We can think about marks (like infinity and other positive numbers) like upper bounds of distance to main node (node C in example). And this idea can make Dijkstra's Algorithm more general: distances no longer constraint to be the numbers, they can be intervals or variables. And we can solve task in reverse order or in inperfect information world: 1. If we have of path, but don't know path exacly and question to find all parameters of graph. 2. ... find all distances. What is interval? Interval [a, b] have lower bound "a" and upper bound "b", a and b is real numbers. What is imperfect information (it comes from game theory)? Imperfect information appears when decisions have to be made simultaneously, and players need to balance all possible outcomes when making a decision. A good example of imperfect information games is a card game (poker for example) where each player’s card are hidden from the rest of the players. Possible generalisation: We don't need proof that algorithm is right if each step in calculation is always not loose information and uses all possible desicions (logic branches).
We can think about marks (like infinity and other positive numbers) like upper bounds of distance to main node (node C in example). And this idea can make Dijkstra's Algorithm more general: distances no longer constraint to be the numbers, they can be intervals or variables. And we can solve task in reverse order or in inperfect information world:
1. If we have of path, but don't know path exacly and question to find all parameters of graph.
2. ... find all distances.
What is interval?
Interval [a, b] have lower bound "a" and upper bound "b", a and b is real numbers.
What is imperfect information (it comes from game theory)?
Imperfect information appears when decisions have to be made simultaneously, and players need to balance all possible outcomes when making a decision. A good example of imperfect information games is a card game (poker for example) where each player’s card are hidden from the rest of the players.
Possible generalisation: We don't need proof that algorithm is right if each step in calculation is always not loose information and uses all possible desicions (logic branches).