# Exercise 6.5.8

The operation

`HEAP-DELETE(A,i)`

deletes the item in node $i$ from heap $A$. Give an implementation of`HEAP-DELETE`

that runs in $\O(\lg{n})$ time for an $n$-element max-heap.

This is the pseudocode is as follows:

```
HEAP-DELETE(A, i):
A[i] = A[A.heap-size]
A.heap-size -= 1
MAX-HEAPIFY(A, i)
```

We just move the last element of the heap to the deleated position and then
call `MAX-HEAPIFY`

on it. This works, because the element is already smaller
than its parent (because it was already under it on the heap), but might be
larger than its children. `MAX-HEAPIFY`

restored the heap property.