Feb 9, 2024 · The time complexity of Prim's algorithm is O(V 2) using an adjacency matrix and O((V +E) log V) using an adjacency list, where V is the number of vertices and E is the number of edges in the graph. The space complexity is O(V+E) for the priority queue and O(V 2 ) for the adjacency matrix representation.

Feb 26, 2025 · Prim’s algorithm is guaranteed to find the MST in a connected, weighted graph. It has a time complexity of O((E+V)*log(V)) using a binary heap or Fibonacci heap, where E is the number of edges and V is the number of vertices.

In this article, we will learn more about Prim's algorithm and analyze its complexity for different cases and implementation approaches. Table of contents. Prim's algorithm; Complexity analysis * Time complexity * Different cases of time complexity * Space complexity; Prim's algorithm

The time complexity of Prim's algorithm is O(VlogV + ElogV). It seems like you understand how the VlogV came to be, so let's skip over that. So where does ElogV come from? Let's start by looking at Prim's algorithm's source code:

The time complexity of Prim's algorithm depends on the data structures used for the graph and for ordering the edges by weight, which can be done using a priority queue. The following table shows the typical choices:

Feb 27, 2025 · Prim’s algorithm is a key method in data structure used to find the Minimum Spanning Tree (MST) of a graph. This algorithm works by starting with a single node and gradually adding the smallest possible edges that connect new nodes to the tree.

Prim's algorithm finds the MST by first including a random vertex to the MST. The algorithm then finds the vertex with the lowest edge weight from the current MST, and includes that to the MST. Prim's algorithm keeps doing this until all nodes are included in the MST.

The time complexity is O(VlogV + ElogV) = O(ElogV), making it the same as Kruskal's algorithm. However, Prim's algorithm can be improved using Fibonacci Heaps (cf Cormen) to O(E + logV).

Oct 30, 2012 · Prim's Algorithm is an algorithm that takes a graph and a starting node, and finds a minimum spanning tree on the graph - that is, it finds a subset of the edges so that the result is a tree that contains all the nodes and the combined edge weights are minimized. It may be summarized as follows: Place the starting node in the tree.

In this article, we will analyze the time complexity of the Prim's algorithm. How Does Prim's Algorithm Work? Prim's algorithm: Chooses a starting vertex and add it to the MST. Adds the edge with the least weight that connects a vertex in MST with the remaining vertices. Repeats the previous step until all vertices are included in the MST.