path: root/utils/d_ary_heap.h

#ifndef D_ARY_HEAP_H
#define D_ARY_HEAP_H


#define D_ARY_PUSH_GRAEHL 0 // untested
#define D_ARY_POP_GRAEHL 0 // untested
#define D_ARY_DOWN_GRAEHL 0 // untested
#define D_ARY_UP_GRAEHL 0 // untested
#define D_ARY_APPEND_ALWAYS_PUSH 1 // heapify (0) is untested.  otherwise switch between push and heapify depending on size (cache effects, existing items vs. # appended ones)

#define D_ARY_TRACK_OUT_OF_HEAP 0 // shouldn't need to track, because in contains() false positives looking up stale or random loc map values are impossible - we just check key
#define D_ARY_VERIFY_HEAP 0
// This is a very expensive test so it should be disabled even when NDEBUG is not defined

/* adapted from boost/graph/detail/d_ary_heap.hpp

  local modifications:

  clear, heapify, append range/container, Size type template arg, reserve constructor arg

  hole+move rather than swap.  note: swap would be more efficient for heavyweight keys, until move ctors exist

  don't set locmap to -1 when removing from heap (waste of time)

  // unlike arity=2 case, you don't gain anything by having indices start at 1, with 0-based child indices
  // root @1, A=2, children indices m={0,1}: parent(i)=i/2, child(i,m)=2*i+m
  // root @0: parent(i)=(i-1)/A child(i,n)=i*A+n+1 - can't improve on this except child(i,m)=i*A+m
  (integer division, a/b=floor(a/b), so (i-1)/A = ceil(i/A)-1, or greatest int less than (i/A))

  actually, no need to adjust child index, since child is called only once and inline

  e.g. for A=3 gorn address in tree -> index

  () = root -> 0
  (1) -> 1
  (2) -> 2
  (3) (A) -> 3
  (1,1) -> (1*A+1) = 4
  (1,2) -> (1*A+2) = 5
  (1,3) -> (1*A+3) = 6
  (2,1) -> (2*A+1) = 7
  etc.

//TODO: block-align siblings!  assume data[0] is 16 or 32-byte aligned ... then we want root @ index (blocksize-1).  see http://www.lamarca.org/anthony/pubs/heaps.pdf pg8.  for pow2(e.g. 4)-ary heap, it may be reasonable to  use root @index A-1.  however, suppose the key size is not padded to a power of 2 (e.g. 12 bytes), then we would need internal gaps at times.  would want to use compile const template based inlineable alignment math for this?  possibly use a container like vector that lets you specify padding relative to some address multiple for v[0].

 optimal D: see http://www.lamarca.org/anthony/pubs/heaps.pdf pg 9.  depedns on relative cost of swap,compare, but in all cases except swap=free, 2 is worse than 3-4.  for expensive swap (3x compare), 4 still as good as 5.  so just use 4.  boost benchmarking djikstra agrees; 4 is best.

 cache-aligned 4-heap speedup over regular 2-heap is 10-80% (for huge heaps, the speedup is more)

 splay/skew heaps are worse than 2heap or aligned 4heap in practice.

 //TODO: switch from heapify (Floyd's method) to repeated push past some size limit (in bytes) due to cache effect -
 #define D_ARY_BYTES_OUT_OF_CACHE 0x1000000

 //TODO: assuming locmap is an lvalue pmap, we can be more efficient.  on the other hand, if it's an intrusive property map to an interned mutable object, there's no difference in performance, and that's what i'm going to do in my first uses.  plus, if keys are indices and the map is a vector, it's barely any overhead.

