Algorithms sanjoy dasgupta solutions
Algorithms by dasgupta papadimitriou, and vazirani pdf.
Solution Manual For Algorithms by Das Gupta Papadimitriou and Vazirani
Since and have the same power of n.
Since n1/2 is smaller than n2/3
Since can always be overcome by above a particular , and so can it be less than below a particular .
Since
Since log 2n = log 2 + log n and log 3n = log 3 + log n.
Algorithms dasgupta solutions pdf github
which makes log 2 and log 3, just constants.
Since log n^2 = 2log n. and 2 is just a constant that can be dropped.
Since power greater than 0 can always overtake log at some point
On comparing n^2 is greater than n, and log’s are not that signifincant in comparison.
Since power greater than 0 can always overtake log at some point
Since (log n)(log n) -1 is greater than n for some value of n.
Since power greater than 0 can always overtake log at some point
Therefore, at some n g will overcome f, by comparison of powers.
Since n2^n will produce a greater value for n than 3^n at some point.
Since the two differ by a constant multiplicative factor, i.e.
2.
g(n) = 1