/* -*- C++ -*-
 * src/lemon/bin_heap.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_RADIX_HEAP_H
#define LEMON_RADIX_HEAP_H

///\ingroup auxdat
///\file
///\brief Radix Heap implementation.
///\todo It should be documented.

#include <vector>
#include <lemon/error.h>

namespace lemon {

  /// \addtogroup auxdat
  /// @{

  /// A Radix Heap implementation.
  
  ///\todo Please document...
  ///
  ///\sa BinHeap
  ///\sa Dijkstra

  class UnderFlowPriorityException : public RuntimeError {
  public:
    virtual const char* exceptionName() const {
      return "lemon::UnderFlowPriorityException";
    }  
  };

  template <typename _Item, typename _ItemIntMap>
  class RadixHeap {

  public:
    typedef _Item Item;
    // FIXME: stl-ben nem ezt hivjak value_type -nak, hanem a kovetkezot...
    typedef int Prio;
    typedef _ItemIntMap ItemIntMap;

    /**
     * Each Item element have a state associated to it. It may be "in heap",
     * "pre heap" or "post heap". The later two are indifferent from the
     * heap's point of view, but may be useful to the user.
     *
     * The ItemIntMap _should_ be initialized in such way, that it maps
     * PRE_HEAP (-1) to any element to be put in the heap...
     */
    ///\todo it is used nowhere
    ///
    enum state_enum {
      IN_HEAP = 0,
      PRE_HEAP = -1,
      POST_HEAP = -2
    };

  private:
    
    struct RadixItem {
      int prev, next, box;
      Item item;
      int prio;
      RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
    };

    struct RadixBox {
      int first;
      int min, size;
      RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
    };

    std::vector<RadixItem> data;
    std::vector<RadixBox> boxes;

    ItemIntMap &iim;


  public:
    ///\e
    explicit RadixHeap(ItemIntMap &_iim) : iim(_iim) {
      boxes.push_back(RadixBox(0, 1));
      boxes.push_back(RadixBox(1, 1));
    }

    ///\e
    RadixHeap(ItemIntMap &_iim, int capacity) : iim(_iim) {
      boxes.push_back(RadixBox(0, 1));
      boxes.push_back(RadixBox(1, 1));
      while (upper(boxes.back(), capacity)) {
	extend();
      }
    }

    ///\e
    int size() const { return data.size(); }
    ///\e
    bool empty() const { return data.empty(); }

  private:

    bool upper(int box, Prio prio) {
      return prio < boxes[box].min;
    }

    bool lower(int box, Prio prio) {
      return prio >= boxes[box].min + boxes[box].size;
    }

    /// \brief Remove item from the box list.
    void remove(int index) {
      if (data[index].prev >= 0) {
	data[data[index].prev].next = data[index].next;
      } else {
	boxes[data[index].box].first = data[index].next;
      }
      if (data[index].next >= 0) {
	data[data[index].next].prev = data[index].prev;
      }
    }

    /// \brief Insert item into the box list.
    void insert(int box, int index) {
      if (boxes[box].first == -1) {
	boxes[box].first = index;
	data[index].next = data[index].prev = -1;
      } else {
	data[index].next = boxes[box].first;
	data[boxes[box].first].prev = index;
	data[index].prev = -1;
	boxes[box].first = index;
      }
      data[index].box = box;
    }

    /// \brief Add a new box to the box list.
    void extend() {
      int min = boxes.back().min + boxes.back().size;
      int size = 2 * boxes.back().size;
      boxes.push_back(RadixBox(min, size));
    }

    /// \brief Move an item up into the proper box.
    void bubble_up(int index) {
      if (!lower(data[index].box, data[index].prio)) return;
      remove(index);
      int box = findUp(data[index].box, data[index].prio);
      insert(box, index);      
    }

    /// \brief Find up the proper box for the item with the given prio.
    int findUp(int start, int prio) {
      while (lower(start, prio)) {
	if (++start == (int)boxes.size()) {
	  extend();
	}
      }
      return start;
    }

    /// \brief Move an item down into the proper box.
    void bubble_down(int index) {
      if (!upper(data[index].box, data[index].prio)) return;
      remove(index);
      int box = findDown(data[index].box, data[index].prio);
      insert(box, index);
    }

