Let's say your current programming project is using a circular queue implementation which uses a simple modulus operation for moving the head and tail forward: p = (p+1)%n. But the queue isn't a purely traditional one and you sometimes have to move backwards during a search. When this search wraps from the front to the rear, you must use this code: p = (p==0?n-1:p-1). One day programmer Sam comes up with this little gem: p=(p+d)%n. Here d is filled in with 1 when moving forward and n-1 when moving backwards. Can Sam's simple solution be correct? Prove or disprove Sam here.

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Depth First Search

Depth-first search (DFS) also known as Depth First traversal is an algorithm used to traverse or search the nodes in a tree or graph data structure. Traversal usually means visiting all the nodes of a graph. DFS performs in a depth-ward manner. It uses a stack to remember the vertices it has visited. The search starts from the root node, where any arbitrary node is selected as a root node in a graph, and then each node is explored along each branch before performing backtracking. The DFS algorithm uses a recursive technique by following the idea of backtracking. DFS algorithm does this by performing an in-depth search of all the nodes by traversing in a forward direction. If the required node is not found, it starts backtracking to previously visited nodes.