Prim Minimum Spanning Tree Algorithm

Previously, we explained the core idea of the Kruskal algorithm for the minimum spanning tree: sort the edges first, and then use the union-find data structure to build the minimum spanning tree.

In terms of approach, the essence of the Prim algorithm is BFS plus a greedy strategy. It sorts and builds the minimum spanning tree at the same time, which is like a dynamic process compared to Kruskal's sort-then-build method.

From a coding perspective, Prim's algorithm is very similar to Dijkstra's algorithm. You only need to change a few lines of code to turn Dijkstra's algorithm into Prim's algorithm. Therefore, before learning Prim's algorithm, you need to thoroughly understand Dijkstra's Algorithm: Principle and Implementation.

This article will first show the implementation of Prim's algorithm, then explain its principle, and why you can directly derive Prim's algorithm from Dijkstra's code.

Prim Algorithm Code

You only need to modify a few lines in the Dijkstra algorithm template to get Prim's algorithm. The modified parts are already highlighted:

Cut Property Theorem

Correctness of the Algorithm

Complexity Analysis

Problem Practice