scala数据结构和算法-08-堆排序

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二叉堆满足二个特性：

1．父结点的键值总是大于或等于（小于或等于）任何一个子节点的键值。

2．每个结点的左子树和右子树都是一个二叉堆（都是最大堆或最小堆）。

当父结点的键值总是大于或等于任何一个子节点的键值时为最大堆。当父结点的键值总是小于或等于任何一个子节点的键值时为最小堆。下图展示一个最小堆：

由于其它几种堆（二项式堆，斐波纳契堆等）用的较少，一般将二叉堆就简称为堆。

堆的存储

一般都用数组来表示堆，i结点的父结点下标就为(i – 1) / 2。它的左右子结点下标分别为2 * i + 1和2 * i + 2。如第0个结点左右子结点下标分别为1和2。

package dataimport scala.collection.mutable.ListBufferobject HeapSort {  def buildHeap[T](comparator:(T,T)=>Boolean)(source:ListBuffer[T],parent:Int){    if(left(parent)>=source.length){      return     }else{      buildHeap(comparator)(source,left(parent));    }    if(right(parent)>=source.length){      return    }else{      buildHeap(comparator)(source,right(parent));    }    if(comparator(source(left(parent)),source(parent))        &&comparator(source(right(parent)),source(parent))){      if(comparator(source(left(parent)),source(right(parent)))){        val p=source(parent)        source(parent)=source(left(parent))        source(left(parent))=p        buildHeap(comparator)(source,left(parent))      }else{        val p=source(parent)        source(parent)=source(right(parent))        source(right(parent))=p        buildHeap(comparator)(source,right(parent))      }    }else if(comparator(source(left(parent)),source(parent))){      val p=source(parent)        source(parent)=source(left(parent))        source(left(parent))=p        buildHeap(comparator)(source,left(parent))    }else if(comparator(source(right(parent)),source(parent))){      val p=source(parent)        source(parent)=source(right(parent))        source(right(parent))=p        buildHeap(comparator)(source,right(parent))    }          }    def left(parent:Int)={    parent*2+1  }    def right(parent:Int)={    parent*2+2  }    def heapfye[T](comparator:(T,T)=>Boolean)(source:ListBuffer[T],parent:Int,rightIndex:Int){    if(left(parent)>rightIndex){      return     }    /*if(right(parent)>rightIndex){      return    }*/    if(left(parent)<=rightIndex&&right(parent)>rightIndex){       if(comparator(source(left(parent)),source(parent))){          val p=source(parent)            source(parent)=source(left(parent))            source(left(parent))=p            heapfye(comparator)(source,left(parent),rightIndex)        }    }else{        if(comparator(source(left(parent)),source(parent))            &&comparator(source(right(parent)),source(parent))){          if(comparator(source(left(parent)),source(right(parent)))){            val p=source(parent)            source(parent)=source(left(parent))            source(left(parent))=p            heapfye(comparator)(source,left(parent),rightIndex)          }else{            val p=source(parent)            source(parent)=source(right(parent))            source(right(parent))=p            heapfye(comparator)(source,right(parent),rightIndex)          }        }else if(comparator(source(left(parent)),source(parent))){          val p=source(parent)            source(parent)=source(left(parent))            source(left(parent))=p            heapfye(comparator)(source,left(parent),rightIndex)        }else if(comparator(source(right(parent)),source(parent))){          val p=source(parent)            source(parent)=source(right(parent))            source(right(parent))=p            heapfye(comparator)(source,right(parent),rightIndex)        }    }  }    def heapSort[T](comparator:(T,T)=>Boolean)(source:ListBuffer[T],rightIndex:Int):ListBuffer[T]={    for(i<-(1 until source.length).reverse){      val tmp=source(i)      source(i)=source(0)      source(0)=tmp;      heapfye(comparator)(source,0,i-1)    }    source  }  def main(args: Array[String]): Unit = {    val source=ListBuffer(3,1,4,9,5,8,7)    buildHeap[Int](_>_)(source,0)    println(source.mkString(","))     println(heapSort[Int](_>_)(source,source.length-1).mkString(","))  }}

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