graph/detail/d_ary_heap.hpp

//
//=======================================================================
// Copyright 2009 Trustees of Indiana University
// Authors: Jeremiah J. Willcock, Andrew Lumsdaine
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//=======================================================================
//
#ifndef BOOST_D_ARY_HEAP_HPP
#define BOOST_D_ARY_HEAP_HPP

#include <vector>
#include <cstddef>
#include <algorithm>
#include <utility>
#include <boost/assert.hpp>
#include <boost/static_assert.hpp>
#include <boost/shared_array.hpp>
#include <boost/property_map/property_map.hpp>

// WARNING: it is not safe to copy a d_ary_heap_indirect and then modify one of
// the copies.  The class is required to be copyable so it can be passed around
// (without move support from C++11), but it deep-copies the heap contents yet
// shallow-copies the index_in_heap_map.

namespace boost {

  // Swap two elements in a property map without assuming they model
  // LvaluePropertyMap -- currently not used
  template <typename PropMap>
  inline void property_map_swap(
         PropMap prop_map,
         const typename boost::property_traits<PropMap>::key_type& ka,
         const typename boost::property_traits<PropMap>::key_type& kb) {
    typename boost::property_traits<PropMap>::value_type va = get(prop_map, ka);
    put(prop_map, ka, get(prop_map, kb));
    put(prop_map, kb, va);
  }

  namespace detail {
    template <typename Value>
    class fixed_max_size_vector {
      boost::shared_array<Value> m_data;
      std::size_t m_size;

      public:
      typedef std::size_t size_type;
      fixed_max_size_vector(std::size_t max_size)
        : m_data(new Value[max_size]), m_size(0) {}
      std::size_t size() const {return m_size;}
      bool empty() const {return m_size == 0;}
      Value& operator[](std::size_t i) {return m_data[i];}
      const Value& operator[](std::size_t i) const {return m_data[i];}
      void push_back(Value v) {m_data[m_size++] = v;}
      void pop_back() {--m_size;}
      Value& back() {return m_data[m_size - 1];}
      const Value& back() const {return m_data[m_size - 1];}
    };
  }

  // D-ary heap using an indirect compare operator (use identity_property_map
  // as DistanceMap to get a direct compare operator).  This heap appears to be
  // commonly used for Dijkstra's algorithm for its good practical performance
  // on some platforms; asymptotically, it has an O(lg N) decrease-key
  // operation while that can be done in constant time on a relaxed heap.  The
  // implementation is mostly based on the binary heap page on Wikipedia and
  // online sources that state that the operations are the same for d-ary
  // heaps.  This code is not based on the old Boost d-ary heap code.
  //
  // - d_ary_heap_indirect is a model of UpdatableQueue as is needed for
  //   dijkstra_shortest_paths.
  //
  // - Value must model Assignable.
  // - Arity must be at least 2 (optimal value appears to be 4, both in my and
  //   third-party experiments).
  // - IndexInHeapMap must be a ReadWritePropertyMap from Value to
  //   Container::size_type (to store the index of each stored value within the
  //   heap for decrease-key aka update).
  // - DistanceMap must be a ReadablePropertyMap from Value to something
  //   (typedef'ed as distance_type).
  // - Compare must be a BinaryPredicate used as a less-than operator on
  //   distance_type.
  // - Container must be a random-access, contiguous container (in practice,
  //   the operations used probably require that it is std::vector<Value>).
  //
  template <typename Value,
            std::size_t Arity,
            typename IndexInHeapPropertyMap,
            typename DistanceMap,
            typename Compare = std::less<Value>,
            typename Container = std::vector<Value> >
  class d_ary_heap_indirect {
    BOOST_STATIC_ASSERT (Arity >= 2);

    public:
    typedef typename Container::size_type size_type;
    typedef Value value_type;
    typedef typename boost::property_traits<DistanceMap>::value_type key_type;
    typedef DistanceMap key_map;

    d_ary_heap_indirect(DistanceMap distance,
                        IndexInHeapPropertyMap index_in_heap,
                        const Compare& compare = Compare(),
                        const Container& data = Container())
      : compare(compare), data(data), distance(distance),
        index_in_heap(index_in_heap) {}
    /* Implicit copy constructor */
    /* Implicit assignment operator */

    size_type size() const {
      return data.size();
    }

    bool empty() const {
      return data.empty();
    }

    void push(const Value& v) {
      size_type index = data.size();
      data.push_back(v);
      put(index_in_heap, v, index);
      preserve_heap_property_up(index);
      verify_heap();
    }

    Value& top() {
      BOOST_ASSERT (!this->empty());
      return data[0];
    }

    const Value& top() const {
      BOOST_ASSERT (!this->empty());
      return data[0];
    }

    void pop() {
      BOOST_ASSERT (!this->empty());
      put(index_in_heap, data[0], (size_type)(-1));
      if (data.size() != 1) {
        data[0] = data.back();
        put(index_in_heap, data[0], (size_type)(0));
        data.pop_back();
        preserve_heap_property_down();
        verify_heap();
      } else {
        data.pop_back();
      }
    }

