## Does minimum spanning tree give shortest path?

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Minimum spanning tree is a tree in a graph that spans all the vertices and total weight of a tree is minimal. Shortest path is quite obvious, it is a shortest path from one vertex to another.

### How do you find the shortest path spanning tree?

If there are N vertices are present inside graph G then the minimum spanning tree of the graph will contain N-1 edges and N vertices. If there are N vertices present inside graph G, then in the shortest path between two vertices there can be at most N-1 edges, and at most N vertices can be present in the shortest path.

#### Does Dijkstra give MST?

Strictly, the answer is no. Dijkstra’s algorithm finds the shortest path between 2 vertices on a graph. However, a very small change to the algorithm produces another algorithm which does efficiently produce an MST. The Algorithm Design Manual is the best book I’ve found to answer questions like this one.

**What is shortest path in a graph?**

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

**Is shortest path a tree?**

A shortest path tree, in graph theory, is a subgraph of a given (possibly weighted) graph constructed so that the distance between a selected root node and all other nodes is minimal.

## What is shortest path in data structure?

In data structures, Shortest path problem is a problem of finding the shortest path(s) between vertices of a given graph. Shortest path between two vertices is a path that has the least cost as compared to all other existing paths.

### Which is better Prims or Kruskal or Dijkstra?

Dijkstra’s algorithm can work on both directed and undirected graphs, but Prim’s algorithm only works on undirected graphs. Prim’s algorithm can handle negative edge weights, but Dijkstra’s algorithm may fail to accurately compute distances if at least one negative edge weight exists.