Algorithm always finds shortest path.
Algorithm does not guarantee shortest path.
Please select an algorithm first.
A* is a weighted algorithm which always finds the shortest path.
A* uses heuristics to find the destination faster. It starts from a specific starting node of a graph, and aims to find a path to the given goal node having the smallest cost. A* does this by maintaining a tree of paths originating at the start node and extending those paths one edge at a time until it reached the destination. At each iteration of its main loop, A* needs to determine which of its paths to extend. It does so based on the cost of the path and an estimate of the cost required to extend the path all the way to the goal, selecting the path which minimizes the sum of the current cost and the estimated remaining cost.
A* terminates when the path it chooses to extend is a path from start to goal or if there are no paths eligible to be extended.
Dijkstra's algorithm can be viewed as a special case of A* without a heuristics function.
A* uses heuristics to find the destination faster. It starts from a specific starting node of a graph, and aims to find a path to the given goal node having the smallest cost. A* does this by maintaining a tree of paths originating at the start node and extending those paths one edge at a time until it reached the destination. At each iteration of its main loop, A* needs to determine which of its paths to extend. It does so based on the cost of the path and an estimate of the cost required to extend the path all the way to the goal, selecting the path which minimizes the sum of the current cost and the estimated remaining cost.
A* terminates when the path it chooses to extend is a path from start to goal or if there are no paths eligible to be extended.
Dijkstra's algorithm can be viewed as a special case of A* without a heuristics function.
Breadth-first search is an unweighted algorithm which always
finds the shortest path.
Breadth-first search starts at the source node, and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. It uses the opposite strategy as depth-first search.
It works similar to Dijkstra's algorithm, the main difference being that it only works with unweighted edges thus not taking weights added by the user into consideration and treating them as simple nodes.
An explanation of the algorithm can be found here.
Breadth-first search starts at the source node, and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. It uses the opposite strategy as depth-first search.
It works similar to Dijkstra's algorithm, the main difference being that it only works with unweighted edges thus not taking weights added by the user into consideration and treating them as simple nodes.
An explanation of the algorithm can be found here.
Depth-first search is an unweighted algorithm which does not
always find the shortest path.
Depth-first search starts at the source node and explores as far as possible along each branch before backtracking. It is thus not the best choice for pathfinding, as it's not guaranteed to find a shortest path and may take a long time to find the destination vertex.
An explanation of the algorithm can be found here.
Depth-first search starts at the source node and explores as far as possible along each branch before backtracking. It is thus not the best choice for pathfinding, as it's not guaranteed to find a shortest path and may take a long time to find the destination vertex.
An explanation of the algorithm can be found here.
Dijkstras algorithm is a weighted algorithm which always finds
the shortest path.
The original algorithm Dijkstra created finds the shortest path from a single starting point to a single target. This is the variant I implemented here. Other variations of Dijkstra's algorithm find the shortest path from the source node to every other node in the graph, thus creating a shortest-path-tree.
The principle behind Dijkstra's algorithm is best explained with an example.
Suppose you're a pirate captain in the 1670's having a base on one of the countless islands in an archipelago somewhere in the carribean. You and your crew hid a treasure on another island far away from your base. Of course you have a map of the archipelago with all the ways to get from one island to another and the length of these routes.
Being a smart pirate you thought of a way to find the shortest path between your location and the treasure.
You start by marking the distance from your location to every other island with infinity, because you don't know yet how far they are from your base. Next you have a look at the islands you can directly reach from your base and update their respective distances. You do this by determining the sum of the distance between an unvisited island and the value of the current island (0 because you're still in your base) and then relabeling the unvisited island with the sum if it is less than the unvisited island's current value, drawing an arrow from the current island to the other one and erasing every other arrow pointing to that island. After marking the current island as "done", you repeat that process for the island closest to yours, once again finding all islands you can reach from that specific island, updating their values and drawing/erasing arrows. You sit the whole night updating the map until you finally mark the treasure island as done.
Now finding the shortest path is done by simply tracing your way back by following the arrows in reverse.
The original algorithm Dijkstra created finds the shortest path from a single starting point to a single target. This is the variant I implemented here. Other variations of Dijkstra's algorithm find the shortest path from the source node to every other node in the graph, thus creating a shortest-path-tree.
The principle behind Dijkstra's algorithm is best explained with an example.
Suppose you're a pirate captain in the 1670's having a base on one of the countless islands in an archipelago somewhere in the carribean. You and your crew hid a treasure on another island far away from your base. Of course you have a map of the archipelago with all the ways to get from one island to another and the length of these routes.
Being a smart pirate you thought of a way to find the shortest path between your location and the treasure.
You start by marking the distance from your location to every other island with infinity, because you don't know yet how far they are from your base. Next you have a look at the islands you can directly reach from your base and update their respective distances. You do this by determining the sum of the distance between an unvisited island and the value of the current island (0 because you're still in your base) and then relabeling the unvisited island with the sum if it is less than the unvisited island's current value, drawing an arrow from the current island to the other one and erasing every other arrow pointing to that island. After marking the current island as "done", you repeat that process for the island closest to yours, once again finding all islands you can reach from that specific island, updating their values and drawing/erasing arrows. You sit the whole night updating the map until you finally mark the treasure island as done.
Now finding the shortest path is done by simply tracing your way back by following the arrows in reverse.
Start
End