    /// \brief Find up the proper box for the item with the given prio.
    int findDown(int start, int prio) {
      while (upper(start, prio)) {
	if (--start < 0) throw UnderFlowPriorityException();
      }
      return start;
    }

    /// \brief Find the first not empty box.
    int findFirst() {
      int first = 0;
      while (boxes[first].first == -1) ++first;
      return first;
    }

    /// \brief Gives back the minimal prio of the box.
    int minValue(int box) {
      int min = data[boxes[box].first].prio;
      for (int k = boxes[box].first; k != -1; k = data[k].next) {
	if (data[k].prio < min) min = data[k].prio;
      }
      return min;
    }

    /// \brief Rearrange the items of the heap and makes the 
    /// first box not empty.
    void moveDown() {
      //      print(); printf("moveDown\n"); fflush(stdout);       
      int box = findFirst();
      if (box == 0) return;
      int min = minValue(box);
      for (int i = 0; i <= box; ++i) {
	boxes[i].min = min;
	min += boxes[i].size;
      }
      int curr = boxes[box].first, next;
      while (curr != -1) {
	next = data[curr].next;
	bubble_down(curr);
	curr = next;
      }      
    }

    void relocate_last(int index) {
      if (index != (int)data.size() - 1) {
	data[index] = data.back();
	if (data[index].prev != -1) {
	  data[data[index].prev].next = index;
	} else {
	  boxes[data[index].box].first = index;
	}
	if (data[index].next != -1) {
	  data[data[index].next].prev = index;
	}
	iim[data[index].item] = index;
      }
      data.pop_back();
    }

  public:

    ///\e
    void push(const Item &i, const Prio &p) {
      fflush(stdout);
      int n = data.size();
      iim.set(i, n);
      data.push_back(RadixItem(i, p));
      while (lower(boxes.size() - 1, p)) {
	extend();
      }
      int box = findDown(boxes.size() - 1, p);
      insert(box, n);
      //      printf("Push %d\n", p);
      //print();
    }

    ///\e
    Item top() const {
      //      print(); printf("top\n");  fflush(stdout);
      const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown();
      return data[boxes[0].first].item;
      //      print(); printf("top_end\n");  fflush(stdout);
    }

    /// Returns the prio of the top element of the heap.
    Prio prio() const {
      //      print(); printf("prio\n"); fflush(stdout);
      const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown();
      return data[boxes[0].first].prio;
     }

    ///\e
    void pop() {
      //      print(); printf("pop\n"); fflush(stdout);
      moveDown();
      int index = boxes[0].first;
      iim[data[index].item] = POST_HEAP;
      remove(index);
      relocate_last(index);
      //      printf("Pop \n");
      //print();
    }

    ///\e
    void erase(const Item &i) {
      int index = iim[i];
      iim[i] = POST_HEAP;
      remove(index);
      relocate_last(index);
   }

    ///\e
    Prio operator[](const Item &i) const {
      int idx = iim[i];
      return data[idx].prio;
    }

    ///\e
    void set(const Item &i, const Prio &p) {
      int idx = iim[i];
      if( idx < 0 ) {
	push(i, p);
      }
      else if( p >= data[idx].prio ) {
	data[idx].prio = p;
	bubble_up(idx);
      } else {
	data[idx].prio = p;
	bubble_down(idx);
      }
    }

    ///\e
    void decrease(const Item &i, const Prio &p) {
      //      print(); printf("decrease\n"); fflush(stdout);
      int idx = iim[i];
      data[idx].prio = p;
      bubble_down(idx);
    }

    ///\e
    void increase(const Item &i, const Prio &p) {
      int idx = iim[i];
      data[idx].prio = p;
      bubble_up(idx);
    }

    ///\e
    state_enum state(const Item &i) const {
      int s = iim[i];
      if( s >= 0 ) s = 0;
      return state_enum(s);
    }

//     void print() const {
//       for (int i = 0; i < boxes.size(); ++i) {
// 	printf("(%d, %d) ", boxes[i].min, boxes[i].size);
// 	for (int k = boxes[i].first; k != -1; k = data[k].next) {
// 	  printf("%d ", data[k].prio);
// 	}
// 	printf("\n");
//       }
//       fflush(stdout);
//     }

  }; // class RadixHeap


  ///@}

} // namespace lemon

#endif // LEMON_RADIX_HEAP_H