The data structure typically used to implement a depth-first search (DFS) algorithm is a stack. A stack is a Last-In-First-Out (LIFO) data structure, meaning that the last element pushed onto the stack is the first one to be popped out.

  In a DFS algorithm, starting from a given vertex, we explore as far as possible along each branch before backtracking. To keep track of the current path, we use a stack to store the nodes that we have encountered. Each time we visit a new node, we push it onto the stack. When we backtrack, we pop the top node from the stack and continue exploring the next adjacent unvisited node.

  The stack is used to maintain the order in which nodes are visited during the search. By pushing the nodes onto the stack, we ensure that we visit the child nodes before exploring the sibling nodes.

  It's important to note that while the stack is the typical data structure used for DFS, other data structures like recursion and explicit stacks can also be used depending on the specific implementation of the algorithm and the problem at hand.