Yaya za ka wakilta jadwal: jerin gida vs matrix gida?

Question

Accepted Answer

**Jadwal** shine saitin **abubuwan gaske** da ke haɗe ta **gefuna**. Abubuwan wakilta gida biyu shine **jerin gida** (kowane abubuwan gaske ya ajiye maɓaliyansa) da **matrix gida** (V×V grid na boolean). Zaɓi yana dogara da **yawa** na jadwal.

## Abubuwan biyu

```text
Graph:  0 - 1
        |   |
        2 - 3

Adjacency list:          Adjacency matrix:
0: [1, 2]                    0 1 2 3
1: [0, 3]                 0 [0 1 1 0]
2: [0, 3]                 1 [1 0 0 1]
3: [1, 2]                 2 [1 0 0 1]
                          3 [0 1 1 0]
```

## Lambar

```python
# Adjacency list (dict of lists) — preferred for sparse graphs
adj = {0: [1, 2], 1: [0, 3], 2: [0, 3], 3: [1, 2]}
neighbors = adj[1]            # O(1) to get a vertex's neighbors

# Adjacency matrix
matrix = [[0]*4 for _ in range(4)]
matrix[0][1] = matrix[1][0] = 1
has_edge = matrix[0][1] == 1  # O(1) edge lookup
```

## Kwatanta (V abubuwan gaske, E gefuna)

| | Jerin gida | Matrix gida |
|---|---|---|
| Sarari | O(V + E) | O(V²) |
| Gefe akwai? | O(digiri) | O(1) |
| Samun maɓaliyan | O(digiri) | O(V) |
| Kyau don | jadwal gajiya | jadwal yawa |

## Me ya sa ya mahimmaci

Yawancin jadwal na ainihi (hanyoyin jama'a, taswirar hanya, jadwalan dogaro) **gajiya** ne, saboda haka jerin gida suna ceton sarari babbar da suna saurin tafiya kamar BFS/DFS.

Sanin jujjuyan aiki ya ba ka damar zaɓar wakilta da ke kiyaye algoritmumin jadwalka aiki ne maimakon saurin amfani da O(V²) alaƙa.

	Jerin gida	Matrix gida
Sarari	O(V + E)	O(V²)
Gefe akwai?	O(digiri)	O(1)
Samun maɓaliyan	O(digiri)	O(V)
Kyau don	jadwal gajiya	jadwal yawa