Menene jerin aiki (array) kuma menene rikitattun ayyukansa?

Question

Accepted Answer

**Jerin aiki** ne tukin ƙaura mai aiki da membobi na nau'i ɗaya, da aka lissafa daga `0`. Saboda membobi sun tsaya juna kusa, adireshin membi `i` ana ƙididdige shi kai tsaye azaman `base + i * elementSize`, yana ba da samun **O(1)** shiryawayya.

## Tsarin ƙaura

```text
index:    0     1     2     3     4
        +-----+-----+-----+-----+-----+
arr =   | 10  | 20  | 30  | 40  | 50  |
        +-----+-----+-----+-----+-----+
address: base  +4    +8    +12   +16   (4-byte ints)
```

## Misali

```python
arr = [10, 20, 30, 40, 50]
x = arr[3]            # O(1) — direct index math
arr.append(60)        # amortized O(1) (dynamic array)
arr.insert(0, 5)      # O(n) — shift every element right
arr.pop(0)            # O(n) — shift every element left
```

## Rikitattun aiki

| Aiki | Lokaci |
|---|---|
| Shiryaya ta indeks | O(1) |
| Bincike (ba-tsara) | O(n) |
| Kari (m) | O(1) matsakaici |
| Saki/cirewa a gida/gida-gida | O(n) |

## Cikin jima'i

- **Kwarewa:** shiryayar sauri, cache-friendly (bayanin ya kasance tsaka tsaki), ƙaura kai tsaye.
- **Raunin:** saki/cirewa a tsakiya shine O(n); jerin tsari na daidaita buƙatar kwafi don girma.

## Yaushe haka makale ne

Jeraye ne gida-gida na yawancin sifofi - jerin kalma, tebur na hash, taro da jerin m suka gina akan su.

Sarin iska na su sau da rua tare da jerin "jiya" Big-O fara jarin "maburi" tushen-tushe a ƙididdige ainihi.

Aiki	Lokaci
Shiryaya ta indeks	O(1)
Bincike (ba-tsara)	O(n)
Kari (m)	O(1) matsakaici
Saki/cirewa a gida/gida-gida	O(n)