算法之斐波那契堆-优快云博客

本文介绍了一种高效的数据结构——斐波那契堆的实现方法。斐波那契堆是一种用于实现优先队列的数据结构，它支持快速的插入、删除最小元素及减少键等操作。文中详细展示了斐波那契堆的各个核心方法，如插入、删除、减少键等，并通过示例代码加以说明。

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  packagecom.eshore.sweetop.exdataframe; 
 /* 
*mark
*/ 
 publicclassFibHeap{ 
 privateFibNodemin; 
 privateintcount; 
 privateFibNoderoot; 
 publicFibHeap(){ 
 root=newFibNode(); 
 root.setChild(null); 
root.setLeft(root);
root.setRight(root);
 root.setDegree(0); 
 root.setMark(false); 
 root.setParent(null); 
}
 publicFibNodemin(){ 
 returnmin; 
}
 publicvoiddelete(FibNodenodex){ 
decereaseKey(nodex,Integer.MIN_VALUE);
extractMin();
}
 publicvoiddecereaseKey(FibNodenodex,intk){ 
 if(nodex.getKey()<k){ 
 thrownewRuntimeException("newkeyisgreaterthancurrentkey"); 
}
nodex.setKey(k);
FibNodenodey=nodex.getParent();
 if(nodey!=null&&nodex.getKey()<nodey.getKey()){ 
cut(nodex,nodey);
cascadingCut(nodey);
}
 if(nodex.getKey()<min.getKey()){ 
min=nodex;
}
}
 publicvoidcut(FibNodenodex,FibNodenodey){ 
nodex.getLeft().setRight(nodex.getRight());
nodex.getRight().setLeft(nodex.getLeft());
 nodey.setDegree(nodey.getDegree()-1); 
 this.insertRoot(nodex); 
 nodex.setParent(null); 
 nodex.setMark(false); 
}
 publicvoidcascadingCut(FibNodenodey){ 
FibNodenodez=nodey.getParent();
 if(nodez!=null){ 
 if(!nodey.getMark()){ 
 nodey.setMark(true); 
 }else{ 
cut(nodey,nodez);
cascadingCut(nodez);
}
}
}
 publicFibNodeextractMin(){ 
FibNodenodez=min;
 if(nodez!=null){ 
 if(nodez.getDegree()!=0){ 
FibNodefc=nodez.getChild();
FibNodefn=fc;
 do{ 
 fn.setParent(null); 
fn=fn.getRight();
 }while(fn!=fc); 
nodez.getLeft().setRight(fc.getRight());
fc.getRight().setLeft(nodez.getLeft());
nodez.getRight().setLeft(fc);
fc.setRight(nodez.getRight());
 }else{ 
nodez.getLeft().setRight(nodez.getRight());
nodez.getRight().setLeft(nodez.getLeft());
}
 if(nodez==nodez.getRight()){ 
 min=null; 
 }else{ 
min=min.getRight();
consolidate();
}
count--;
}
 returnnodez; 
}
 publicvoiddisplayRoot(){ 
FibNodefr=root.getRight();
 while(fr!=root){ 
System.out.println(fr.getKey());
fr=fr.getRight();
}
}
 publicvoidconsolidate(){ 
 //this.displayRoot(); 
  FibNode[] a = new FibNode[(int)(Math.log(count)/Math.log(2))+1];//这一步比较难证明，下了些功夫 
FibNodenodew=root.getRight();
 //System.out.println("root:"+root.getKey()); 
 while(nodew!=root){ 
FibNodenodex=nodew;
 //System.out.println(nodex.getKey()); 
nodew=nodew.getRight();
 intd=nodex.getDegree(); 
 while(a[d]!=null){ 
FibNodenodey=a[d];
 if(nodex.getKey()>nodey.getKey()){ 
FibNodetemp=nodex;
nodex=nodey;
nodey=temp;
}
link(nodey,nodex);
 a[d]=null; 
d++;
}
a[d]=nodex;
}
 //this.displayRoot(); 
 min=null; 
 //root=null; 
 //System.out.println("a==============="); 
 for(inti=0;i<a.length;i++){ 
 if(a[i]!=null){ 
 //root=a[i]; 
 if(min==null||a[i].getKey()<min.getKey()){ 
min=a[i];
}
}
}
 //System.out.println("new:"+min.getKey()); 
}
 publicvoidlink(FibNodenodey,FibNodenodex){ 
nodey.getLeft().setRight(nodey.getRight());
nodey.getRight().setLeft(nodey.getLeft());
nodey.setParent(nodex);
 if(nodex.getDegree()==0){ 
nodex.setChild(nodey);
nodey.setLeft(nodey);
nodey.setRight(nodey);
 }else{ 
nodey.setLeft(nodex.getChild().getLeft());
nodex.getChild().getLeft().setRight(nodey);
nodey.setRight(nodex.getChild());
nodex.getChild().setLeft(nodey);
}
 nodex.setDegree(nodex.getDegree()+1); 
 nodey.setMark(false); 
}
 publicvoidinsert(FibNodenodex){ 
 nodex.setDegree(0); 
 nodex.setParent(null); 
 nodex.setChild(null); 
nodex.setLeft(nodex);
nodex.setRight(nodex);
 nodex.setMark(false); 
insertRoot(nodex);
 if(min==null||nodex.getKey()<min.getKey()){ 
min=nodex;
}
count++;
}
 publicvoidunion(FibHeapheap){ 
 if(heap.count==0){ 
 return; 
}
FibNodefn=heap.root;
fn.getRight().setLeft(root.getLeft());
root.getLeft().setRight(fn.getRight());
fn.getLeft().setRight(root);
root.getLeft().setLeft(fn);
 if(min==null||heap.min.getKey()<min.getKey()){ 
min=heap.min;
}
 this.count+=heap.count; 
}
 privatevoidinsertRoot(FibNodenodex){ 
nodex.setLeft(root.getLeft());
root.getLeft().setRight(nodex);
nodex.setRight(root);
root.setLeft(nodex);
}
 publicstaticvoidmain(String[]args){ 
 FibHeapfh=newFibHeap(); 
 int[]keys={9,10,5,14,12,13,8,3}; 
 for(inti=0;i<keys.length;i++){ 
 FibNodefn=newFibNode(); 
fn.setKey(keys[i]);
fh.insert(fn);
}
 //FibHeapfh2=newFibHeap(); 
 //int[]keys2={3,7,2,7,9,14,66}; 
 //for(inti=0;i<keys2.length;i++){ 
 //FibNodefn=newFibNode(); 
 //fn.setKey(keys2[i]); 
 //fh2.insert(fn); 
 //} 
 //fh.union(fh2); 
 //System.out.println(fh.min().getKey()); 
 //fh.displayRoot(); 
 //System.out.println("min:"+fh.extractMin().getKey()); 
 //System.out.println("min:"+fh.extractMin().getKey()); 
 //System.out.println("min:"+fh.extractMin().getKey()); 
fh.delete(fh.min());
System.out.println(fh.min().getKey());
}
}
 