Retrieve the two highest item from a list containing 100,000 integers

Question

How can retrieve the two highest item from a list containing 100,000 integers without having to sort the entire list first?

Answer 1

The best time you can expect is linear, since you have to at least look through all the elements.

Here is my pseudocode to solve the problem:

//assume list has at least 2 elements
(max, nextMax) = if (list[0] > list[1])
                 then (list[0], list[1])
                 else (list[1], list[0])

for (2 <= i < length) {
    (max, nextMax) = if       (max < list[i])     => (list[i], max)
                     elseif   (nextMax < list[i]) => (max, list[i])
                     else     (no change)         => (max, nextMax)
}

return (max, nextMax)