo_cb,
  std::function<void()> found_cb,
  std::function<void(std::size_t)> stuck_cb) -> void
{
  auto const recurse = [&](auto const& self) -> void {
    auto c = root_->R;
    if (c == root_) {
      found_cb();
      return;
    }

    auto s = std::numeric_limits<std::size_t>::max();  // S-heuristic: choose first most-constrained column.
    for (auto i = root_->R; i != root_; i = i->R) {
      if (i->s < s) {
        s = (c = i)->s;
      }
    }
    
    if (!s) {
      stuck_cb(c->n);
      return;
    }

    c->CoverCol();
    for (auto r = c->D; r != c; r = r->D) {
      try_cb(c->n, s, r->n);
      for (auto j = r->R; j != r; j = j->R) {
        j->c->CoverCol();
      }
      self(self);
      undo_cb();
      for (auto j = r->L; j != r; j=j->L) {
        j->c->UncoverCol();
      }
    }
    c->UncoverCol();
  };
  recurse(recurse);
}