 */

//
//=======================================================================
// 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)
//=======================================================================
//

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


  // 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's not optimal; it has an O(lg N) decrease-key
  // operation, which is (amortized) constant time on a relaxed heap or fibonacci 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 Better = std::less<Value>,
            typename Container = std::vector<Value>,
            typename Size = typename Container::size_type,
            typename Equal = std::equal_to<Value> >
  class d_ary_heap_indirect {
    BOOST_STATIC_ASSERT (Arity >= 2);
# undef D_ARY_HEAP_NULL_INDEX
# define D_ARY_HEAP_NULL_INDEX ((size_type)(-1))
    public:
    typedef Container container_type;
    typedef Size size_type;
    typedef Value value_type;
    typedef typename Container::const_iterator const_iterator;
    typedef const_iterator iterator;
    // The distances being compared using better and that are stored in the
    // distance map
    typedef typename boost::property_traits<DistanceMap>::value_type distance_type;
    d_ary_heap_indirect(DistanceMap const& distance,
                        IndexInHeapPropertyMap const& index_in_heap,
                        const Better& better = Better(),
                        size_type container_reserve = 100000,
                        Equal const& equal = Equal()
      )
      : better(better), data(), distance(distance),
        index_in_heap(index_in_heap) {
      data.reserve(container_reserve);
    }
    /* Implicit copy constructor */
    /* Implicit assignment operator */

    template <class C>
    void append_heapify(C const& c) {
      data.reserve(data.size()+c.size());
      append_heapify(c.begin(),c.end());
    }

    template <class I>
    void append_heapify(I begin,I end) {
      data.insert(data.end(),begin,end);
      heapify();
    }

    template <class C>
    void append_push(C const& c) {
      data.reserve(data.size()+c.size());
      append_push(c.begin(),c.end());
    }

    // past some threshold, this should be faster than append_heapify.  also, if there are many existing elements it will be faster.
    template <class I>
    void append_push(I begin,I end) {
      for (;begin!=end;++begin)
        push(*begin);
    }

    template <class C>
    void append(C const& c) {
      if (D_ARY_APPEND_ALWAYS_PUSH || data.size()>=c.size()/2)
        append_push(c);
      else
        append_heapify(c);
    }

    // past some threshold, this should be faster than append_heapify.  also, if there are many existing elements it will be faster.
    template <class I>
    void append(I begin,I end) {
      if (D_ARY_APPEND_ALWAYS_PUSH || data.size()>=0x10000)
        append_push(begin,end);
      else
        append_heapify(begin,end);
    }

    // could allow mutation of data directly, e.g. push_back 1 at a time - but then they could forget to heapify()

    //from bottom of heap tree up, turn that subtree into a heap by adjusting the root down
    // for n=size, array elements indexed by floor(n/2) + 1, floor(n/2) + 2, ... , n are all leaves for the tree, thus each is an one-element heap already
    // warning: this is many fewer instructions but, at some point (when heap doesn't fit in Lx cache) it will become slower than repeated push().
    void heapify() {
      for (size_type i=parent(data.size()-1);i>0;--i) // starting from parent of last node, ending at first child of root (i==1)
        preserve_heap_property_down(i);
    }

    void reserve(size_type s) {
      data.reserve(s);
    }

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

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

    const_iterator begin() const {
      return data.begin();
    }

    const_iterator end() const {
      return data.end();
    }

    void clear() {
#if D_ARY_TRACK_OUT_OF_HEAP
      using boost::put;
      for (typename Container::iterator i=data.begin(),e=data.end();i!=e;++i)
        put(index_in_heap,*i,D_ARY_HEAP_NULL_INDEX);
#endif
      data.clear();
    }

    void push(const Value& v) {
      if (D_ARY_PUSH_GRAEHL) {
        size_type i = data.size();
        data.push_back(Value()); // (hoping default construct is cheap, construct-copy inline)
        preserve_heap_property_up(v,i); // we don't have to recopy v, or init index_in_heap
      } else {
        size_type index = data.size();
        data.push_back(v);
        using boost::put;
        put(index_in_heap, v, index);
        preserve_heap_property_up(index);
      }
      verify_heap();
    }

    Value& top() {
      return data[0];
    }

    const Value& top() const {
      return data[0];
    }

    void pop() {
      using boost::put;
      if(D_ARY_TRACK_OUT_OF_HEAP)
        put(index_in_heap, data[0], D_ARY_HEAP_NULL_INDEX);
      if (data.size() != 1) {
        if (D_ARY_POP_GRAEHL) {
          preserve_heap_property_down(data.back(),0,data.size()-1);
          data.pop_back();
        } else {
          data[0] = data.back();
          put(index_in_heap, data[0], 0);
          data.pop_back();
          preserve_heap_property_down();
        }
        verify_heap();
      } else {
        data.pop_back();
      }
    }

