How does Dijkstra's algorithm ensure that it finds the shortest path?

How does Dijkstra's algorithm ensure that it finds the shortest path?

Step 1: Start with a graph that has nodes (vertices) and edges (connections between nodes).
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 (meaning they are initially unreachable).
Step 4: Mark all nodes as unvisited.
Step 5: While there are unvisited nodes, do the following:
Step 5a: Select the unvisited node with the smallest distance (this is the nearest node).
Step 5b: Mark this node as visited.
Step 5c: Update the distances to its neighboring unvisited nodes. If the new calculated distance is smaller than the current distance, update it.
Step 6: Repeat Step 5 until all nodes are visited.
Step 7: The algorithm finishes when all nodes are visited, and the shortest path to each node is determined.

Greedy Algorithm – Dijkstra's algorithm uses a greedy approach by selecting the nearest unvisited vertex to ensure the shortest path is found.
Graph Theory – The algorithm operates on weighted graphs, where edges have non-negative weights.
Priority Queue – Dijkstra's algorithm utilizes a priority queue to efficiently select the next vertex to process.