Implementation of topological sorting algorithm (Python)

Implementation of topological sorting algorithm (Python)

Topological sorting is a node sorting algorithm used in Directed Acyclic Graph (DAG). It can sort the nodes in the graph according to their dependencies so that all dependencies are satisfied. In practical applications, topological sorting is often used to solve problems such as task scheduling and dependency analysis. This article will introduce how to use Python to implement the topological sorting algorithm.

Before we begin, we need to clarify some basic concepts. In topological sorting, we represent the nodes in the graph as vertices (Vertex), and the dependencies between nodes as directed edges (Directed Edge). If node A depends on node B, then node B should be ranked in front of node A in the sorting result.

The algorithm implementation steps are as follows:

1. Constructing the representation of the graph: We first need to represent the graph in an appropriate data structure. In Python, we can use dictionaries to represent graphs. The key of the dictionary represents the node, and the corresponding value represents the node's direct successor node.

2. Calculate the in-degree of a node: Next, we need to calculate the in-degree of each node, which is the number of edges pointing to the node. We can do this by traversing all the edges of the graph and counting the number of times each node serves as an end point.

3. Initialize topological sorting results: We use a list to save the results of topological sorting. Initially, the list is empty.

4. Find the node with in-degree 0: We traverse all the nodes in the graph, find the node with in-degree 0, and add it to the topological sorting result list.

5. Removing nodes and updating in-degree: For each node with in-degree 0, we remove it from the graph and update the in-degree of all direct successor nodes.