Array representation of max heap

Question

I am trying to create a max heap , the logic is simple , if parent is smaller then one of its childre, swap them. I tried implementing it using

void maxHeapify( int i , int *a , int n ){

    int largest = i;
    int left    = ( i * 2 ) + 1;
    int right    = ( i * 2 ) + 2;

    if( left < n && a[ largest] < a[ left ])
        largest = left;
    if( right < n  && a[ largest ] < a[right])
        largest = right;
    if( largest != i ){
        swap( a[i], a[largest]);
        maxHeapify( largest , a,  n );
    }
}


int main(){
    int n;
    int * a;
    cout << "Number of elements : ";
    cin >> n ;
    a = new int[n];
    for( int i = 0; i < n ; i++){
        cin >> a[i];
    }

    for( int i = n/2 -1 ; i >= 0 ; i-- ){
        maxHeapify( i , a, n);
    }
    for(int i = 0; i < n ; i++){
        cout << a[i] << " ";
    }

    return 0;
}

i am using input

2 7 26 25 19 17 1 90 3 36

the tree shoud look like

90
      36    17
   25   26 7   1
 2   3 19

so array representation should be 90 36 17 25 26 7 1 2 3 19 yet the output of the code is

90 36 26 25 19 17 1 7 3 2

i looked it up and found many same codes in many tutorials. How come the output isnt representation of the tree in array? Did i misunderstood it?

Thanks for explanation

Answer 1

Why do you expect your heap to look in a specific way? There are many ways in which these input numbers can be arranged into a heap. The result you are getting is also a valid heap - each parent is bigger, than its children:

        90
    36      26
 25   19  17  1
7 3  2

Answer 2

Final heap structure will vary based on insertion order and initial structure. In your case, 2 7 26 25 19 17 1 90 3 36 would yield result you expect if you started with empty heap, inserted elements in given order and heapifed after each insertion.

This code will yield result you expect:

std::vector<int> b = {2, 7, 26, 25, 19, 17, 1, 90, 3, 36};
auto it = b.begin();
while (it != b.end())
{
    std::make_heap(b.begin(), it+1);
    ++it;
}

However, what your code does is preinserts all elements into heap, and then arranges it, equivalent to this:

std::vector<int> b = {2, 7, 26, 25, 19, 17, 1, 90, 3, 36};
std::make_heap(b.begin(), b.end());

Both results are equally valid.