Worst-Case Linear-Time Selection
(Sketch situation on the board)
How many of the 5-element medians are ? x?
- At least 1/2 of the medians = ? ?n/5?/ 2 ? = ?n/10?
How many elements are ? x?
- At least 3 ?n/10? elements
For large n, 3 ?n/10? ? n/4 (How large?)
So at least n/4 elements ? x
Similarly: at least n/4 elements ? x