Shortest Path 2
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Question 1 of 4
1. Question
Find the sequence of the shortest path from point `A` to point `F`.Hint
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Dijkstra’s Algorithm is a method of finding a shortest path from a vertex to another by comparing multiple paths and finding the shortest value or sum of values.First, start finding the shortest paths to the vertices one edge away from `A`, which are `B`, and `J`.Always check for multiple paths and find the one with the lowest value.`B` `:` `8` or `5` `J` `:` `2` Now start finding the shortest paths to the vertices two edges away from `A`, which are `C` and `I`.Always check for multiple paths and find the one with the lowest value.`C` `:` `6` `I` `:` `8` or `7` Then start finding the shortest paths to the vertices three edges away from `A`, which are `H` and `D`.Always check for multiple paths and find the one with the lowest value.`H` `:` `11` or `8` `D` `:` `12` or `10` Next, start finding the shortest paths to the vertices four edges away from `A`, which are `G` and `E`.Always check for multiple paths and find the one with the lowest value.`G` `:` `16` or `9` `E` `:` `15` or `11` Now start finding the shortest paths to the vertex `F`.Always check for multiple paths and find the one with the lowest value.`F` `:` `14` or `12` Finally, mark the shortest path from `A` to `F` to find its sequence.Therefore, the sequence of the shortest path is `ABCHGEF`.`ABCHGEF` 
Question 2 of 4
2. Question
The network shows the time table of a bus to travel to between bus stops. Find the sequence with the shortest time to travel from bus stop `Q` to `W`.Hint
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Dijkstra’s Algorithm is a method of finding a shortest path from a vertex to another by comparing multiple paths and finding the shortest value or sum of values.First, start finding the shortest paths to the vertices one edge away from `Q`, which are `R`, `U` and `X`.Always check for multiple paths and find the one with the lowest value.`R` `:` `25` or `13` `U` `:` `15` `X` `:` `14` Now start finding the shortest paths to the vertices two edges away from `Q`, which are `Y`, `S` and `V`.Always check for multiple paths and find the one with the lowest value.`Y` `:` `23` `S` `:` `27` or `24` `V` `:` `34, 30` or `28` Then start finding the shortest paths to the vertices three edges away from `Q`, which are `T` and `Z`.Always check for multiple paths and find the one with the lowest value.`T` `:` `39` or `35` `Z` `:` `32` or `29` Now start finding the shortest paths to the vertex `W`.Always check for multiple paths and find the one with the lowest value.`F` `:` `46, 45` or `44` Finally, mark the shortest path from `Q` to `W` to find its sequence.Therefore, the sequence that will take the shortest time from `Q` to `W` is `QUVTW`.`QUVTW` 
Question 3 of 4
3. Question
Find the sequence of the shortest path from point `A` to point `E`.Hint
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Dijkstra’s Algorithm is a method of finding a shortest path from a vertex to another by comparing multiple paths and finding the shortest value or sum of values.First, start finding the shortest paths to the vertices one edge away from `A`, which are `B`, `I` and `H`.Always check for multiple paths and find the one with the lowest value.`B` `:` `12` or `11` `I` `:` `5` `H` `:` `7` Now start finding the shortest paths to the vertices two edges away from `A`, which are `G`, `C` and `J`.Always check for multiple paths and find the one with the lowest value.`G` `:` `17` or `12` `C` `:` `22` or `11` `J` `:` `22, 21` or `14` Then start finding the shortest paths to the vertices three edges away from `A`, which are `F` and `D`.Always check for multiple paths and find the one with the lowest value.`F` `:` `26` or `20` `D` `:` `24` or `22` Now start finding the shortest paths to the vertex `E`.Always check for multiple paths and find the one with the lowest value.`E` `:` `25` or `24` Finally, mark the shortest path from `A` to `E` to find its sequence.Therefore, the sequence that will take the shortest path from `A` to `E` is `AIGFDE`.`AIGFDE` 
Question 4 of 4
4. Question
The network shows the time in minutes for a car to travel to between points. Find the sequence with the shortest possible time to travel from `E` to `J`.Hint
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Dijkstra’s Algorithm is a method of finding a shortest path from a vertex to another by comparing multiple paths and finding the shortest value or sum of values.First, start finding the shortest paths to the vertices one edge away from `E`, which are `F`, `M` and `L`.Always check for multiple paths and find the one with the lowest value.`F` `:` `20` `M` `:` `15` `L` `:` `18` Now start finding the shortest paths to the vertices two edges away from `E`, which are `N`, `G`, `O` and `P`.Always check for multiple paths and find the one with the lowest value.`N` `:` `29` or `22` `G` `:` `36` or `32` `O` `:` `29` or `25` `P` `:` `32` or `28` Then start finding the shortest paths to the vertices three edges away from `E`, which are `Q`, `K` and `H`.Always check for multiple paths and find the one with the lowest value.`Q` `:` `29` `K` `:` `39, 36` or `35` `H` `:` `41` or `37` Now start finding the shortest paths to the vertices `J` and `I`.Always check for multiple paths and find the one with the lowest value.`J` `:` `41` or `39` `I` `:` `51` or `44` Finally, mark the shortest path from `E` to `J` to find its sequence.Therefore, the sequence that will take the shortest time from `E` to `J` is `EMNOQKJ`.`EMNOQKJ`
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