Yadda tebur hash ke sarrafa watsiya, halin jiya, da sake girma?

Question

Accepted Answer

Albarkatun mabudi daban-daban na iya zama jiya zuwa **bokiti gida** — **watsiya** aka kira shi. Tebur hash suke tsaye O(1) a matsakaita ta hutu watsiyoyi da **sake girma** kafin bokitoci suke cikakke, aka sarrafawa ta **halin jiya**.

## Wajen hutu watsiyoyi

```text
Separate chaining: each bucket holds a list
  [3] -> ("cat",9) -> ("rat",2)   # both hashed to 3

Open addressing: probe to the next free slot
  hash=3 taken -> try 4 -> try 5 ... (linear probing)
```

## Halin jiya da sake girma

```text
load factor α = number_of_entries / number_of_buckets
α rises -> more collisions -> slower lookups
When α exceeds a threshold (e.g. 0.75):
  -> allocate a bigger array (usually 2x)
  -> REHASH every existing key into new buckets
```

```python
# Conceptual resize
def _resize(self):
    old = self.buckets
    self.buckets = [None] * (len(old) * 2)
    for entry in all_entries(old):
        self._insert(entry.key, entry.value)   # rehash into new array
```

## Mahimmanci

| Aiki | Matsakaita | Mafi Munƙaci |
|---|---|---|
| neman / saka / gida | O(1) | O(n) |
| sake girma gida | — | O(n) |
| saka (amortized, da sake girma) | O(1) | — |

Sake girma shine O(n) amma yana faruwa da baje-baje, don haka yana **amortized zuwa O(1)** a kowane saka.

## Janyewar kwanan gida

- **Kulle:** sauƙi, yana runtowa kyau, amma yana amfani da ƙarin maƙogi da ke da rashin kyau cache locality.
- **Buɗewar adreshi:** cache-friendly da ƙankara, amma abin mamakin babbar jiya-halin jiya da buje buɗe tsare-tsarewa (tombstones).

## Me yasa haka muhimmi ne

Wannan abubuwa na ciki suna bayyana *me yasa* taswira hash suke sauƙi a matsakaita duk da kuwa suna iya zuwa O(n) — mahimmanci sosai don lambar da ta dadi matukaci da kuma gida na abin amfani-rika (hash-flooding).

Sanin halin jiya kuma yana bayyana bisisin tunewar ƙarfi / gudu da ingantattun gidaje suka falleta.

Aiki	Matsakaita	Mafi Munƙaci
neman / saka / gida	O(1)	O(n)
sake girma gida	—	O(n)
saka (amortized, da sake girma)	O(1)	—