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/******************************************************************************************[Heap.h] 
MiniSat -- Copyright (c) 2003-2005, Niklas Een, Niklas Sorensson 
 
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and 
associated documentation files (the "Software"), to deal in the Software without restriction, 
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sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is 
furnished to do so, subject to the following conditions: 
 
The above copyright notice and this permission notice shall be included in all copies or 
substantial portions of the Software. 
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT 
NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, 
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OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 
**************************************************************************************************/ 
#include <vector> 
#include <iostream> 
//================================================================================================= 
 
 
static inline int left  (int i) { return i+i; } 
static inline int right (int i) { return i+i + 1; } 
static inline int parent(int i) { return i >> 1; } 
 
using namespace std; 
 
template<class C> 
class Heap { 
  typedef vector<int> vectint; 
private : 
  C* comp; 
public :  
  vectint heap;     // heap of ints 
  vectint indices;  // int -> index in heap 
  Heap() { 
    heap.push_back(-1); 
  } 
 
  Heap(C* co) { 
    comp=co; 
    heap.push_back(-1); 
  } 
 
  void initcomp(C* co) { 
    comp=co; 
  } 
   
  inline void percolateUp(int i) 
  { 
    int x = heap[i]; 
    while (parent(i) != 0 && (*comp)(x,heap[parent(i)])) { 
      heap[i]          = heap[parent(i)]; 
      indices[heap[i]] = i; 
      i                = parent(i); 
    } 
    heap   [i] = x; 
    indices[x] = i; 
  } 
   
  inline void percolateDown(int i) 
  { 
    int x = heap[i]; 
    while (left(i) < heap.size()){ 
      int child = right(i) < heap.size() && (*comp)(heap[right(i)],heap[left(i)]) ? right(i) : left(i); 
      if (!(*comp)(heap[child],x)) break; 
      heap[i]          = heap[child]; 
      indices[heap[i]] = i; 
      i                = child; 
    } 
    heap   [i] = x; 
    indices[x] = i; 
  } 
   
  bool ok(int n) {  
    return n >= 0 && n < indices.size(); 
  } 
   
public: 
   
  int size() { 
    return heap.size()-1; 
  } 
 
  void setBounds (int size) { /*assert(size >= 0);*/  
    for (int i=indices.size();i<=size;i++) { 
      indices.push_back(0); 
    } 
  } 
   
  bool inHeap (int n)    { 
      /*assert(ok(n));*/ 
    return indices[n] != 0;  
  } 
   
  void increase  (int n)    { 
      /*assert(ok(n));*/ 
      /*assert(inHeap(n));*/ 
    percolateUp(indices[n]); 
  } 
 
  void decrease (int n) { 
      /*assert(ok(n));*/ 
      /*assert(inHeap(n));*/ 
    percolateDown(indices[n]); 
  } 
   
  bool empty () { 
    return heap.size() == 1; 
  } 
   
  void insert(int n) { 
//    cout<<"Insertion de "<<n<<endl; 
      /*assert(ok(n));*/ 
      if (inHeap(n)) return;
    indices[n] = heap.size(); 
    heap.push_back(n); 
    percolateUp(indices[n]); } 
   
  int getminwopop() {
      return heap[1];
  }
  
  int  getmin() { 
    int r            = heap[1]; 
    heap[1]          = heap.back(); 
    indices[heap[1]] = 1; 
    indices[r]       = 0; 
    heap.pop_back(); 
    if (heap.size() > 1) 
      percolateDown(1); 
    return r; } 
   
  bool heapProperty() { 
    return heapProperty(1); } 
   
  bool heapProperty(int i) { 
    return (size_t)i >= heap.size() 
      || ((parent(i) == 0 || !(*comp)(heap[i],heap[parent(i)])) && heapProperty(left(i)) && heapProperty(right(i))); } 
  
  void print() {
      cout<<"heap: ";
      for (int i=0;i<heap.size();i++) cout<<"-"<<heap[i];
      cout<<"-"<<endl;
      cout<<"indices: ";
      for (int i=0;i<indices.size();i++) cout<<"-"<<indices[i];
      cout<<"-"<<endl;
  }
}; 

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