# Algorithms | Graph Traversals | Question 1

Which of the following algorithms can be used to most efficiently determine the presence of a cycle in a given graph ?

(A)

Depth First Search

(B)

(C)

Prim\’s Minimum Spanning Tree Algorithm

(D)

Kruskal\’ Minimum Spanning Tree Algorithm

Explanation:

To find cycle in a graph we can use the Depth First Traversal (DFS) technique. It is based on the idea that there is a cycle in a graph only if there is a back edge [i.e., a node points to one of its ancestors] present in the graph.

To detect a back edge, we need to keep track of the nodes visited till now and the nodes that are in the current recursion stack [i.e., the current path that we are visiting]. If during recursion, we reach a node that is already in the recursion stack, there is a cycle present in the graph.

Hence Option (B) is the correct answer.

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