Polynomial time complexity in algorithms causes tasks to become increasingly complex with each additional input, much like managing a family WhatsApp group. Joining the group is O(n), deciphering messages is O(n^2), and managing disputes is O(n^3). Nested loops and multiple operations on the entire dataset indicate polynomial time complexity, such as O(n^2) or O(n^3).

In a linear time scenario, the time taken to complete a task grows with the size of the input. Like avoiding pesky questions at a big family gathering, each relative must be checked before finding the relative of interest. Similarly, in algorithms, checking each element in a list one by one creates a linear relationship. As datasets grow, efficient algorithms become crucial.

O(logn) indicates logarithmic time complexity, where the algorithm’s efficiency grows as the problem size reduces. For instance, in a sorted list search, you progressively eliminate half the list at each step, akin to finding a word in a dictionary by halving the search space. Various examples illustrate logarithmic time complexity, emphasizing its efficiency for large datasets.