The big O specifies 2 positive constants c and n_0 but there can be multiple c and n_0 values that are solutions. How can we decide which one is the best. What does having multiples solutions signify ?
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Big o notation is useful for situations like this: I have tested my code on a small input dataset of 1000 entries, and it took ten seconds to run. I’d now like to analyze a million entries. How long will that take? A few hours? A few months? Years? Centuries?
All of these are possible depending on the complexity of the algorithm. Since it’s the same algorithm in either case the multiplicative constant is identical and since the numbers are huge the additive constant is irrelevant: all that matters is the power of N.
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