Re-adding the selected route
Sum the displayed path weights and confirm that no unsettled relaxation offers a smaller endpoint distance.
Math calculator
Dijkstra Shortest Path Calculator
Find a minimum-weight path between two vertices in a nonnegative weighted graph. The page traces how the inputs determine shortest path and its finite structure.
Dijkstra Shortest Path inputs
Enter the source values
Boundary checks for Dijkstra Shortest Path
Keep the Dijkstra Shortest Path ordering and membership rules attached to Vertices. Read Weighted edges under that same Dijkstra Shortest Path convention.
List a small nonempty Dijkstra Shortest Path example. When allowed, compare it with an empty Dijkstra Shortest Path case.
The Dijkstra Shortest Path case starts with Vertices and Weighted edges. Recalculate Shortest path from those entries. A nearby Start vertex can challenge the Dijkstra Shortest Path relationship, but its Shortest path belongs to a separate Dijkstra Shortest Path record.
Cross-checking Dijkstra Shortest Path
Check the direction of Shortest path by changing Vertices slightly. Hold Weighted edges steady during this Dijkstra Shortest Path trial. The new Shortest path should move as the Dijkstra Shortest Path relationship predicts unless the calculation crosses a stated boundary.
Compare Shortest path with the quantity named in the Dijkstra Shortest Path question. Re-read Vertices, Weighted edges, and Start vertex before accepting the number. This noun check catches cases where valid arithmetic produces a related value rather than the requested Shortest path.
An independent estimate makes Dijkstra Shortest Path easier to trust. Derive a rough Shortest path from Vertices and Weighted edges, then compare its magnitude with the calculated Shortest path. Large disagreement deserves attention before the Dijkstra Shortest Path output is rounded or reused.
Validating Dijkstra Shortest Path
Choose a familiar Vertices and rerun Dijkstra Shortest Path. With Weighted edges unchanged, estimate Shortest path by hand. This small Dijkstra Shortest Path case provides context for the original Shortest path without duplicating it.
Reviewing Dijkstra Shortest Path in context
Shortest-path work depends on the same vertices and edges used to describe a graph's structure. For that connected step, see graph structure.
Questions about Dijkstra Shortest Path
What does Dijkstra Shortest Path calculate?
Dijkstra’s algorithm repeatedly settles the closest unvisited vertex and relaxes its outgoing nonnegative edges.
When is Dijkstra Shortest Path useful?
It routes transportation, networks, workflows, game maps, and dependency costs when every weight is nonnegative.
What can make Dijkstra Shortest Path misleading?
Negative edge weights invalidate Dijkstra’s settled-distance guarantee, and disconnected endpoints have no path.