## Asymptotic-Complexity

Question 1 |

Consider the following functions from positives integers to real numbers

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

Question 1 Explanation:

In this problem, they are expecting to find us “increasing order of asymptotic complexity”.

Step-1: Take n=2048 or 2

Step-2: Divide functions into 2 ways

1. Polynomial functions

2. Exponential functions

Step-3: The above functions are belongs to polynomial. So, simply substitute the value of n,

First compare with constant values.

→ 100 / 2048 = 0.048828125

→ 10 > 100/ 2048

→ log

→ √n = 45.25483399593904156165403917471

→ n = 2048

So, Option B is correct

Step-1: Take n=2048 or 2

^{11}(Always take n is very big number)Step-2: Divide functions into 2 ways

1. Polynomial functions

2. Exponential functions

Step-3: The above functions are belongs to polynomial. So, simply substitute the value of n,

First compare with constant values.

→ 100 / 2048 = 0.048828125

→ 10 > 100/ 2048

→ log

_{2}2048 =11→ √n = 45.25483399593904156165403917471

→ n = 2048

So, Option B is correct

Question 2 |

f _{3}, f_{2}, f_{4}, f_{1} | |

f _{3}, f_{2}, f_{1}, f_{4} | |

f _{2}, f_{3}, f_{1}, f_{4} | |

f _{2}, f_{3}, f_{4}, f_{1} |

Question 2 Explanation:

If they are expecting to find an asymptotic complexity functions means

→ Divide functions into 2 categories

1. Polynomial functions

2. Exponential functions

Above 4 functions we have only one exponential function is f

Substitute log on both sides then we get an ascending order is f

→ Divide functions into 2 categories

1. Polynomial functions

2. Exponential functions

Above 4 functions we have only one exponential function is f

_{1}(n) = 2n . So, It’s value is higher than to rest of the functions.Substitute log on both sides then we get an ascending order is f

_{3}, f_{2}, f_{4}.
There are 2 questions to complete.