list manipulation - Find the longest constant sublist

Given a list

list = {1,2,2,2,2,5,1,3,2,6,6,6,6,6,6,6,6,6,6,6,10,-3};

how to find the longest constant sublist (or equivalently the element and the number of times it is repeated)?

(in this example, {6,6,6,6,6,6,6,6,6,6,6} or {6,11})

Answer

Concisely and reasonably efficiently:

Last @ Sort @ Split @ list

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

More efficiently:

# ~Extract~ Ordering[#, -1] & @ Split @ list

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

Multiple longest runs:

longestRuns[x_List] :=
  With[{sp = Split[x]},
    sp ~Extract~ Position[#, Max@#] &[Length /@ sp] & @ x
  ]

{1, 2, 2, 3, 4, 4, 5, 6} // longestRuns

{{2, 2}, {4, 4}}

Less efficiently but having fun with patterns:

list /. {___, seq : Longest[x_ ..], ___} :> {seq}

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}