JAVA Which of these are in increasing order of complexity a

JAVA: Which of these are in increasing order of complexity?

(a) O(n) < O(log n) < O(n^2) < O(n^3) < O(2^n)
(b) O(n) < O(log n) < O(2^n) < O(n^2) < O(n^3)
(c) O(log n) < O(n) < O(2^n) < O(n^2) < O(n^3)
(d) O(log n) < O(n) < O(n^2) < O(n^3) < O(2^n)

Solution

Answer:

d) O(log n) < O(n) < O(n^2) < O(n^3) < O(2^n)

If we check between n^ 3 and 2^n

n^3 2^n

taking log on both sides

log(n^3) log(2^n)

3logn nlog2

chech at higher values of n , n = 128

3 * log(128) 128 *log2

3 * 7 128

21 < 128

means 2^n > n^3

Hence O(n^3) < O(2^n) , with this way we can check for others.