X'inhu heap u kif jimplementa cue ta' prijorita?

Question

Accepted Answer

**binary heap** huwa siġra binarja kompleta maħżuna f'array li tippreserva l-**heap property**: f'**min-heap**, kull parent huwa ≤ it-tfal tiegħu, għalhekk il-**minimu huwa dejjem mal-għerq**. Dan jagħmel implimentazzjoni standard ta' **priority queue**.

## Array layout

```text
       1               index: 0  1  2  3  4
      / \              array: [1, 3, 5, 8, 4]
     3   5             parent(i) = (i-1)//2
    / \                left(i)   = 2i+1
   8   4               right(i)  = 2i+2
```

## Operations

```python
import heapq
h = []
heapq.heappush(h, 5)   # O(log n) — bubble up
heapq.heappush(h, 1)
heapq.heappush(h, 3)
smallest = h[0]        # peek min -> O(1)
heapq.heappop(h)       # O(log n) — remove root, sift down -> 1
```

## Complexity

| Operation | Time |
|---|---|
| peek min/max | O(1) |
| push (insert) | O(log n) |
| pop (extract) | O(log n) |
| build heap from n items | O(n) |

## When to use

- **Scheduling** by priority (e.g. OS task schedulers).
- **Dijkstra / Prim** shortest-path and MST algorithms.
- **Top-K** problems and streaming medians.
- **Heap sort** (in-place O(n log n)).

## Għaliex huwa importanti

Heap jagħtik l-element li jmiss l-aktar importanti istantanjament mingħajr ma żtrid iżżomm dak kollu ordnat perfettament, li huwa ħafna iżjed irħis minn sortar mill-ġdid.

Huwa l-fondazzjoni ta' algoritmi ddrivati minn prijorita u għodda ta' intervista frekwenti għal mistoqsija "k l-akbar/l-iżgħar".

Operation	Time
peek min/max	O(1)
push (insert)	O(log n)
pop (extract)	O(log n)
build heap from n items	O(n)