RECURSIVE ALGORITHM COMPLEXITY
Part 1 : Homogeneous Linear Recurrence
Review : Time Complexity
T(n) ≈ copC(n)
Where :
T(n) : running time
n : input size
cop : execution time for basic operation
C(n) : number of times basic operation is executed
Counting the number of times the algorithm’s basic operation is executed on input of
size n.
There are several things to consider about recursive algorithm :
1. Recursive algorithm doesn’t use sum
2. The number of basic operations is difficult to identify how many times it is
executed
3. Find the recurrence relations
4. Solve the recurrence relation to get algorithm efficiency.
Example of recurrence relation
tn – 3tn-1 – 4tn-2 = 0 for n > 1
t0 = 0
t1 = 1
tn – 5tn-1 + 6tn-2 = 0 for n > 1
t0 = 0
t1 = 1
