Count Non-Connected Subsystems

Problem Given n entities in a system and m relationships between pairs of them, find how many non-connected subsystems exist — i.e. the number of connected components in the resulting graph.

Input / Output

• Input: integer n (entities labelled 0 .. n-1 or 1 .. n) and a list of m relationship pairs.
• Output: the number of connected components.

Constraints

• Relationships are undirected.
• Up to ~10^5 entities and relationships.
• Duplicate edges and self-loops may appear and must not affect the count.

Example

• Entities {1,2,3,4,5}, relationships {(1,2),(2,3),(4,5)} → 2 components: {1,2,3} and {4,5}.
• Tricky case: an entity with no relationships at all is still its own component — so n=3 with zero edges → 3. Solutions that iterate over edges rather than nodes routinely miss isolated entities.