scala数据结构和算法-08-堆排序

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 data

import scala.collection.mutable.ListBuffer

object 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(","))
  }
}