Question

Matching A function fin) is of higher order than gin) if f (n) E 2 (9 (n)) In other words, f(n) is of higher order than gín) if g(n) is an asymptotic lower bound to fín) Match the following functions based on their order. Assign the number 1 to the function with the lowest order. Assign the same number to functions with the same order I Choose ] 2A(n-1) I Choose Square Root (n) I Choose l 1000lg 2(n) I Choose l [Choose l 2An

Answer 1

1.

n! ------> 5

2^n-1 ------> 3

sqrt(n) ----> 2

1000lg²n -----> 1

2ⁿ ------> 4

5.

n! = 1 * 2 * .... * n

1 * 2 * .... * n <= n * n * .... * n (n terms)

or, n! <= nⁿ

Hence, n! = O(nⁿ)

7.

The smallest value can be found by:

10n² >= 0

or, n >= 0

Hence, the smallest value is 0.

8. The smallest value can be found by:

40n - 400 >= 0

or, n >= 10

Hence, the smallest value is 10.