Feature/hierholzer_algorithm pr#392
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Add Hierholzer's algorithm (C++) to CPP/algorithms/graph_algorithms
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Problem
Given a connected graph (directed or undirected), find:
Eulerian Path → visits every edge exactly once.
Eulerian Circuit → visits every edge exactly once and starts/ends at the same vertex.
Conditions
Undirected Graph
Eulerian Circuit → all vertices have even degree.
Eulerian Path → exactly 2 vertices have odd degree.
Directed Graph
Eulerian Circuit → indegree = outdegree for all vertices.
Eulerian Path → exactly one vertex has (out = in + 1), one has (in = out + 1), rest balanced.
Approach (Hierholzer’s Algorithm)
Choose a starting node:
Circuit → any node.
Path → vertex with (outdegree > indegree).
Traverse edges using a stack, removing them as you go.
When stuck, backtrack and add vertex to path.
Continue until all edges are used.
Reverse result → Eulerian Path / Circuit.
Visualization Example
Graph: 0→1, 1→2, 2→0, 0→3, 3→0
Walk: 0 → 3 → 0 → 1 → 2 → 0
Backtrack order: 0, 2, 1, 0, 3, 0
Final Path: 0 → 3 → 0 → 1 → 2 → 0 (Eulerian Circuit)
Complexity
Time: O(E) → each edge is used exactly once.
Space: O(V + E) → adjacency list + stack.