I'm solving some recurrence relation problems for Big O and so far up till this point have only encountered recurrence relations that involved this form:
T(n) = a*T(n/b) + f(n)
For the above, it's quite easy for me to find the Big O notation. But I was recently thrown a curve ball with the following equation:
T(n) = T(n-1) + 2
I'm not really sure how to go around solving this for Big O. I've actually tried plugging in the equation as what follows:
T(n) = T(n-1) + 2
T(n-1) = T(n-2)
T(n-2) = T(n-3)
I'm not entirely sure if this is correct, but I'm stuck and need some help. Thanks!
Assuming T(1) = 0
T(n) = T(n-1) + 2
= (T(n-2) + 2) + 2
= T(n-2) + 4
= (T(n-3) + 2) + 4
= T(n-3) + 6
= T(n-k) + 2k
Set k to n-1 and you have
T(n) = 2n - 2
Hence, it's O(n)