Heapsort

In-place sort.

Running time: O(n lg n)

Heaps

Heap: An array A representing a complete binary tree for HeapSize(A) elements satisfying the heap property:

A[parent(i)] >= A[i]

for every node i except the root node.

Because the array may hold more numbers than are contained in the heap, HeapSize(A) $\leq$ length(A) (heap insertion and deletion)

• parent(i) =

  
  

  
  

• left(i) = 2i ; left child

  
  

  
  

• right(i) = 2i + 1 ; right child