Dual Graph Face Count

Problem

Compute the number of faces of a connected plane graph from its edge count and vertex count.

Euler's formula V - E + F = 2 gives F = E - V + 2, where the outer face is included. n is the number of vertices and edges is the edge list of the embedded connected planar graph. Return F as an integer.

Hint

Every face of the plane graph becomes a vertex of the dual graph.

Test cases

case 1

in: [3,[[0,1],[1,2],[2,0]]]

expected: 2

case 2

in: [4,[[0,1],[1,2],[2,3],[3,0]]]

expected: 2

case 3

in: [4,[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]]

expected: 4

case 4

in: [5,[[0,1],[1,2],[2,3],[3,4],[4,0]]]

expected: 2

Starter codePython

def dual_graph_face_count(n, edges):
    # Your code here
    pass

4 test cases · run your code against them in the editor