    // This function assumes the key has been improved
    // (distance has become smaller, so it may need to rise toward top().
    // i.e. decrease-key in a min-heap
    void update(const Value& v) {
      using boost::get;
      size_type index = get(index_in_heap, v);
      preserve_heap_property_up(v,index);
      verify_heap();
    }

    // return true if improved.
    bool maybe_improve(const Value& v,distance_type dbetter) {
      using boost::get;
      if (better(dbetter,get(distance,v))) {
        preserve_heap_property_up_dist(v,dbetter);
        return true;
      }
      return false;
    }


#include "warning_push.h"
#pragma GCC diagnostic ignored "-Wtype-limits"
      // because maybe size_type is signed or unsigned
    inline bool contains(const Value &v,size_type i) const {
      return D_ARY_TRACK_OUT_OF_HEAP ?
        (i != D_ARY_HEAP_NULL_INDEX) :
        i>=0 && i<data.size() && equal(v,data[i]); // note: size_type may be signed (don't recommend it, though) - thus i>=0 check to catch uninit. data
    }
#include "warning_pop.h"

    inline bool contains(const Value& v) const {
      using boost::get;
      return contains(v,get(index_in_heap, v));
    }

    void push_or_update(const Value& v) { /* insert if not present, else update */
      using boost::get;
      size_type index = get(index_in_heap, v);
      if (D_ARY_PUSH_GRAEHL) {
        if (contains(v,index))
          preserve_heap_property_up(v,index);
        else
          push(v);
      } else {
        if (!contains(v,index)) {
          index = data.size();
          data.push_back(v);
          using boost::put;
          put(index_in_heap, v, index);
        }
        preserve_heap_property_up(index);
      }
      verify_heap();
    }

    private:
    Equal equal;
    Better better;
    Container data;
    DistanceMap distance;
    IndexInHeapPropertyMap index_in_heap;

    // Get the parent of a given node in the heap
    static inline 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 inline 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
    inline 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;
      using boost::put;
      put(index_in_heap, value_a, index_b);
      put(index_in_heap, value_b, index_a);
    }

    inline void move_heap_element(Value const& v,size_type ito) {
      using boost::put;
      put(index_in_heap,v,ito);
      data[ito]=v; //todo: move assign?
    }

    // 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 D_ARY_VERIFY_HEAP
      using boost::get;
      for (size_t i = 1; i < data.size(); ++i) {
        if (better(get(distance,data[i]), get(distance,data[parent(i)]))) {
          assert (!"Element is smaller than its parent");
        }
      }
#endif
    }

    // we have a copy of the key, so we don't need to do that stupid find # of levels to move then move.  we act as though data[index]=currently_being_moved, but in fact it's an uninitialized "hole", which we fill at the very end
    inline void preserve_heap_property_up(Value const& currently_being_moved,size_type index) {
      using boost::get;
      preserve_heap_property_up(currently_being_moved,index,get(distance,currently_being_moved));
    }

    inline void preserve_heap_property_up_set_dist(Value const& currently_being_moved,distance_type dbetter) {
      using boost::get;
      using boost::put;
      put(distance,currently_being_moved,dbetter);
      preserve_heap_property_up(currently_being_moved,get(index_in_heap,currently_being_moved),dbetter);
      verify_heap();
    }

    void preserve_heap_property_up(Value const& currently_being_moved,size_type index,distance_type currently_being_moved_dist) {
      using boost::put;
      using boost::get;
      if (D_ARY_UP_GRAEHL) {
        for (;;) {
          if (index == 0) break; // Stop at root
          size_type parent_index = parent(index);
          Value const& parent_value = data[parent_index];
          if (better(currently_being_moved_dist, get(distance, parent_value))) {
            move_heap_element(parent_value,index);
            index = parent_index;
          } else {
            break; // Heap property satisfied
          }
        }
        //finish "swap chain" by filling hole w/ currently_being_moved
        move_heap_element(currently_being_moved,index); // note: it's ok not to return early on index==0 at start, even if self-assignment isn't supported by Value - because currently_being_moved is a copy.
      } else {
        put(index_in_heap,currently_being_moved,index);
        put(distance,currently_being_moved,currently_being_moved_dist);
        preserve_heap_property_up(index);
      }
    }

