Leetcode Problem 2097. Valid Arrangement of Pairs

2097. Valid Arrangement of Pairs

Leetcode Solutions

Hierholzer's Algorithm for Eulerian Path

  1. Create a graph representation from the given pairs, with each starti as a key in a dictionary pointing to a list of endi values.
  2. Calculate the in-degree and out-degree for each vertex.
  3. Find the starting vertex for the Eulerian path. It will be the vertex with out-degree - in-degree = 1. If no such vertex exists, start from any vertex with an outgoing edge.
  4. Use a stack to perform a Depth-First Search (DFS). As you traverse an edge, remove it from the graph.
  5. Once you reach a vertex with no more outgoing edges, add it to the path.
  6. Continue until all edges are used.
  7. Reverse the path to get the Eulerian path in the correct order.
  8. Convert the path to the required pairs format and return it.
UML Thumbnail

Backtracking to Construct a Valid Arrangement

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