Question

PYTHON Im kinda stuck here for this question, could use some help! Python please, and please follow the requirements.
09 5 Points Al and Bob are arguing about their algorithurs. Al claims his Oinlogn time method is always faster than Bob's O(n^2)-time method. To settle the issue they perform a set of experiments. To Al's dismay, they find that if n < 100 the On/2)-time algorithm runs faster and only when na 100. O(nlog n)-time one runs faster. Explain how this is possible. Enter your answer here

Answer 1

Ans:-

Let Al function is c*nlogn where c is constant>0

Bob function is b*n² where b is constant > 0

Let base of logarithm is 2,

Compare them,

if n<=100, then

c*nlogn >= b*n²

c*logn >= b*n

when n = 100,

c* log(100) >= b*100

c/b >= 100/log(100)

c/b >= 166.1 (condition 1)

if n> 100 i.e n = 101

c*nlogn < b*n²  

c*101*log(101) < b* 101²

c/b < 167.4 (condition 2)

Values exist for constants c and b that satisfies both conditions 1 and 2

Hence this can be possible.

If any doubt ask in the comments.