# Searches: Efficiency

### Problems

Problem : Define "Big-O notation".

Problem : Prove that the function f (n) = n 2 + 3n + 1 is O(n 2) .

Problem : You are given two functions, one which has an average case running time of O(n 2) and the other which has an average running time of O(nlogn) . In general, which would you choose?

Problem : True or false: A function with O(n) efficiency will always run faster than a function with O(n 2) efficiency?

Problem : Draw a graph showing how n , logn , n 2 , and 2n compare as n increases.

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