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What is the difference between sorting and topological,[link widoczny dla zalogowanych]
At an abstract level they are connected: As Saeed and Stefan say,[link widoczny dla zalogowanych], it's the difference between a total order and a partial order. That is a fantastically concise description, but sometimes not helpful when you're learning.
A total order means that,[link widoczny dla zalogowanych], in the absence of repeats, when you sort something,[link widoczny dla zalogowanych], you're going to get one unique proper answer. If you sort 3,[link widoczny dla zalogowanych], 6, 2 in ascending order, you had better get one answer: 2, 3, 6.
A partial order is a little looser. The canonical example is the order in which you put your clothes on: You could put your shorts,[link widoczny dla zalogowanych], then your pants, then your socks, then your shoes. That's a valid order. Or you could do shorts,[link widoczny dla zalogowanych], socks, pants,[link widoczny dla zalogowanych], shoes. But intuitively, you can't do shorts,[link widoczny dla zalogowanych], pants,[link widoczny dla zalogowanych], shoes, socks. It doesn't make sense to put the socks on after the shoes.
To formalize that dressing example,[link widoczny dla zalogowanych], you usually show a dependency graph with actions ("put on shoes") as nodes, and directed arcs showing what node must precede what other nodes. A topological sort is an ordering of all nodes in a graph like that which respects the arcs. Meaning,[link widoczny dla zalogowanych], if there's an arc from socks to shoes, then socks better be before shoes in the order.
So again,[link widoczny dla zalogowanych], at an abstract level,[link widoczny dla zalogowanych], they're connected. But they are absolutely NOT the same thing.
If a total order is available every object can be compared with every object. In this case you can sort wrt,[link widoczny dla zalogowanych]. that order,[link widoczny dla zalogowanych]. Examples are the integers wrt,[link widoczny dla zalogowanych]. > (or
If only a partial order is available,[link widoczny dla zalogowanych], not every object can be compared with every other object. Only a relation between certain objects is available. An example are dependencies between compilation units. by compiling units which depend on some other unit after these units). orderings) are possible: If A depends on B and there is some other unit C, possible compilation sequences are B,A,[link widoczny dla zalogowanych],C and C,A,[link widoczny dla zalogowanych],B (every sequence where A is compiled before B).
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