Question

Order following function by growth rate: N, √N, N^1.5, NlogN, log(N^2 ), N^2 , 2^N , 300

Answer 1

300 is constant.so 300 should come first compared to all.

Now compare  N, N^0.5 ,N^1.5 .0.5<1<1.5 so N^0.5 is less compared to N and N is less compared to N^1.5.

so order of N,N^0.5,N^1.5 is N^0.5<N<N^1.5.

Take NlogN and log(N^2)..log(N^2) is also written as 2logN.

Here 2logN is less compared to NlogN .So order is 2logN<NlogN.

compare logN and N^0.5...N^0.5>logN

compare NlogN and N^0.5...here NlogN>N^0.5

here N^1.5 >NlogN

2^N is larger than all the given times..so 2^N come at the end

order is 300<2logN<N^0.5<N<NlogN<N^1.5.<2^N