Cad is heap ann agus conas a bhainistionna sé fiú priorité?

Question

IT Interview Practice · Accepted Answer

Is éard is **binary heap** ann ná crann dhénártha iomlán atá stóráilte in array a choinníonn an **heap property**: i **min-heap**, tá gach páirent ≤ a leanaí, agus dá bhrí sin tá an **íosmhéan i gcónaí ag an bhfréamh**. Is í seo an **priority queue** a chur i bhfeidhm go caighdeánach.

## 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

- **Sceidealú** de réir tosaíochta (ex. task schedulers an OS).
- **Dijkstra / Prim** algartaim gearr-chonair agus crainn is lú.
- Fadhbanna **Top-K** agus meánacha i sruth.
- **Heap sort** (in-place O(n log n)).

## Cén fáth a bhfuil sé tábhachtach

Tugann heap an geal is tábhachtaí eile duit ar an toirt gan gach rud a bhheith sórtáilte go hiomlán, atá i bhfad níos saoire ná athannadh.

Is é seo an bhunús algartaim thógtha ar thosaíochta agus uirlis dhéanúsach agus ea le haghaidh ceisteanna "k is mó/is lú".

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

Array layout

Operations

Complexity

When to use

Cén fáth a bhfuil sé tábhachtach

Ceisteanna gaolmhara