Where does the constant 5 come from the median median algorithm?

Question

I tried to figure out where the “5” comes from the Median of Medians algorithm , but I can't seem to find a simple description of how it comes about and why it is optimal.

For example, why not say 7 is a viable option?

The only advantage I can see for 5 is that it has 2 elements on each side of the middle, making sorting by 5 elements a simple case of no more than three swaps.

Answer 1

5 , , O (n). 7 , .

: 5, :

T (n) ≤ T (n/5) + T (7n/10) + O (n)

O (n), .

3,

T (n) ≥ T (n/3) + T (2n/3) + O (n)

& Omega; (n log n).

7

T (n) ≤ T (n/7) + T (5n/7) + O (n)

O (n), . big-O , 5, n/7 7 , n/5 5. , .

, !