How to get the shortest path from $s$ to $t$ in a graph $G_1(V,E_1)$ after using Dijkstra's algorithm?
I'm looking at Dijkstra's algorithm in the introduction to algorithms book by Cormen, which calculates the optimal path for each vertex starting from a source.
Unlike the implementation of the algorithm in Wikipedia where they save previous nodes in optimal path from source in the prev array and update the array at every relaxation,the algorithm in the book only Relaxes the edges and doesn't save the previous vertex.
Is there a way to use the output of Dijkstra's algorithm from the book and after that to populate the prev array without modifying the algorithm in the book?
graph-theory algorithms
edited 2 days ago
greedoid
38.3k114797
asked 2 days ago
user3133165user3133165
1838
add a comment |
I'm looking at Dijkstra's algorithm in the introduction to algorithms book by Cormen, which calculates the optimal path for each vertex starting from a source.
Unlike the implementation of the algorithm in Wikipedia where they save previous nodes in optimal path from source in the prev array and update the array at every relaxation,the algorithm in the book only Relaxes the edges and doesn't save the previous vertex.
Is there a way to use the output of Dijkstra's algorithm from the book and after that to populate the prev array without modifying the algorithm in the book?
graph-theory algorithms
edited 2 days ago
greedoid
38.3k114797
asked 2 days ago
user3133165user3133165
1838
Can you upload a screenshot or picture of the algorithm your taking about? Without seeing the algorithm you're discussing, it's hard to say if the shortest path can be found without modifying the algorithm or not.
– Noble Mushtak
2 days ago
Here it is in the question now
– user3133165
2 days ago
What does RELAX(u,v,w) do?
– Hagen von Eitzen
2 days ago
add a comment |
I'm looking at Dijkstra's algorithm in the introduction to algorithms book by Cormen, which calculates the optimal path for each vertex starting from a source.
Unlike the implementation of the algorithm in Wikipedia where they save previous nodes in optimal path from source in the prev array and update the array at every relaxation,the algorithm in the book only Relaxes the edges and doesn't save the previous vertex.
Is there a way to use the output of Dijkstra's algorithm from the book and after that to populate the prev array without modifying the algorithm in the book?
graph-theory algorithms
edited 2 days ago
greedoid
38.3k114797
asked 2 days ago
user3133165user3133165
1838
I'm looking at Dijkstra's algorithm in the introduction to algorithms book by Cormen, which calculates the optimal path for each vertex starting from a source.
Unlike the implementation of the algorithm in Wikipedia where they save previous nodes in optimal path from source in the prev array and update the array at every relaxation,the algorithm in the book only Relaxes the edges and doesn't save the previous vertex.
Is there a way to use the output of Dijkstra's algorithm from the book and after that to populate the prev array without modifying the algorithm in the book?
graph-theory algorithms
graph-theory algorithms
edited 2 days ago
greedoid
38.3k114797
asked 2 days ago
user3133165user3133165
1838
edited 2 days ago
greedoid
38.3k114797
asked 2 days ago
user3133165user3133165
1838
edited 2 days ago
greedoid
38.3k114797
edited 2 days ago
greedoid
38.3k114797
edited 2 days ago
greedoid
38.3k114797
38.3k114797
asked 2 days ago
user3133165user3133165
1838
asked 2 days ago
user3133165user3133165
1838
asked 2 days ago
user3133165user3133165
1838
1838
Can you upload a screenshot or picture of the algorithm your taking about? Without seeing the algorithm you're discussing, it's hard to say if the shortest path can be found without modifying the algorithm or not.
– Noble Mushtak
2 days ago
Here it is in the question now
– user3133165
2 days ago
What does RELAX(u,v,w) do?
– Hagen von Eitzen
2 days ago
add a comment |
Can you upload a screenshot or picture of the algorithm your taking about? Without seeing the algorithm you're discussing, it's hard to say if the shortest path can be found without modifying the algorithm or not.
– Noble Mushtak
2 days ago
Here it is in the question now
– user3133165
2 days ago
What does RELAX(u,v,w) do?
– Hagen von Eitzen
2 days ago
Can you upload a screenshot or picture of the algorithm your taking about? Without seeing the algorithm you're discussing, it's hard to say if the shortest path can be found without modifying the algorithm or not.
– Noble Mushtak
2 days ago
Can you upload a screenshot or picture of the algorithm your taking about? Without seeing the algorithm you're discussing, it's hard to say if the shortest path can be found without modifying the algorithm or not.
– Noble Mushtak
2 days ago
Here it is in the question now
– user3133165
2 days ago
Here it is in the question now
– user3133165
2 days ago
What does RELAX(u,v,w) do?
– Hagen von Eitzen
2 days ago
What does RELAX(u,v,w) do?
– Hagen von Eitzen
2 days ago
add a comment |
1 Answer
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Once your algorithm has computed the distance to $s$ for all vertices, you can compute (a possible choice of) $prev$ in $O(|E|)$:
For each directed edge $(u,v)$, if $operatorname{dist}(v)=operatorname{dist}(u)+operatorname{cost}(u,v)$, set $operatorname{prev}(v)=u$.
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Once your algorithm has computed the distance to $s$ for all vertices, you can compute (a possible choice of) $prev$ in $O(|E|)$:
For each directed edge $(u,v)$, if $operatorname{dist}(v)=operatorname{dist}(u)+operatorname{cost}(u,v)$, set $operatorname{prev}(v)=u$.
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
add a comment |
Once your algorithm has computed the distance to $s$ for all vertices, you can compute (a possible choice of) $prev$ in $O(|E|)$:
For each directed edge $(u,v)$, if $operatorname{dist}(v)=operatorname{dist}(u)+operatorname{cost}(u,v)$, set $operatorname{prev}(v)=u$.
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
add a comment |
Once your algorithm has computed the distance to $s$ for all vertices, you can compute (a possible choice of) $prev$ in $O(|E|)$:
For each directed edge $(u,v)$, if $operatorname{dist}(v)=operatorname{dist}(u)+operatorname{cost}(u,v)$, set $operatorname{prev}(v)=u$.
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
Once your algorithm has computed the distance to $s$ for all vertices, you can compute (a possible choice of) $prev$ in $O(|E|)$:
For each directed edge $(u,v)$, if $operatorname{dist}(v)=operatorname{dist}(u)+operatorname{cost}(u,v)$, set $operatorname{prev}(v)=u$.
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
276k21269496
add a comment |
add a comment |
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Can you upload a screenshot or picture of the algorithm your taking about? Without seeing the algorithm you're discussing, it's hard to say if the shortest path can be found without modifying the algorithm or not.
– Noble Mushtak
2 days ago
Here it is in the question now
– user3133165
2 days ago
What does RELAX(u,v,w) do?
– Hagen von Eitzen
2 days ago