    // Starting at a node, move up the tree swapping elements to preserve the
    // heap property.  doesn't actually use swap; uses hole
    void preserve_heap_property_up(size_type index) {
      using boost::get;
      if (index == 0) return; // Do nothing on root
      if (D_ARY_UP_GRAEHL) {
        Value copyi=data[index];
        preserve_heap_property_up(copyi,index);
        return;
      }
      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
      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 (better(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;
      using boost::put;
      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.  v is placed at data[i], but then pushed down (note: data[i] won't be read explicitly; it will instead be overwritten by percolation).  this also means that v must be a copy of data[i] if it was already at i.
    // e.g. v=data.back(), i=0, sz=data.size()-1 for pop(), implicitly swapping data[i], data.back(), and doing data.pop_back(), then adjusting from 0 down w/ swaps.  updates index_in_heap for v.
    inline void preserve_heap_property_down(Value const& currently_being_moved,size_type i,size_type heap_size) {
      using boost::get;
      distance_type currently_being_moved_dist=get(distance,currently_being_moved);
      Value* data_ptr = &data[0];
      size_type index = 0; // hole at index - currently_being_moved to be put here when we find the final hole spot
      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; // using index of first_child_index+smallest_child_index because we hope optimizer will be smart enough to const-unroll a loop below if we do this.  i think the optimizer would have gotten it even without our help (i.e. store root-relative index)

        // begin find best child index/distance
        size_type smallest_child_index = 0; // don't add to base first_child_index every time we update which is smallest.
        distance_type smallest_child_dist = get(distance, child_base_ptr[smallest_child_index]);
#undef D_ARY_MAYBE_IMPROVE_CHILD_I
#define D_ARY_MAYBE_IMPROVE_CHILD_I \
            distance_type i_dist = get(distance, child_base_ptr[i]); \
            if (better(i_dist, smallest_child_dist)) { \
              smallest_child_index = i; \
              smallest_child_dist = i_dist; \
            }
        if (first_child_index + Arity <= heap_size) {
          // avoid repeated heap_size boundcheck (should test if this is really a speedup - instruction cache tradeoff - could use upperbound = min(Arity,heap_size-first_child_index) instead.  but this optimizes to a fixed number of iterations (compile time known) so probably worth it
          for (size_t i = 1; i < Arity; ++i) {
            D_ARY_MAYBE_IMPROVE_CHILD_I
          }
        } else {
          for (size_t i = 1,e=heap_size - first_child_index; i < e; ++i) {
            D_ARY_MAYBE_IMPROVE_CHILD_I
          }
        }
        //end: know best child

        if (better(smallest_child_dist, currently_being_moved_dist)) {
          // instead of swapping, move.
          move_heap_element(child_base_ptr[smallest_child_index],index); // move up
          index=first_child_index+smallest_child_index; // descend - hole is now here
        } else {
          move_heap_element(currently_being_moved,index); // finish "swap chain" by filling hole
          break;
        }
      }
      verify_heap();
    }

    inline void preserve_heap_property_down(size_type i) {
      preserve_heap_property_down(data[i],i,data.size());
    }

    void preserve_heap_property_down() {
      using boost::get;
      if (data.empty()) return;
      if (D_ARY_DOWN_GRAEHL) { // this *should* be more efficient because i avoid swaps.
        Value copy0=data[0];
        preserve_heap_property_down(copy0,0,data.size());
        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) {
          for (size_t i = 1; i < Arity; ++i) { // can be unrolled completely.

            D_ARY_MAYBE_IMPROVE_CHILD_I
          }
        } else {
          for (size_t i = 1,e=heap_size - first_child_index; i < e; ++i) {
            D_ARY_MAYBE_IMPROVE_CHILD_I
          }
        }
        if (better(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();
    }

  };

#endif