self doubt

Question

Please explain what is mean by asymptotically faster?

okk so if we have two time complexity T(n) and F(n)

T(n)=O(n^2)

F(n)= O(n^2 logn)

i am actually confused by the fact that asymptotically faster means it is doing faster than other one for same input or getting less time ( MEANS ONE GETTING LOWER VALUE IS MORE FASTER) OR IT IS JUST SIMPLE TIME COMPLEXITY COMPARISON.

means from my 1st case  O(n^2)> O(n^2logn)

for 2nd O(n^2)<O(n^2logn)

so please help what does it exactly means

Comments

i think this will clear your doubt https://cs.stackexchange.com/questions/69819/what-does-it-mean-by-saying-asymptotically-more-efficient/69824

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@Rishav Kumar Singh I READ THE REFERENCE THAT YOU PUT UP THERE. BUT  THAT ALL IS IN LITTLE COMPLEX LANGUAGE.

 

SO PLEASE CAN YOU ELABORATE IN THIS SIMPLE LANGUAGE......

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check the answer

Answer 1

Asymptotically faster means that eventually it grows larger, but doesn't strictly mean that it's always going to be faster at the beginning. i.e. n^2 grows asymptotically faster than 10*n as n goes to infinity. For n < 10, n^2 < 10*n, but for n > 10, n^2 > 10*n. This is what big-O is about, eventually O(n^2) will grow faster than O(n).

NOTE: if an algorithm X  is asymptotically Faster than other algorithm Y for same set of input, it means X will take more time than Y so, Y is efficient than X.