Menene trie (prefix tree) kuma yaushe yana da amfani?

Question

Accepted Answer

A **trie** (prefix tree) shine bishiyar inda kowane **edge** wakilta harafin kuma kowane **hanya daga tushe** tana buga prefix. Kalmomin da ke raba prefix suna raba hanya daya, yana basa hanyoyin neman prefix gaggawa.

## Structure

```text
Insert "cat", "car", "dog":
        root
       /    \
      c      d
      |      |
      a      o
     / \     |
    t*  r*   g*       (* marks end-of-word)
```

## Code

```python
class TrieNode:
    def __init__(self):
        self.children = {}   # char -> TrieNode
        self.is_end = False

class Trie:
    def __init__(self):
        self.root = TrieNode()
    def insert(self, word):           # O(L), L = word length
        node = self.root
        for ch in word:
            node = node.children.setdefault(ch, TrieNode())
        node.is_end = True
    def starts_with(self, prefix):    # O(L)
        node = self.root
        for ch in prefix:
            if ch not in node.children: return False
            node = node.children[ch]
        return True
```

## Complexity

| Operation | Time |
|---|---|
| insert | O(L) |
| search | O(L) |
| prefix query | O(L) |

Crucially, cost depends on the **word length L**, *not* the number of stored words.

## Trade-offs

- **Strengths:** fast prefix search; autocomplete; shared prefixes save space for similar words.
- **Weaknesses:** high memory overhead per node (a child map for each); can use more space than a hash set for unrelated keys.

## Me yaushe yana da matukar muhimmanci

Tries suna bugi autocomplete, duba-duba haruffan, teburin yada IP, da binciken da aka tushe da jariha inda **prefix** daidai ya kasance mahalaci.

Lokacin da hash set kawai ya amsa "daidai daidai", trie kuma ya ba da amsa ga "wace kalmomin suna farawa da X?" da arewa.