Minimum spanning tree for [Data Structure & Algrithom] without graphs

Min Spanning tree (Minimum Spanning tree)-the smallest of the weights that connect the edges of all vertices

Prim algorithm

• Basic idea-Set the vertex set of the graph to V; the vertex set of the minimum spanning tree is U
  1. Place a vertex into u
  2. In one vertex belonging to u, the other vertex belongs to all the edges of the v-u, and the least weighted edge is found
  3. The vertex that will be found does not belong to u, put in U, repeat 2 until you include all vertices in u
• Specific implementation
  • Introduce auxiliary array edge[], length equals the number of vertices
    • Node structure-data field vertex (another vertex connected to the vertex) | weight cost (weight of this edge)
    • For nodes in U i-edge[i].cost = 0
    • For node J-edge[j in V-u] represents the least-weighted edge of the node J
  • Time complexity O (n2) (independent of the number of edges)
• Suitable for edge-dense graphs

Kruskal algorithm

• Basic ideas
  1. Select the edge with the least weight in the diagram
  2. If this edge does not form a loop, select this edge; otherwise, find the edge of the next weighted value
• Time complexity (independent of vertex count)
  • O (n2)-already sorted by the weight of the edge
  • O (ELOG2E)-not sorted by the weight of the edge
• Graphs for edge coefficients

Minimum spanning tree for [Data Structure & Algrithom] without graphs