Give the time complexities (Big-O notation) of the following running times expressed as a function of the input size N.
a) N12+ 25N10+ 8
b) N + 3logN + 12n√n
c) 12NlogN + 15N2 logN
Big - O notation is used to give the time complexity of a function. It describes the worst case scenario on the running time of a program.
(a)
n12 + 25n10 + 8
Here the n12 term grows faster than 25n10 for large inputs.
So time complexity is O(n12) .
(b)
n + 3logn + 12n√n
Here the 12n√n term grows faster than both 3logn and n for large inputs.
So time complexity is O(n√n) .
(c)
12nlogn + 15n2 logn
Here the 15n2 logn term grows faster than 12nlogn for large inputs.
So time complexity is O(n2 logn) .
Note that the time complexity notation subsumes any multiplied constant terms
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