How does Dijkstra's algorithm ensure that the shortest path is found?

How does Dijkstra's algorithm ensure that the shortest path is found?

Step 1: Start with a graph that has nodes (points) and edges (connections between points).
Step 2: Choose a starting node and set its distance to 0 (since it's the starting point).
Step 3: Set the distance to all other nodes to infinity (unknown distance).
Step 4: Create a list of unvisited nodes that includes all nodes in the graph.
Step 5: While there are unvisited nodes, do the following:
Step 5a: Select the unvisited node with the smallest distance (this is the current node).
Step 5b: For each neighbor of the current node, calculate the distance from the start node to that neighbor through the current node.
Step 5c: If this new distance is less than the previously recorded distance for that neighbor, update the neighbor's distance.
Step 5d: Once all neighbors are checked, mark the current node as visited (it won't be checked again).
Step 6: Repeat Step 5 until all nodes are visited or the shortest path to the target node is found.
Step 7: The shortest path is determined by tracing back from the target node to the starting node using the recorded distances.

Greedy Algorithm – Dijkstra's algorithm employs a greedy strategy by selecting the node with the lowest cumulative cost at each step.
Graph Theory – The algorithm operates on weighted graphs, where edges have associated costs.
Optimal Substructure – Dijkstra's algorithm relies on the principle that the shortest path to a node can be constructed from the shortest paths to its predecessors.