What is the difference between the Dijkstra Algorithm and the Kruskal's Algorithm?

The Dijkstra Algorithm and Kruskal's Algorithm are both popular algorithms used in graph theory, but they serve different purposes and have distinct differences.

1. Purpose:
- Dijkstra Algorithm: It is primarily used to find the shortest path between a source node and all other nodes in a weighted graph. It calculates the minimum distance from the source node to all other nodes, considering the weights of the edges.
- Kruskal's Algorithm: It is used to find the minimum spanning tree (MST) of a connected weighted graph. The MST is a tree that connects all the vertices of the graph with the minimum total weight.

2. Approach:
- Dijkstra Algorithm: It uses a greedy approach, where it starts from the source node and iteratively selects the node with the minimum distance and adds it to the set of visited nodes. It then updates the distances of the neighboring nodes based on the selected node, until all nodes are visited.
- Kruskal's Algorithm: It uses a greedy approach as well, but it focuses on selecting the edges with the minimum weight. It starts with an empty set of edges and iteratively adds the edges with the minimum weight that do not form a cycle, until all vertices are connected.

3. Output:
- Dijkstra Algorithm: It provides the shortest distance from the source node to all other nodes in the graph, along with the shortest path from the source node to each node.
- Kruskal's Algorithm: It outputs the set of edges that form the minimum spanning tree, which connects all the vertices of the graph with the minimum total weight.

4. Graph Type:
- Dijkstra Algorithm: It can be applied to both directed and undirected graphs, as long as the graph has non-negative edge weights.
- Kruskal's Algorithm: It is specifically designed for undirected graphs, as it assumes symmetry in edge weights.

In summary, the main difference between Dijkstra Algorithm and Kruskal's Algorithm lies in their purpose and the type of output they provide. Dijkstra Algorithm finds the shortest path between a source node and all other nodes, while Kruskal's Algorithm finds the minimum spanning tree of a graph.