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Could you give me examples of polynomial-time algorithms that must compute a global property over their entire input? A purely illustrative example of this might be a graph algorithm that somehow must count the total number of nodes before computing its final answer.

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    $\begingroup$ Finding the minimum element of an array or a list? $\endgroup$ – Pseudonym Sep 2 '20 at 0:32
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A silly example: Checking if a graph has more than m nodes. :-)

Some more interesting examples:

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