Day 51
Day 51: Hamiltonian Cycle
51/60 Days
Day 51: Hamiltonian Cycle #
Welcome to Day 51 of our 60 Days of Coding Algorithm Challenge! Today, we’ll explore the Hamiltonian Cycle problem, a classic problem in graph theory that demonstrates the power and limitations of backtracking algorithms.
What is a Hamiltonian Cycle? #
A Hamiltonian cycle (or Hamiltonian circuit) is a cycle in an undirected graph that visits each vertex exactly once and returns to the starting vertex. It’s named after the mathematician William Rowan Hamilton.
Understanding the Problem #
- We have an undirected graph G = (V, E), where V is the set of vertices and E is the set of edges.
- We need to find a cycle that visits every vertex exactly once and returns to the starting vertex.
- If such a cycle exists, the graph is called Hamiltonian.
Backtracking Approach #
We’ll use a backtracking approach to solve this problem:
- Start from a vertex (typically vertex 0).
- Add the current vertex to the path.
- If all vertices are visited and there’s an edge from the last vertex to the first vertex, we’ve found a Hamiltonian cycle.
- Otherwise, try adding each adjacent unvisited vertex to the path.
- If adding a vertex …
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