    // This function assumes the key has been updated (using an external write
    // to the distance map or such)
    // See http://coding.derkeiler.com/Archive/General/comp.theory/2007-05/msg00043.html
    void update(const Value& v) { /* decrease-key */
      size_type index = get(index_in_heap, v);
      preserve_heap_property_up(index);
      verify_heap();
    }

    bool contains(const Value& v) const {
      size_type index = get(index_in_heap, v);
      return (index != (size_type)(-1));
    }

    void push_or_update(const Value& v) { /* insert if not present, else update */
      size_type index = get(index_in_heap, v);
      if (index == (size_type)(-1)) {
        index = data.size();
        data.push_back(v);
        put(index_in_heap, v, index);
      }
      preserve_heap_property_up(index);
      verify_heap();
    }

    DistanceMap keys() const {
      return distance;
    }

    private:
    Compare compare;
    Container data;
    DistanceMap distance;
    IndexInHeapPropertyMap index_in_heap;

    // The distances being compared using compare and that are stored in the
    // distance map
    typedef typename boost::property_traits<DistanceMap>::value_type distance_type;

    // Get the parent of a given node in the heap
    static size_type parent(size_type index) {
      return (index - 1) / Arity;
    }

    // Get the child_idx'th child of a given node; 0 <= child_idx < Arity
    static size_type child(size_type index, std::size_t child_idx) {
      return index * Arity + child_idx + 1;
    }

    // Swap two elements in the heap by index, updating index_in_heap
    void swap_heap_elements(size_type index_a, size_type index_b) {
      using std::swap;
      Value value_a = data[index_a];
      Value value_b = data[index_b];
      data[index_a] = value_b;
      data[index_b] = value_a;
      put(index_in_heap, value_a, index_b);
      put(index_in_heap, value_b, index_a);
    }

    // Emulate the indirect_cmp that is now folded into this heap class
    bool compare_indirect(const Value& a, const Value& b) const {
      return compare(get(distance, a), get(distance, b));
    }

    // Verify that the array forms a heap; commented out by default
    void verify_heap() const {
      // This is a very expensive test so it should be disabled even when
      // NDEBUG is not defined
#if 0
      for (size_t i = 1; i < data.size(); ++i) {
        if (compare_indirect(data[i], data[parent(i)])) {
          BOOST_ASSERT (!"Element is smaller than its parent");
        }
      }
#endif
    }

    // Starting at a node, move up the tree swapping elements to preserve the
    // heap property
    void preserve_heap_property_up(size_type index) {
      size_type orig_index = index;
      size_type num_levels_moved = 0;
      // The first loop just saves swaps that need to be done in order to avoid
      // aliasing issues in its search; there is a second loop that does the
      // necessary swap operations
      if (index == 0) return; // Do nothing on root
      Value currently_being_moved = data[index];
      distance_type currently_being_moved_dist =
        get(distance, currently_being_moved);
      for (;;) {
        if (index == 0) break; // Stop at root
        size_type parent_index = parent(index);
        Value parent_value = data[parent_index];
        if (compare(currently_being_moved_dist, get(distance, parent_value))) {
          ++num_levels_moved;
          index = parent_index;
          continue;
        } else {
          break; // Heap property satisfied
        }
      }
      // Actually do the moves -- move num_levels_moved elements down in the
      // tree, then put currently_being_moved at the top
      index = orig_index;
      for (size_type i = 0; i < num_levels_moved; ++i) {
        size_type parent_index = parent(index);
        Value parent_value = data[parent_index];
        put(index_in_heap, parent_value, index);
        data[index] = parent_value;
        index = parent_index;
      }
      data[index] = currently_being_moved;
      put(index_in_heap, currently_being_moved, index);
      verify_heap();
    }

    // From the root, swap elements (each one with its smallest child) if there
    // are any parent-child pairs that violate the heap property
    void preserve_heap_property_down() {
      if (data.empty()) return;
      size_type index = 0;
      Value currently_being_moved = data[0];
      distance_type currently_being_moved_dist =
        get(distance, currently_being_moved);
      size_type heap_size = data.size();
      Value* data_ptr = &data[0];
      for (;;) {
        size_type first_child_index = child(index, 0);
        if (first_child_index >= heap_size) break; /* No children */
        Value* child_base_ptr = data_ptr + first_child_index;
        size_type smallest_child_index = 0;
        distance_type smallest_child_dist = get(distance, child_base_ptr[smallest_child_index]);
        if (first_child_index + Arity <= heap_size) {
          // Special case for a statically known loop count (common case)
          for (size_t i = 1; i < Arity; ++i) {
            Value i_value = child_base_ptr[i];
            distance_type i_dist = get(distance, i_value);
            if (compare(i_dist, smallest_child_dist)) {
              smallest_child_index = i;
              smallest_child_dist = i_dist;
            }
          }
        } else {
          for (size_t i = 1; i < heap_size - first_child_index; ++i) {
            distance_type i_dist = get(distance, child_base_ptr[i]);
            if (compare(i_dist, smallest_child_dist)) {
              smallest_child_index = i;
              smallest_child_dist = i_dist;
            }
          }
        }
        if (compare(smallest_child_dist, currently_being_moved_dist)) {
          swap_heap_elements(smallest_child_index + first_child_index, index);
          index = smallest_child_index + first_child_index;
          continue;
        } else {
          break; // Heap property satisfied
        }
      }
      verify_heap();
    }

  };

} // namespace boost

#endif // BOOST_D_ARY_HEAP_HPP