Understanding depth-first search pattern

The depth-first search algorithm starts from a node and explores all the nodes in a branch before backtracking and choosing other paths. It makes arbitrary choices of nodes at each depth until it can no longer make a choice and backtracks to update previous choices. It is a recursive algorithm that keeps track of all nodes in the path using a stack, enabling backtracking. The recursive implementation of the algorithm uses the function call stack to store nodes and any additional context at each step. Many graph problems can be efficiently solved using depth-first search.