T(n)=4T(n^{0.5)} +(logn)^{2}
put n=2^{k}
T(2^{k})=4T(2^{k/2}) +(k)^{2}
make T(2^{k})=s(k)
s(k)=4s(k/2) +(k)^{2} use master thm 2nd case
_{k}log_{b}a=_{k}log_{2}4 =_{k}2
tc=theta(k^{2} logk) put k=logn
tc=theta((logn)^{2}.loglogn)

Best algorithm for this set: 1.Independently sorting each of 1,000,000 arrays, each with 5 elements. 2.Sorting a set of 4,000,000 numbers in worst case O(n lg n) time.