Longest List

n = 8*10^4;
list = RandomSample[Range[Range[n]]]; // AbsoluteTiming
f1 = Function[list, Ordering[list, 1, Length[#1] > Length[#2] &]];
First /@ Table[AbsoluteTiming[f1@list], {100}] // Mean
f2 = Function[list, With[{lengths = Length /@ list},
    Position[lengths, Max[lengths], \[Infinity], 1]]];
First /@ Table[AbsoluteTiming[f2@list], {100}] // Mean
f3 = Function[list, Ordering[list, -1]];
First /@ Table[AbsoluteTiming[f3@list], {100}] // Mean