BackhardGraphs

Minimum Cycle Basis Enumeration Solution

Problem Statement

Given an undirected graph represented as an adjacency list, find a minimum cycle basis, which is a set of simple cycles with the minimum total length such that any other cycle in the graph can be expressed as a linear combination of these cycles.

Example 1

Input

Let the graph be represented as an adjacency list: {0: [1, 2], 1: [0, 2, 3], 2: [0, 1, 3], 3: [1, 2]}

Output

[[0, 1, 2, 0], [1, 2, 3, 1]]

Explanation: The minimum cycle basis consists of two cycles: 0-1-2-0 and 1-2-3-1.

Example 2

Input

Consider the graph represented as an adjacency list: {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}

Output

[[0, 1, 2, 3, 0]]

Explanation: The minimum cycle basis consists of a single cycle: 0-1-2-3-0.

Constraints

The graph is represented as an adjacency list.
The graph may contain self-loops and parallel edges.
The graph has at most 100 vertices and 500 edges.
All edge weights are assumed to be 1 for simplicity.

Minimum Cycle Basis Enumeration Solution

Problem Statement

Input

Output

Input

Output

Constraints

More Graphs Problems

Optimized Approach

Step-by-Step Dry Run

Tested Solutions