54
Relatives of Big-Oh
(cont)
Examples:
¼n
2
∈ Ω(n
2
)
need c > 0 and n
0
≥ 1 such that ¼n
2
≥ c·n
2
for n≥n
0
let c=¼ and n
0
=1
¼n
2
∈ Ω(n)
need c > 0 and n
0
≥ 1 such that ¼n
2
≥ c·n for n≥n
0
let c=1 and n
0
=4
¼n
2
∈ Θ(n
2
)
since ¼n
2
belongs to Ω(n
2
) and O(n
2
)
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