What happens when Dijkstra's algorithm visits a node?

The algorithm examines each unvisited neighbour and adds the edge weight to the current distance. A neighbour's tentative distance is replaced if the new total is smaller.

When does Dijkstra's algorithm stop?

The algorithm stops when every node has been visited, or when the destination node has been settled. Further improvement is impossible at that point.

Why is a visited node never reconsidered?

A visited node was chosen because it had the smallest tentative distance of all remaining nodes. A later path through a more distant node can never beat it while weights stay non-negative.

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Searching and Shortest-Path Algorithms

Dijkstra's shortest-path algorithm

3 things to know
Component 1

Overview

Settling the nearest unvisited node, relaxing the distances to its neighbours, and repeating — the algorithm that finds the lowest-cost route rather than the fewest hops.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What does Dijkstra's algorithm compute?

Key term

Describe the first step of Dijkstra's algorithm.

Key term

Which node does Dijkstra's algorithm visit next at each step?

Questions from this subtopic

Each one with the model answer underneath.

1
What does Dijkstra's algorithm compute?
Model answer
Dijkstra's algorithm computes the lowest cost path from one starting node to every other node. The algorithm works on graphs with non-negative edge weights.
2
Describe the first step of Dijkstra's algorithm.
Model answer
The distance to the start node is set to 0 and every other node is set to infinity. All nodes begin in the unvisited set.
3
Which node does Dijkstra's algorithm visit next at each step?
Model answer
The algorithm visits the unvisited node with the smallest tentative distance. The distance to that node is then treated as final.
4
What happens when Dijkstra's algorithm visits a node?
Model answer
The algorithm examines each unvisited neighbour and adds the edge weight to the current distance. A neighbour's tentative distance is replaced if the new total is smaller.
5
When does Dijkstra's algorithm stop?
Model answer
The algorithm stops when every node has been visited, or when the destination node has been settled. Further improvement is impossible at that point.
6
Why is a visited node never reconsidered?
Model answer
A visited node was chosen because it had the smallest tentative distance of all remaining nodes. A later path through a more distant node can never beat it while weights stay non-negative.

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Boolean Logic and Simplification

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