Binary vs Linear searches for unsorted N elements

Question

I try to understand a formula when we should use quicksort. For instance, we have an array with N = 1_000_000 elements. If we will search only once, we sho

Answer 1

Assuming n elements and m searches, with crude approximations

• the cost of the sort will be C0.n.log n,

• the cost of the m binary searches C1.m.log n,

• the cost of the m linear searches C2.m.n,

with C2 ~ C1 < C0.

Now you compare

C0.n.log n + C1.m.log n vs. C2.m.n

or

C0.n.log n / (C2.n - C1.log n)  vs. m

For reasonably large n, the breakeven point is about C0.log n / C2.

For instance, taking C0 / C2 = 5, n = 1000000 gives m = 100.