Grafu ni seti ya nodi zilizounganishwa na kingo. Maamuzi mawili ya kawaida ni orodha ya jibu (kila nodi huhifadhi jibu lake) na matrix ya jibu (gridi ya V×V ya thamani za boolean). Chaguo linategemea uzani wa grafu.
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]
# 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
| Orodha ya jibu | Matrix ya jibu | |
|---|---|---|
| Nafasi | O(V + E) | O(V²) |
| Kingo ipo? | O(degree) | O(1) |
| Kuruka jibu | O(degree) | O(V) |
| Bora kwa | grafu nyinyi | grafu nene |
Grafu nyingi za ulimwengu halisi (mitandao ya kijamii, ramani za barabara, grafu ya utegemezi) ni nyinyi, kwa hivyo orodha ya jibu inaokoa nafasi kubwa na kuharakisha traversals kama BFS/DFS.
Kujua kilipuka hiki kukuruhusu kuchagua uwakilishi unaofikia algorithms ya grafu kuwa ya ufanisi badala ya kuakamatia kutumia O(V²) kumbukumbu.
Maktaba ya maswali ya mahojiano ya IT yenye majibu ya kina — kutoka Junior hadi Senior.
Changia