Kruskal’s algorithm and Prim’s algorithm are both used to find the minimum spanning tree of a weighted graph. Here are the differences between the two algorithms:

Algorithm | Approach | Data Structure | Time Complexity |

Kruskal’s Algorithm | Greedy | Disjoint Set | O(E log E) |

Prim’s Algorithm | Greedy | Priority Queue | O(E log V) |

**1. Approach:** Kruskal’s algorithm is a Greedy approach that starts with an empty spanning tree and adds edges to it one at a time, while ensuring that no cycle is formed. Prim’s algorithm, on the other hand, starts with a single vertex and adds edges to it until it forms a spanning tree.

**2. Edge selection: **Kruskal’s algorithm selects the minimum weighted edge that does not form a cycle at each step, while Prim’s algorithm selects the minimum weighted edge that connects a vertex in the tree to a vertex outside the tree.

**3. Data structure: **Kruskal’s algorithm uses a Disjoint Set Data Structure to maintain the disjoint sets of vertices and detect cycles. Prim’s algorithm uses a priority queue or a heap to select the minimum weighted edge.

**4. Running time: **The worst-case running time of Kruskal’s algorithm is O(E log E), where E is the number of edges in the graph. The worst-case running time of Prim’s algorithm is O(E log V), where V is the number of vertices in the graph.

**5. Complexity:** Kruskal’s algorithm has a space complexity of O(E), while Prim’s algorithm has a space complexity of O(V).

**6. Performance:** Kruskal’s algorithm performs better on sparse graphs with a large number of edges, while Prim’s algorithm performs better on dense graphs with a large number of vertices.