Find minimum weight cycle in an undirected graph
Given a positive weighted undirected graph, find the minimum weight cycle in it.
Minimum weighted cycle is :
Minimum weighed cycle : 7 + 1 + 6 = 14 or 2 + 6 + 2 + 4 = 14
The idea is to use shortest path algorithm. We one by one remove every edge from the graph, then we find the shortest path between two corner vertices of it. We add an edge back before we process the next edge.
1). create an empty vector 'edge' of size 'E' ( E total number of edge). Every element of this vector is used to store information of all the edge in graph info 2) Traverse every edge edge[i] one - by - one a). First remove 'edge[i]' from graph 'G' b). get current edge vertices which we just removed from graph c). Find the shortest path between them "Using Dijkstra’s shortest path algorithm " d). To make a cycle we add the weight of the removed edge to the shortest path. e). update min_weight_cycle if needed 3). return minimum weighted cycle
Below is the implementation of the above idea
Time Complexity: O( E ( E log V ) )
Space Complexity : O(V^2)
For every edge, we run Dijkstra’s shortest path algorithm so over all time complexity E2logV.
In set 2 | we will discuss optimize the algorithm to find a minimum weight cycle in undirected graph.
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