Jul 23, 2025 · The time complexity of Prim's algorithm is O (V2) 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 …

Using a simple binary heap data structure, Prim's algorithm can now be shown to run in time O (|E| log |V|) 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.

I found the time complexity of Prims algorithm everywhere as O ( (V + E) log V) = E log V. But as we can see the algorithm: It seems like the time complexity is O (V (log V + E log V)).

The reason why we get this time complexity is because of the nested loops inside the Prim's algorithm (one for-loop with two other for-loops inside it). The first for-loop (line 24) goes through all …

Feb 14, 2026 · Learn about the Prim algorithm with examples in this tutorial. Understand how it works, why it’s important, and how it can be applied to solve various problems.

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).

Jan 11, 2026 · Learn Prims Algorithm for finding the Minimum Spanning Tree (MST) in connected, weighted graphs using the Greedy approach. Understand its steps, time complexity, advantages, …

May 19, 2025 · Dive into step-by-step implementation of Prim's algorithm, time complexity, variations, and applications in network design.

Mar 27, 2026 · 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 …