For a detailed description of**Dijkstra's algorithm**, please refer to[1514. Path with Maximum Probability](../1001-2000/1514-path-with-maximum-probability.md).

|Algorithm name|Main application scenarios|Optimization methods|Importance|Difficulty|min_distances|Additional application scenarios|

|--------------|--------------------------|--------------------|----------|----------|-------------|--------------------------------|

|[Prim's algorithm](../1001-2000/1584-min-cost-to-connect-all-points.md)|Minimum Spanning Tree|Heap Sort|Important|Medium|Used||

|[Kruskal's algorithm](../1001-2000/1584-min-cost-to-connect-all-points-2.md)|Minimum Spanning Tree|Heap Sort|important|Relatively hard|Not used|Relative scenarios:[Undirected Graph Cycle Detection](./684-redundant-connection.md),[Directed Graph Cycle Detection](./685-redundant-connection-ii.md)|

|[Dijkstra's algorithm](../1001-2000/1514-path-with-maximum-probability.md)|Single-Source Shortest Path|Heap Sort|Very important|Medium|Used||

|[Bellman-Ford algorithm](./743-network-delay-time.md)|Single-Source Shortest Path|Queue-Improved|Very Important|Easy|Used|Negative Edge Weights,<br>[Detect Negative Cycles](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/),<br>[Shortest Hop-Bounded Paths](./787-cheapest-flights-within-k-stops.md)|

|Algorithm name|Main application scenarios|Optimization methods|Importance|Difficulty|min_distances|Negative weights|Additional application scenarios|

|--------------|--------------------------|--------------------|----------|----------|-------------|----------------|--------------------------------|

|[Prim's algorithm](../1001-2000/1584-min-cost-to-connect-all-points.md)|Minimum Spanning Tree|Heap Sort|Important|Medium|Used|Able to handle||

|[Kruskal's algorithm](../1001-2000/1584-min-cost-to-connect-all-points-2.md)|Minimum Spanning Tree|Heap Sort|important|Relatively hard|Not used|Able to handle|Relative:[Undirected Graph Cycle Detection](./684-redundant-connection.md),[Directed Graph Cycle Detection](./685-redundant-connection-ii.md)|

|[Dijkstra's algorithm](../1001-2000/1514-path-with-maximum-probability.md)|Single-Source Shortest Path|Heap Sort|Very important|Medium|Used|Unable to handle||

|[Bellman-Ford algorithm](./743-network-delay-time.md)|Single-Source Shortest Path|Queue-Improved|Very Important|Easy|Used|Able to handle|[Detect Negative Cycles](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/),<br>[Shortest Hop-Bounded Paths](./787-cheapest-flights-within-k-stops.md)|

**V**: vertex count,**E**: Edge count.

**Dijkstra算法**的详细说明，请参考[1514. 概率最大的路径](../1001-2000/1514-path-with-maximum-probability.md)。

|算法名称|主要的适用场景|优化方式|重要程度|难度|min_distances|额外的适用场景|

|-------|-----------|-------|-------|---|-------------|------------|

|[Prim算法](../1001-2000/1584-min-cost-to-connect-all-points.md)|最小生成树|堆排序|重要|中等|用到||

|[Kruskal算法](../1001-2000/1584-min-cost-to-connect-all-points-2.md)|最小生成树|堆排序|重要|较难|不用|相关场景：[无向图环检测](./684-redundant-connection.md),<br>[有向图环检测](./685-redundant-connection-ii.md)|

|[Dijkstra算法](../1001-2000/1514-path-with-maximum-probability.md)|单源最短路径|堆排序|非常重要|中等|用到||

|[Bellman-Ford算法](./743-network-delay-time.md)|单源最短路径|~~队列~~`集合`优化|非常重要|简单|用到|负边权值，[负环检测](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/),<br>[限定步数最短路径](./787-cheapest-flights-within-k-stops.md)|

|算法名称|主要的适用场景|优化方式|重要度|难度|min_<br>distances|负边权值|额外的适用场景|

|-------|-----------|-------|-------|---|-------------|--------|------------|

|[Prim算法](../1001-2000/1584-min-cost-to-connect-all-points.md)|最小生成树|堆排序|重要|中等|用到|能处理||

|[Kruskal算法](../1001-2000/1584-min-cost-to-connect-all-points-2.md)|最小生成树|堆排序|重要|较难|不用|能处理|相关：[无向图环检测](./684-redundant-connection.md),[有向图环检测](./685-redundant-connection-ii.md)|

|[Dijkstra算法](../1001-2000/1514-path-with-maximum-probability.md)|单源最短路径|堆排序|很重要|中等|用到|不能处理||

|[Bellman-Ford算法](./743-network-delay-time.md)|单源最短路径|集合优化|很重要|简单|用到|能处理|[负环检测](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/),[限定步数最短路径](./787-cheapest-flights-within-k-stops.md)|

**V**: 顶点数量，**E**: 边的数量。