为什么我的HeapSort跳过数组中的第一个元素

Why is my HeapSort skipping the first element in the array?

本文关键字：第一个 元素 数组 我的 HeapSort 为什么      更新时间：2023-10-16

我在我的算法类中实现了一个赋值的HeapSort，我终于完成了，但由于某种原因，排序跳过了数组中的第一个元素。

原数组:

int heapArray[SIZE] = {  5 ,99, 32, 4, 1, 12, 15 , 8, 13, 55 };

HeapSort()后的输出

5 99 32 15 13 12 8 4 1

我看了所有的函数，不明白为什么它跳过了第一个元素。有人能帮我吗?我包含了下面所有的HeapSort函数。我知道它看起来很多，但我太接近了。

int main()
{
int heapArray[SIZE] = {  5 ,99, 32, 4, 1, 12, 15 , 8, 13, 55 };
HeapSort(heapArray);

return 0;
}

.........................................................................................

void HeapSort(int heapArray[])
{   
int heap_size = SIZE;
int n = SIZE;
int temp;
Build_Max_Heap(heapArray);
for(int i = n-1; i >= 2; i--)
{
    temp = heapArray[1];
    heapArray[1] = heapArray[i];
    heapArray[i] = temp;
    heap_size = heap_size-1;
    Max_Heapify(heapArray,1);
}
return;
}

...........................................................................................

void Build_Max_Heap(int heapArray[])
{
double n = SIZE;
for(double i = floor((n-1)/2); i >= 1; i--)
{
    Max_Heapify(heapArray,i);
}
return;
}

...........................................................................................

void Max_Heapify(int heapArray[],int i)
{
int n = SIZE;
int largest = 0;
int l = Left(i);
int r = Right(i);
if(( l <= n) && (heapArray[l] > heapArray[i]))
{
    largest = l;
}
else
{
    largest = i;
}
if( (r <= n) && ( heapArray[r] > heapArray[largest]))
{
    largest = r;
}
int temp;
if(largest != i)
{
    temp = heapArray[i];
    heapArray[i] = heapArray[largest];
    heapArray[largest] = temp;
    Max_Heapify(heapArray,largest);
}
return;
}

...........................................................................................

int Parent(int i)
{
return (i/2);
}
int Left(int i)
{
return (2*i);
}
int Right(int i)
{
return ((2*i)+1);
}

您的代码中有几个问题:

首先:数组的索引从0开始，而不是从1开始，因此，索引错误的地方很多，如下所示:

HeapSort函数:

for(int i = n-1; i >= 2; i--)  {
                   //should be 1 not 2
    temp = heapArray[1]; //should be 0 not 1 in those 2 statements
    heapArray[1] = heapArray[i];
     heapArray[i] = temp;  
}
Max_Heapify(heapArray,1);
                  //should start from 0 not 1
除了:

for(double i = floor((n-1)/2); i >= 1; i--)
{                             //should start from 0 not 1
    Max_Heapify(heapArray,i);
}

You Parent, Left和Right有类似的错误，你可以看到上面两个帖子。

同时，你有逻辑错误在你的HeapSort和max_heapify函数。您定义了heap_size并更新了它，但从未真正使用过它。您必须将其传递给Max_Heapify函数。因为每次当您将当前最大的元素放到数组的末尾时，您只需要对剩余的元素进行堆积，而不再需要对整个堆进行堆积。这也意味着您的heapify函数有错误，因为您从未真正使用过heap_size。正确的HeapSort和Max_Heapify以及Build_Max_Heap函数应该是:

堆排序:

void HeapSort(int heapArray[]) 
{   
  //do what you did before this sentence
  Build_Max_Heap(heapArray,heap_size); 
  //need to pass heap_size since Max_Heapify use heap_size
  for(int i = n-1; i >= 1; i--)
  {
     //...same as you did but pay attention to index
     heap_size = heap_size-1;
     Max_Heapify(heapArray,0,heap_size); //remember to use heap_size
   }
   //you declared void, no need to return anything
 }

Build_Max_Heap功能:

void Build_Max_Heap(int heapArray[], int heapSize) //should use heapSize
{
    int n = SIZE;
    for(int i = floor((n-1)/2); i >= 0; i--) //here should be 0 not 1
   {
      Max_Heapify(heapArray,i,heapSize); //should use heapSize
    }
 }

Max_Heapify功能:

void Max_Heapify(int heapArray[],int i, int heap_size) //should use heap_size
{
    //....here similar to what you did
    if(( l < heap_size) && (heapArray[l] > heapArray[i]))
    {   //^^compare with heap_size not SIZE
        //skip identical part
    }
    if( (r < heaps_ize) && ( heapArray[r] > heapArray[largest]))
    {
       //same error as above
    }
   //skip identical part again
   Max_Heapify(heapArray,largest, heap_size); //have to use heap_size
 }
}

您可能需要从伪代码中更好地理解HeapSort算法。

here

Build_Max_Heap(heapArray);
for(int i = n-1; i >= 2; i--)
{                 ^^^^^
    temp = heapArray[1];
    heapArray[1] = heapArray[i];
    heapArray[i] = temp;
    heap_size = heap_size-1;
    Max_Heapify(heapArray,1);
}
return;
}

在i=2时停止循环，将其减为1，不取heapArray的第一个元素它的索引是0

Parent, Left和Right函数适用于基于1的数组。对于基于0的，您需要使用:

int Parent(int i)
{
    return (i - 1) / 2;
}
int Left(int i)
{
    return (2 * i) + 1;
}
int Right(int i)
{
    return 2 * (i + 1);
}

您可以在示例堆中检查:

    0
   / 
  1   2
 /  / 
3  4 5  6
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