Insertion and Deletion in Heaps in Data Sturcture

Here we will see how to insert and delete elements from binary heap data structures. Suppose the initial tree is like below −

Insertion Algorithm

insert(heap, n, item):
Begin
   if heap is full, then exit
   else
      n := n + 1
      for i := n, i > 1, set i := i / 2 in each iteration, do
         if item <= heap[i/2], then break
         heap[i] = heap[i/2]
      done
   end if
   heap[i] := item
End

Example

Suppose we want to insert 30 into the heap −

Deletion Algorithm

delete(heap, n):
Begin
   if heap is empty, then exit
   else
      item := heap[1]
      last := heap[n]
      n := n – 1
      for i := 1, j := 2, j <= n, set i := j and j := j * 2, do
         if j < n, then
            if heap[j] < heap[j + 1], then j := j + 1
         end if
         if last >= heap[j], then break
         heap[i] := heap[j]
      done
   end if
   heap[i] := last
End

Example

Suppose we want to delete 30 from the final heap −