# Insertion and Deletion in Heaps in Data Sturcture

Data StructureAnalysis of AlgorithmsAlgorithms

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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 −

Updated on 10-Aug-2020 08:59:32