如何使用heap-Sort执行min-heap的inplace排序？

Question

每当我在最小堆上进行堆排序时，我得到反向排序的数组。

  

有没有办法在不使用额外空间的情况下使用堆排序对min heap进行排序？

Answer 1

使用max-heapify按升序排序，min-heapify按降序排序。

这是堆排序的psudocode。

Heapsort(A) {
   BuildHeap(A)
   for i <- length(A) downto 2 {
      exchange A[1] <-> A[i]
      heapsize <- heapsize -1
      Heapify(A, 1)
} 

BuildHeap(A) {
   heapsize <- length(A)
   for i <- floor( length/2 ) downto 1
      Heapify(A, i)
}


Heapify(A, i) {
   le <- left(i)
   ri <- right(i)
   if (le<=heapsize) and (A[le]>A[i])
      largest <- le
   else
      largest <- i 
   if (ri<=heapsize) and (A[ri]>A[largest])
      largest <- ri
   if (largest != i) {
      exchange A[i] <-> A[largest]
      Heapify(A, largest)
   }
}

MaxHeapify的Java实现

MaxHeapify( int[ ] arr, int i )
{
    int left = 2 * i + 1;
    int right = 2 * i + 2;
    int largest = i;

    if( left < arr.length && arr[ left ] > arr[ largest ] )
        largest = left;
    if( right < arr.length && arr[ right ] > arr[ largest ] )
        largest = right;
    if( largest != i )
    {
        int temp = arr[ i ];
        arr[ i ] = arr[ largest ];
        arr[ largest ] = temp;
        MaxHeapify( arr, largest );
    }
}

Here是算法的动画。