How Depth First Works - Learning How AI works in Harvard's EAD

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Depth-First Search is a type of Search algorithm that uses the Stack data-type (Last-in First-out) and it works by choosing a path and following it until the Dead-end, but how it does when put to solve a simple puzzle?

Harvard's EAD (The one I'm using):
https://learning.edx.org/course/course-v1:HarvardX+CS50AI+1T2020/home

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