READ_ONLY_ACCESS
[
  {
    "id": "maths1-w11-000",
    "front": "Relaxation step for edge $(u, v)$ with weight $w(u, v)$",
    "back": "If $dist[u] + w(u, v) < dist[v]$: $dist[v] = dist[u] + w(u, v)$"
  },
  {
    "id": "maths1-w11-001",
    "front": "Dijkstra's algorithm requirement",
    "back": "All edge weights must be nonnegative ($w(u, v) \\ge 0$)"
  },
  {
    "id": "maths1-w11-002",
    "front": "Bellman–Ford algorithm number of relaxation rounds",
    "back": "$|V| - 1$ rounds over all edges"
  },
  {
    "id": "maths1-w11-003",
    "front": "How Bellman–Ford detects negative-weight cycles",
    "back": "A negative cycle exists if an edge can still be relaxed in the $|V|$-th round"
  },
  {
    "id": "maths1-w11-004",
    "front": "Adjacency matrix power $(A^k)_{ij}$ interpretation",
    "back": "Number of walks of length exactly $k$ from vertex $i$ to vertex $j$"
  },
  {
    "id": "maths1-w11-005",
    "front": "Transitive closure definition",
    "back": "Reachability matrix indicating if a path of any length exists from $i$ to $j$"
  },
  {
    "id": "maths1-w11-006",
    "front": "Algorithm for single-source shortest path in DAG with arbitrary weights",
    "back": "Topological sort + single relaxation pass in $O(|V| + |E|)$"
  }
]